____ ____ _________ _________
/ / / / / \ / /
/ / / / / ___ / / _____/
/ / ____ / / / /__/ / / / _____
/ / / / / / / ___/ / / /_ /
/ /_/__ /_/ / / /\ \ / /___/ /
/ / / / / \ \ / /
/________/______/ /___/ \___\ \_________/
Logical Japanese Rules of Go
Germany
Spring 2002
Robert M. Pauli
(c)
all rights of the author are preserved
according to international law
last update
June 2003
INTRO OVERVIEW POPULAR RULES PRECISE RULES COMPENSATION new grade system CYCLE REMOVAL CONTROL BEFORE END Iwamoto's refusal Go Seigen's refusal ENDING ko mark AFTER END dispute breaker JRG89 IN DEPTH Correcting Three Points Without Capturing BESTIARY CONCLUSION REF's
INTRO
Go is an ancient strategic board game where two players compete for territory. This text presents new rules for it. It is not meant to explain the game to beginners. So, in case you are one, please don't care about the rule version you're using because it won't change the overall characteristic of the game anyway. Take the simple ones just below (with H=V=9), or, if you prefer to start with more commonly used rules, read the introduction to Japanese rules provided by the British Go Association. In either case leave now and enjoy playing. Why do we need a new set of rules? Well, in one way we don't. Very simple rules can be used. Here's my guess how original go rules could have looked like ("stone scoring", no suicide, simple ko rule, pass as trivial ko threat, no compensation): 1. Go is played on a grid formed by H horizontal and V vertical lines, producing H times V intersections or locations. 2. Each location of the grid is initially empty. 3. One player owns black stones. The other white ones. 4. The goal is to get more of one's stones onto the grid than one's opponent. 5. The owner of the black stones starts, after which both players take turns. 6. In each of one's turns one can add a new own stone to the grid by putting it on an empty location - provided this doesn't create a suicide or immediate ko recapture pattern. 7. After one added a stone, one has to identify all stones of one's opponent without liberties and remove'em from the grid. 8. If the last three turns added no new stone, the game is over. 9. A suicide pattern is there if the last stone added to the grid has no liberties, but all stones of opposite color have. 10. An immediate ko recapture pattern is there if exactly two stones are without liberties and this just happened on the same two locations during the last turn. 11. A stone has liberties if by starting on it and repeatedly (including zero times) jumping to a horizontal or vertical neighboring stone of same color one can reach a stone that has a horizontal or vertical neighboring empty location. These rules are "stone scoring" ones. Modifying rule 4 to include eyes in the count leads to "area scoring" ones (which are now used in China, Taiwan, and the USA, each with its own flavor). But since go has spread around the western world from Japan, their "territory scoring" rules are used widely and, unfortunately, happen to be the most challenging (if one tries to pin them down). Japanese-style rules can be characterized as being the ones that stop playing soonest. This isn't merely a convention, but is part of the rules. It leads to the question if stones are dead or not at the end of the game and to the necessity for the rules to define this. In 1989 the Japanese rules were revised unanimously by the two Japanese go associations, Nihon Ki-in and Kansai Ki-in, and a new version of "The Japanese Rules of Go" took effect on May 15 - "JRG89" for short. Even though this was a major improvement over the 1949 version (which was Japan's first written one), replacing all special rulings (precedents) by general rules, they still have errors and are ambiguous. First I thought of just fixing this errors and completing what seemed to miss, but eventually I came to the conclusion that in the 1989 effort of getting rid of all special rulings the wrong track was chosen: sekis remain an exception and slightly too much is ruled to be dead. The problem is that internal ko threats have no meaning any more for life and death because of the special pass-for-ko rule JRG89 adopts in the analysis. A ko may then only be recaptured by a player if he passes once for this single ko. In the hypothetical phase several kos can therefore be hot simultaneously, each waiting for its own pass. The intention is to localize ko fights in the analysis. Normal ko threats, including internal ones, become useless. An example (see beast 8): Imagine the game ending in this position. White declares the black stones to be dead and asks if he may take'em out. Black disagrees. You're the referee, but forgot your rule book (if you ever saw one). Would you agree? Please think about it. Under JRG89 White is right - under LJRG ("loja") he is NOT. Or look at this one (beast 18): White, muttering something about "bent four", insists that all black stones are dead and ready for take off. Black desperately cries for help. You rush to the scene. Could you help? Again JRG89 supports White (at least its example does) - LJRG sees ALL stones alive. You may shrug: who cares? I never experienced those positions either, but it's a matter of aesthetics to have rules that judge all cases in a way most of us would agree - and I bet you'd find good arguments to disagree with White in both cases if you happened to be Black. Note that LJRG follows JRG89 again in both cases if the double ko is "external" (separate): moonshine life as well as bent four in the corner is dead no matter how many (external) double kos are around (see beast 11 for the first case). But this new rules offer more: - Komi is decentralized and free - no Big Brother dictates his komi (nor gets fed with individual komi preferences) - Defects get fixed ("teire") before game end in self-interest - Neutrals ("dame") haven't to be filled before game end (JRG89 technically forces this to cope with sekis) - No discussion if a game is over - there's a simple definition - No resumption of a stopped game - there's neither a stop nor a (ridiculous) resumption - Internal ko threats play their role after game end (as mentioned) - Sekis are no mysterious exception any longer - without even having to mention them (!) they're treated perfectly - "Cycle removal" prevents no outcome ("mushobu") and avoids hairy and unfair super-kos - without forcing bookkeeping in advance (!) - Evaluation of life and death is easier and more intuitive than under JRG89 because the focus is on "control" of area, not on life of stones - "control" can be seen ideally as well as be played out (see "dispute breaker") In contrast to other rules, these rules not just describe how things are but explain why - in the sense that an explanation is a more elegant description. For instance, describing planet movement via epicycles works, but only after treating the sun as the center you end up with something worth being called an explanation. I'd neither grant JRG89 nor any of the various (multi-phase) "play it out" rules, emulating Japanese rules, an explaining quality: JRG89 produces almost all effects of Japanese rules, but fails to do this in an elegant way. Its capturable alive stones aren't very appealing, and its treatment of sekis still is ad hoc and invites nagging questions. Play-it-out rules, on the other hand, are either blind about sekis for the sake of simplicity, or they turn out to be a total mess. In either case, playing it out inherently fails to localize kos. Calling this new rules "Logical" Japanese Rules of Go refers to their explaining quality - it shouldn't be misunderstood in that other rules are not logical. See the chapter about JRG89 for my logical interpretation of them. In designing these rules, I couldn't resist the temptation to add some fancy stuff you never heard of, like color choice and cycle removal, or to kick out the fixed handicap sequence. But since all this, as I hope, is still in line with the spirit of Japanese rules, and in respect to Japan's contribution to go's development and spread, I resisted to use "Territory" instead of "Japanese" in the name. The reason for using a second qualifier at all was to make clear that it isn't my intention to propose international rules. Diversity shall prevail.
OVERVIEW
In the following we'll go through two simple games on unusual mini boards (3x3 instead of the 19x19 standard) to get a quick overview of what LJRG is about (of course not what go is about): The first example demonstrates how live and death is defined. It was played without komi or any other compensation (for whatever reason):
| 0 0 B 0 | 0 0 W 0 | 0 0 B 0 | 0 0 W 0 |
| 0 0 B 0 | 0 0 W 0 | 0 0 B 1 | 0 0 W 2 |
| 0 0 B 0 | 0 0 B 0 |
Here's another 3x3 game. It demonstrates how LJRG tames cycles. Traditionally, cycles other than a ko prevent a game from ending - giving no result ("mushobu") under Japanese-style rules. Kos are tiny cycles one has no problem to keep in mind. Longer cycles could in principle be handled in the same way, but are very confusing in practice. Since they are rare, not handling them is an option. But the possibility that the sure winner could be stopped by a nasty cycle is nevertheless a nuisance. Therefore LJRG includes a new idea called "cycle removal" - to happen in the next game. Above we saw new stuff accompanying the board. Now we'll see new stuff on it: marks. They explicitly make clear which locations are prohibited to change their color - either just for one turn (temporary marks = squares) or forever (permanent marks = circles). This game was played with compensation. One player chose the initial situation (one temporary mark on the center and no komi in this case), and the other chose the colors (see chapter about compensation). Here's the game (after colors were assigned):
| 0 0 B -1 | 0 0 W 0 | 0 0 B 0 | 0 0 W 0 |
| 0 0 B 0 | 0 0 W 0 | 1 0 B -1 | 1 0 W 0 |
| 2 0 B -1 | 2 1 W -1 | 3 1 B -1 | 3 2 W -1 |
| 4 2 B -1 | 4 3 W -1 | 5 3 B -1 | 5 4 W -1 |
| 6 4 B -1 | 8 7 W 0 | 8 7 B 1 | 8 7 W 2 |
| 1 0 W 0 | 5 4 W -1 |
| 2 0 B -1 | 6 4 B -1 |
POPULAR RULES
For those that hate the idea of shuffling around marks or those not able or willing (including me for most of the time) to enter my "torture chamber" below and digest precise rules - here are equivalent "unofficial" rules in a more popular form: Logical Japanese Rules of Go (popular version) 1. "Go" is played by two players with black and white lens-shaped stones on a finite set of locations (for instance, the 361 intersections created when 19 parallel lines cross a second set of 19 parallel lines - to take the standard). Additionally, it must somehow be defined if any two (different) locations are neighbors or not (for instance, when both share the same line without a third location between - to again take the standard). All locations start empty. 2. To start, one of the players, randomly chosen, has to decide which locations are initially prohibited (possibly none) and how much points (a non-negative integer) the player getting second turn is ahead ("komi"). The other player then has to decide whom to give first and whom second turn. The player that got first turn is called "Black" and uses black stones. The other player is called "White" and uses white stones. 3. The players take turns. The player having the turn has up to two actions at his disposal: - he can remove a disturbing cycle, and - he can play a stone (the normal action). Each action may (occasionally must) be omitted, but if both are performed, this must happen in the given order. 4. If a player neither adds nor removes stones in his turn, this is called a "pass". If a player passes in a situation in which no location is temporarily prohibited and his opponent then passes too, the game is over and scores are compared. 5. A player scores one point - for each location he controls that is not occupied by one of his stones ("territory"), - for each opposing stone that sits on a location controlled by him ("dead stones"), and - for each opposing stone that was removed (no matter by whom) during the game ("prisoners"). White's score additionally benefits from komi. The player with the higher score wins - otherwise it's a tie ("jigo"). 6. "Playing" a stone means - to put a new stone on an unprohibited empty location, - to identify all opposing stones thereafter being without liberties, and, in case some are around, - to remove them from their locations. 7. To "remove a cycle" means to remove all stones sitting on locations "used" by the cycle - which are those locations to which stones were added or from which stones were removed while the game went from the cycle's start to the cycle's end. 8. A "cycle" exists if a former situation (its "start") is similar to the current situation (its "end"). Two situations are "similar" if in both - the same player just has got the turn, - the same number of passes are needed to reach game end, - the same locations are occupied by black stones, - the same locations are occupied by white stones, - the same locations are temporarily prohibited, and - the same locations are permanently prohibited. A cycle only is "disturbing" if a pass in the current situation wouldn't end the game. 9. An empty location is "prohibited" if - putting a stone on it makes suicide or pseudo suicide, - it is initially prohibited and no turn yet was made, - it was cleared by a ko capture in the preceding turn, or - it was once used by a removed cycle. Locations prohibited because a removed cycle once used them are called "permanently" prohibited. Those prohibited initially or after a ko capture are called "temporarily" prohibited. 10. Putting a stone on an empty location makes "suicide" if after placement all stones of opposite color still have liberties, but this stone has none. 11. Putting a stone on an empty location makes "pseudo suicide" if after placement this stone and all stones of opposite color still have liberties, but this stone only has permanently prohibited ones. 12. Putting a stone on an empty location is a "ko capture" if after placement exactly two stones have no liberties and their colors don't match. 13. A stone "has liberties" if by starting from its location and repeatedly (including zero times) jumping to a neighboring location that is occupied by a stone of the same color one can reach a location that has an empty neighbor. Each such empty location is called a "liberty" of the original stone. 14. A player "controls" a location if it is member of a set of locations he has bordered and he can't be prevented from building a 2-eye formation on this set even if - all locations outside this set are cleared and each becomes occupied with a new stone of his opponent, - two new empty locations are created and each becomes a new neighbor of each location outside this set, - all stones thereafter being without liberties are identified and then removed, - all former situations are forgotten, - all permanent prohibitions stay in effect, and - his opponent is allowed to start. 15. A player has "bordered" a set of locations if - each location inside this set that has a neighbor outside this set is occupied by one of his stones, but - each location outside this set that has a neighbor inside this set is not occupied by one of his stones. 16. A player has build a "2-eye formation" on a set of locations if - this set is not empty, - no stone of his opponent sits on a location in this set, - he has bordered this set, - each location in this set has at least one neighbor (possibly outside this set), - no empty location in this set ("eye") has an empty neighbor, and - each stone sitting on a location in this set has at least two liberties inside this set.
PRECISE RULES
Here are precise rules, but be warned - it's in a h e a v i l y mathematical style (no time, no space, no change). Maybe you should skip it first (grin). Who's familiar with Prolog will recognize similarities, but it's no pure Prolog: this avoids to clutter up things with even more details (implementing sets as lists, for instance) and helps to be widely understood (if I'm not too optimistic about that one). This doesn't mean that it's nonconstructive in the sense that an answer is certain if only someone knew how to find it. This is trivially true because each answer is always searched in a finite domain, but I hope it's also practically constructive in the sense that one could develop a computer program that gives answers in an acceptable time - at least for "regularly" sized territories. However, that a 19x19 board with 72 black stones filling the first line and an empty "outback" is lockable by Black will probably never be proven, even if it seems to be in practice [RGG300196]. This mathematical form is admittedly somewhat awkward, but that's the price to pay for referential transparency: names never change their meaning or value. For instance, in formal mathematics you don't speak of changing the board by putting a stone on an empty location. Instead you talk of one board B1 related to a second board B2 in such a way, that all locations on B1 are in the same state as on B2 - except for one, which is empty on B1 and colored on B2 (and B1 and B2 floating in the Platonic world of ideas). The only mathematical objects - not to mention integers, of course - you need to be familiar with are (finite) lists and sets. So let me risk some words on them: Lists are ... well, you know what lists are, don't you? So let me just make clear what it means that "L2 is L1 with X appended to it": this means that L2's value is similar to that of L1, except that it has the further member X at its END. And what's a set? You can think of a set as a list that "hates" repetition and order: it deletes duplicates as soon as they enter and does not order its members in any way. Therefore it makes no sense to speak of a set's first or last member, to ask how often something is in a set - either it is or it is not - or if it compared to another set has something appended to it - it's added to it. Therefore two sets are the same only if each member of one of them also is member of the other. Sets as "defined" above would produce the well known antinomies, for instance, try to figure out if Russell's set of all sets that aren't member of themselves is member of itself. But since the sets we deal with here are not of this pathological type - they're finite and finitely nested - this won't bother us. The following rules are meant to be precise and complete. They therefore are designed not to depend on any commentary. I hope this excuses their degree of detail and hyper-fussy style. The rules are ordered top-down (B and C being parallel). If you rather prefer reading a definition before its first use, please start at the end and work your way up (advised).
Logical Japanese Rules of Go (precise version) A. Game A1. "Two players play an even game of go on some board according to Logical Japanese Rules of Go " by doing - essentially - the following in the given order: 1. Randomly decide which player chooses first and which last. 2. The player choosing first must choose an initial state whose board is the one in use. This state is called "current state". 3. The player choosing last must choose which player is called "Black". The other is called "White". 4. While the current state is not final, the player having the turn in it must replace it with one of its successors. 5. When the current state is final, the player with the higher score in it wins. If both are equal, it's a "jigo" (tie). A2. "A state is initial" only if all this holds: 1. Its set of black locations is empty. 2. Its set of white locations is empty. 3. Its set of temporarily marked locations is a subset of its set of locations. (Includes the case that both are the same.) 4. Its set of permanently marked locations is empty. 5. Its black captive count is a non-negative integer not greater than the number of members of its set of locations. 6. Its white captive count is 0. 7. Its turn is "black". 8. Its pass count is 0 if its set of temporarily marked locations is empty, otherwise its pass count is -1. 9. Its history is empty. (A state's "komi" is its first situation's black captive count minus its first situation's white captive count, and a state's "first situation" is the first member of the list formed by appending its situation to its history.) A3. "Black has the turn in a state" only if this state's turn is "black". A4. "White has the turn in a state" only if this state's turn is "white".
B. Successor B1. "State S4 is a successor of state S1" only if some state S2 and S3 fulfill all this: 1. S1 is not final. 2. a) S1's turn is "black", and S4 is a white successor of S1; or b) S1's turn is "white", S2 is colored reverse to S1, S3 is a white successor of S2, and S4 is colored reverse to S3. B2. "State S4 is a white successor of state S1" only if some state S2 and S3, text T1 and T2, integer set K, and integer P fulfill all this: 1. S1's turn is "black". 2. a) S2 is S1, and T1 is "no cycle removed"; or b) S2 is reachable by removing a cycle in S1, and T1 is "cycle removed". 3. a) S3 is S2, K is empty, and T2 is "no stone played"; or b) S3 is reachable by playing a black stone in S2 that clears set K by ko, and T2 is "stone played". 4. a) T1 is "no cycle removed", T2 is "no stone played", and P is S1's pass count plus 1; or b) K is not empty, and P is -1; or c) K is empty, T1 is "cycle removed" or T2 is "stone played", and P is 0. 5. S4's history is S1's history with S1's situation appended to it, S4's set of temporarily marked locations is K, S4's pass count is P, S4's turn is "white", and everything else in S4 is as in S3. B3. "State S2 is reachable by removing a cycle in state S1" only if some list of situations H, list of integer sets L, integer set B and C and D, and integer NB and NW fulfill all this: 1. S1's pass count isn't 1. 2. H is a trailing sub-list (a suffix) of S1's history, and H's first member is similar to S1's situation. (This includes the case that H is S1's history.) 3. L is the list that would result if every member of H would be replaced by the union of its set of black locations with its set of white locations. 4. B is the union of all members of L. 5. C is the intersection of all members of L. 6. D is the set of those members of B not member of C. 7. NB is the number of members of the intersection of D with S1's set of black locations. 8. NW is the number of members of the intersection of D with S1's set of white locations. 9. S2's black captive count is S1's black captive count plus NB, S2's white captive count is S1's white captive count plus NW, S2's set of black locations is the set of those members of S1's set of black locations not member of D, S2's set of white locations is the set of those members of S1's set of white locations not member of D, S2's set of permanently marked locations is the union of S1's set of permanently marked locations with D, and everything else in S2 is as in S1. B4. "State S3 is reachable by playing a black stone in state S1 that clears integer set K by ko" only if some integer X and Y and N, state S2, and integer set W fulfill all this: 1. S1's turn is "black". 2. X is member of S1's set of locations, but neither colored nor marked in S1. 3. S2's set of black locations is S1's set of black locations extended by X, and everything else in S2 is as in S1. 4. W is the set of all members of S2's set of white locations that have no liberties in S2. 5. If W is empty, then X has contact to Y in S2 and either Y is not colored and not permanently marked in S2 or Y is black and permanently marked in S2. 6. N is the number of members of W. 7. S3's set of white locations is the set of those members of S2's set of white locations not member of W, S3's white captive count is S2's white captive count plus N, and everything else in S3 is as in S2. 8. K is W if N is 1 and each neighbor of X in S2 is white in S2, otherwise K is empty.
C. Score C1. "Integer N is Black's score in state S1" only if some integer set L and integer N1 and N2 and N3 fulfill all this: 1. L is the set of those members of S1's set of locations that Black controls in S1. 2. N1 is the number of members of L that aren't black in S1. 3. N2 is the number of members of L that are white in S1. 4. N3 is S1's white captive count. 5. N is the sum of N1, N2, and N3. C2. "Integer N is White's score in state S1" only if some state S2 fulfills all this: 1. S2 is colored reverse to S1. 2. N is Black's score in S2. C3. "Black controls integer X in state S1" only if some integer set L fulfills all this: 1. X is member of L. 2. Black can lock L in S1. C4. "Black can lock integer set L in state S1" only if some state S2 fulfills all this: 1. L is bordered by Black in S1. 2. S2 is Black's worst case for L in S1. 3. White can't prevent a black 2-eye formation on L in S2. C5. "Integer set L is bordered by Black in state S1" only if all this holds: 1. L is a subset of S1's set of locations (this includes the case that both are the same), and 2. for every member X of L that is neighbor of a Y not member of L all this holds: 1. X is black in S1, and 2. Y is not black in S1 C6. "State S3 is Black's worst case for integer set L1 in state S1" only if some integer set L2 and state S2 fulfill all this: 1. S1's set of locations is the union of L1 with L2. 2. S2's history is empty, S2's set of temporarily marked locations is empty, S2's black captive count is 0, S2's white captive count is 0, S2's pass count is 0, S2's turn is "white, S2's set of black locations is the intersection of S1's set of black locations with L1, S2's set of white locations is the union of S1's set of white locations with L2, S2's set of permanently marked locations is the union of S1's set of permanently marked locations with L2, and everything else in S2 is as in S1. 3. S3's set of black locations is the set of those members of S2's set of black locations that have liberties in S2, and everything else in S3 is as in S2. C7. "White can't prevent a black 2-eye formation on integer set L in state S1" only if at least one holds: 1. Black has build a 2-eye formation on L in S1; or 2. S1's turn is "black", S1's situation is not final, S1's situation is not similar to a member of S1's history, and at least one successor S2 of S1 has the property that White can't prevent a black 2-eye formation on L in S2; or 3. S1's turn is "white", S1's situation is not final, S1's situation is not similar to a member of S1's history, and each successor S2 of S1 has the property that White can't prevent a black 2-eye formation on L in S2. C8. "Black has build a 2-eye formation on integer set L in state S1" only if all this holds: 1. L is not empty. 2. L shares no member with S1's set of white locations. 3. L is bordered by Black in S1. 4. Every member of L is member of at least one member of S1's neighbor relation. 5. Every member of S1's neighbor relation that's subset of L shares at least one member with S1's set of black locations. 6. Every member of L that is colored in S1 has contact to at least two (different) members of L in S1 which both are not colored in S1.
D. Contact D1. "Integer X has liberties in state S1" only if at least one holds: 1. X is colored and permanently marked in S1. Or 2. X has contact to some Y in S1; and either a) Y is not colored in S1, or b) Y has the same color as X in S1 and Y is permanently marked in S1. D2. "Integer X has contact to integer Y in state S1" only if X has contact to Y in state S1 avoiding V, and V is the set whose only member is X. ("contact" neither is symmetric, reflexive, nor transitive.) D3. "Integer X has contact to integer Y in state S1 avoiding integer set V1" only if some integer Z and integer set V2 fulfill at least one: 1. X is neighbor of Y in S1; or 2. Z is neighbor of X in S1, Z has the same color as X in S1, Z is not member of V1, V2 is V1 extended by Z, and Z has contact to Y in S1 avoiding V2. D4. "Integer X is neighbor of integer Y in state S1" only if the set whose only members are X and Y is member of S1's neighbor relation. ("neighbor" is symmetric, but neither reflexive nor transitive.) D5. "Integer X is black in state S1" only if X is member of S1's set of black locations. D6. "Integer X is white in state S1" only if X is member of S1's set of white locations. D7. "Integer X is marked temporarily in state S1" only if X is member of S1's set of temporarily marked locations. D8. "Integer X is marked permanently in state S1" only if X is member of S1's set of permanently marked locations. D9. "Integer X is colored in state S1" only if at least one holds: 1. X is black in S1, or 2. X is white in S1. D10."Integer X is marked in state S1" only if at least one holds: 1. X is marked temporarily in S1, or 2. X is marked permanently in S1. D11."Integer X has the same color as integer Y in state S1" only if all this holds: 1. X is black in S1 only if Y is black in S1, and 2. X is white in S1 only if Y is white in S1.
E. State E1. "A state is final" only if its situation is final. E2. "A situation is final" only if its pass count is 2. E3. "Two situations are similar" only if either 1. they are the same, or 2. they are not the same, but only differ in their captive counts. E4. "State S2 is colored reverse to state S1" only if some text T fulfills all this: 1. a) T is "black" and S1's turn is "white", or b) T is "white" and S1's turn is "black". 2. S2's set of black locations is S1's set of white locations, S2's set of white locations is S1's set of black locations, S2's black captive count is S1's white captive count, S2's white captive count is S1's black captive count, S2's turn is T, and everything else in S2 is as in S1. E5. A "state" consists of exactly 3 parts of the given names and sorts: 1. its "board" - a board 2. its "situation" - a situation 3. its "history" - a list of situations The first two parts again consist of named parts - subparts of the state. Since all these subparts have unique names, it's save to omit the part name when referring to a state's subpart. (For example, "the state's set of black locations" is short for "the state's situation's set of black locations".) E6. A "board" consists of exactly 2 parts of the given names and sorts: 1. its "set of locations" - a finite integer set 2. its "neighbor relation" - a set of unordered pairs, where each such pair is a set containing exactly two (different) members of the board's set of locations E7. A "situation" consists of exactly 8 parts of the given names and sorts: 1. its "set of black locations" - an integer set 2. its "set of white locations" - an integer set 3. its "set of temporarily marked locations" - an integer set 4. its "set of permanently marked locations" - an integer set 5. its "black captive count" - a non-negative integer 6. its "white captive count" - a non-negative integer 7. its "turn" - either the text "black" or "white" 8. its "pass count" - either the integer -1, 0, 1, or 2
COMPENSATION
In this chapter I'll try to motivate LJRG's style of compensation and also talk about handicap and grades. Compensation is a means to give both players equal opportunities. It depends on the board in use (a 19x19 grid being the standard) and on the players' strengths. If strengths differ, one can make up for it by allowing some stones in advance on the board ("handicap stones"), some points in advance ("handicap points" or "komi"), or a combination of both. If strengths match ("even" games), one either has to play a series of games and alternate who starts in each or one has to compensate the one not starting. The usual compensation for White not having the first turn is to give him a lead of points, called "komi" (short for "komi-dashi"). The first komi game was played 1852 [RGG090299]. Honinbo Shuwa gave 5 points to a team led by Yasui Sanchi at a promotion party for Hattori Hajime (and no idea if "jigo" was White's win or not). Japan mostly used komis of 4.5 (or as they said: 4 with White winning "jigo") as well as 5.5. Prior to 1976 both were in use (depending on the title), from 1976 on only 5.5 [RGG090299]. The first title to increase from 4.5 to 5.5 was Oza in 1955. Meijin was last - 1975, after a sponsor switch from Yomiuri to Asahi. Recently, September 2002, komi was scheduled to increase to 6.5. Two months later it first appeared in the Women's Honinbo, and just a day later in the Gosei. All other Japanese tournaments will catch up as soon as each's new term starts. [W-NK0902] ([DGZ0502c])
So, what's my reason to abandon this tradition? The first reason is to make the rules independent from a special board. They would either have to prescribe a komi for each board possible or make an exception for a bunch of selected boards - the former is impossible and the latter is odd. On the other hand, a fair start should be part of core rules, not tournament rules. The second reason is the main one: nobody certainly knows what komi is fair - knows the "perfect" komi (for the standard board). Therefore nobody is in the position to dictate "his" komi to all of us. Since this includes myself, I'll not do it either. For instance, compensation for the Milton Keynes go board (simply those town's street map [W-MK]) is defined by following formula: handicap = 1 + (X DIV 6) [free placement] komi = 6 - ((X MOD 6) * 2) [possibly negative] with X being the (positive) strength difference (e.g., a 10-kyu facing a 1-dan places 2 stones and GETS 2 prisoners). But I wonder how they concluded that 6 (for X=0) is the perfect komi for this board, and I wonder how they found out that strength differences defined via the standard (!) board translate exactly this way ?? The first time new komi of 6.5 points actually affected the outcome of a game (according to www.go4go.net) was in the quarter final of the 16th Fujitsu Cup on 07.06.2003: Takao Shinji (B) lost by half a point against Song Taekon (who additionally was the youngest player ever to enter Fujitsu's semi-final - he's 16). Honda Kunihiso (9d), who experienced the change from 4.5 to 5.5 in the late 50s and 60s as well as that from 5.5 to 6.5 now, neither thought about komi nor changed his way of play in either case [W-NK0902]. It's not unlikely that Takao and Song neither would, producing the very same game even under old komi. Now, isn't it a nuisance for Takao to imagine that he'd have won in this case? Under compensation a la LJRG this can't happen. Either you yourself proposed the komi, or you had the chance to refuse it (by choosing black). In either case it makes no sense to complain about it afterwards - you only can regret your decision.
And what's the reason for ruling out fractional komis? The answer again is quite simple: they're unfair. Why? Because the perfect komi, which certainly exists, must tie all games between two perfect players, and since the difference of their scores certainly is an integer, the equalizing komi has to be one too. (Couldn't it vary? No, because perfect players always wring out the maximum of points possible.) The idea behind fractional komi is to force a winner, but this is as silly as its origin (if the story in [GW50c] is true): Around 1935, drawn games had to be replayed in knockout tournaments. Two pros took advantage of this and faked two jigos in a row to earn some additional game fees. The sponsoring Nichinichi Newspaper felt fooled and protested to the Nihon Ki-in. After the two culprits "begged for forgiveness on bended knees and promised to play the next game seriously", the furiously fought third game turned out to be - you guessed it - a jigo. To calm the heat the Nihon Ki-in took up an idea of Murashima Yoshinori, 5-dan then, and declared to play all future newspaper knockouts with a half-point komi extension. The sponsor wants the crowd, and the crowd wants a hero or winner, but to force one by half points is as unreasonable as tossing a coin. There's nothing wrong with a jigo. It's a perfect game. It's very satisfying. In case you've already assimilated the "there must be a winner" idea and consequently are striving to become the best, you should reconsider your attitude. Why? Because if everybody else had the same goal and reached it - nobody would have reached it. Until then everybody will realize what he should instead strive for: perfection - which naturally leads to jigo. Since perfection never will be reached in practice - at least not on a 19x19 board - these thoughts admittedly are somewhat philosophical, but nevertheless convince me (as well as I'm convinced that zero neither is a positive nor a negative number). Certainly I don't know if statistics along with human efforts to improve play will approximate perfect komi in the end, but I neither can imagine that we're far off.
But how do we then decide what komi to use? A fair way to divide a cake between two persons is to let one person split it into two pieces and then to let the other person choose whichever piece seems bigger. The same idea can be applied to fix the komi. One player chooses a komi, and the other chooses which player has to take it. Since traditionally Black starts, always White takes the komi (in even games). Therefore we could also say that the second step chooses the color. This would be totally fair. In case the existing perfect komi was chosen, don't care about your color. But if not, you can refuse one that's too small by choosing to be Black, or you can accept one that's too big by choosing to be White. Of course, since nobody knows the perfect komi, you have to guess - to refuse or accept as well as how much to offer. Statistics are welcome to guide us, but they shouldn't rule us. Exactly this was practiced in a match between Imamura Fumiaki and Hirata Hironori in May 1994 for the title of the strongest Japanese amateur [DGZ0794a]. In the first game, Imamura chose 6.5 and Hirata black. In the second game, Hirata chose 7.5 and Imamura white. (Imamura won both games (with white) and the title.) With this scheme nobody can take an edge by choosing a fractional komi, so why not allow it again? In practice we could, but I hate both the idea that the player choosing first could rule out jigo at his will as well as the idea to rule out jigo completely by always having to choose a fractional komi. (The latter wouldn't fit the needs of perfect players, and why should we exclude them?)
And why those additional temporary marks? Take a 3x3 board as example. Its perfect komi is 8. The proof is simple. After Black takes the center, he controls the whole board. But since controlled locations colored by the controller aren't counted, Black's score isn't 9 but 8. White's is 0. He therefore needs a komi of 8 to level up. Since Black certainly can't do better, 8 is the perfect komi for a 3x3 board. Now suppose for the moment that we would have no komi. To be fair we could adopt following alternative scheme: Black plays the first stone as usual, but White is allowed to switch colors instead of playing his first stone if he feels Black's start was too good. This idea is from hex. (In hex two players each try to connect their two edges. Since the game is played by putting black and white stones on the hexagonal cells of a honeycomb, only one side will succeed. Actually hex lets White exchange Black's first stone with a white one [SW0902]. This would be equally fair for go - of course, without capturing the initial black stone - but in hex the edge colors would have to be switched too. Instead, the replacing white stone is "swapped into White's coordinates" [W-PS].) Is this scheme fair on the 3x3 board? Yes, it is. Black won't start with the center any more because White would switch colors and win by 8. But if Black starts on one of the center's neighbors, a jigo by seki will result (and therefore Black fears no color switch). The advantage of this scheme over komi on the 3x3 board is that jigo is made on the board and not by adjustment afterwards. I'd have kicked out komi completely for this scheme if there weren't one problem: since nobody knows if there's a jigo start on every board, this might be as unfair as fractional komis (which, of course, is only slightly unfair, but I'm striving for perfection). So if a board has no jigo start, then we would additionally need some komi to adjust for a perfect compensation. This komi will certainly be less than that without color switching, going in the right direction, but will only be zero if that jigo start exists. (By the way, is d4 a jigo start on 5x5 under LJRG?) If we now translate this scheme back into the choosing scheme, we get: the player choosing first chooses a komi and Black's start, and the player choosing second chooses the color. But choosing Black's start is the same as to prohibit all but one location for Black's start, which is almost the same as to prohibit some (or all) for Black's start - and to prohibit locations for exactly one turn is, guess what, nothing else than to mark them with temporary marks. It would, of course, be very painful to put coins or whatever on hundreds of locations on a 19x19. A way out would, for instance, be that everybody prepares some cards with his believed fair initial states. If he happens to choose first, he simply "plays" one of them. Or - if we don't want to risk go to fall between board and card games - we could exploit symmetry and restrict us to one sector of the board (a triangle area bounded by a center diagonal, the center horizontal or vertical, and one edge - like c3,d3,d4,e3,e4,e5 on the 5x5) and either mark the allowed starts with black or the prohibited starts with white stones - whatever takes less. Needless to say that these stones go back to their source uncaught after serving their purpose. Please note that if the game starts with at least one temporary mark on the board, the pass count has to start with -1, not 0. This admittedly only serves aesthetics: after two passes Black could make use of the by now unmarked locations, so the rules shouldn't prevent him from doing so by declaring the game ended. But analyzing the case that both players initially pass (B1, W2) and Black then continues (B3) reveals that it wouldn't happen in the perfect world: If Black would gain X points by continuing with B3, White should have continued himself with W2 to gain X points in the same manner, and if Black would gain nothing or would even lose points by continuing with B3, Black should, of course, have passed with B3 to either end sooner or lose by less. komi result advice reason new result ------------------------------------------------------------- 0 W wins B3 pass better jigo 0 jigo B3 pass shorter jigo 0 B wins by X W2 stone better W wins by X N+1 W wins by N+1+X B3 pass better W wins by N+1 N+1 W wins by N+1 B3 pass shorter W wins by N+1 N+1 W wins by N+1-X W2 stone better W wins by N+1+X N+1 jigo W2 stone better W wins by 2(N+1) N+1 B wins by X W2 stone better W wins by 2(N+1)+X But nevertheless it pleases me more to always (and only) have a pass count of -1 if there are some temporary marks around. Since practical matters are excluded from these rules, I'll have to mention it here: Choosing the initial state and the color is part of the game and can take its time, especially the latter. Therefore both choices should be done while the clock is running (if one is used).
Some words on how to decide whom to give the first choice: The traditional Japanese way to toss the dice is that one player takes a handful of stones and the other guesses if it's an odd or even number by putting one or two stones on the board ("nigiri"). But deciding who has to (or may?) guess by checking who's younger, weaker, less honorable, or whatever is just ridiculous. I would therefore advice to replace it by "symmetric nigiri": EACH player takes a handful of stones. If their sum is odd, the player using black stones has won, otherwise the one using white stones did (odd for black and even for white for the obvious reason - an even game's record). The rest of this chapter covers board, handicap, and grades. Since it's a side-issue and not very LJRG-specific, you might want to skip it.
Go can be played on all kinds of boards (or topologies), not only on the standard 19x19 grid. The simplest variation, of course, is to shrink the board's size. Many modern books introduce the game via 9x9 or even 5x5 boards. This should also become practice in face-to-face introduction. I really wonder how I survived dragging through my first games on a 19x19. Increasing the board size, on the other hand, seems to be less common: In the year 1915, for instance, a no-komi game between two Japanese pros took place on a 21x21 "monster" board - on the second day and 335 moves later, Black had won by (just) 2 points [GW60]. Need something a bit more freaky? Here you are: - the void board: to start with the simplest, having not one location - those boards composed of triangles instead of squares: never worry about a cut - there's none - cylinders (pipe surfaces): glue two opposite edges without a twist together (the letters below only connect - they're no locations) - tori (plural of "torus" - ring surfaces): glue all opposite edges without a twist together - Moebius strips: glue two opposite edges with a twist together - Klein bottles: glue all opposite edges together - one pair without and the other with a twist - projective planes (ball surfaces identifying diametric points): glue all opposite edges with a twist together - round boards ("diagonal" cylinders): take a diagonal strip, glue two opposite edges together, and seam the other two then - to please the eyes, justify the name, but add confusion - arrange the two seams (beyond D) as concentric circles [DGZ0796] - map boards: play on your home town's street map - each street intersection and each end of a dead end being one location [W-MK] - 3-D boards: plenty of liberties - but pretty involved - etc... an endless list - and absolutely irrelevant to rules
Ok - back to our standard board (and sorry in advance for defining something that's obvious - fading jerks of my "be formal" trip): S1. "The standard board" is the normal rectangle board with 19 columns and 19 rows. S2. "A board is the normal rectangular board with C columns and R rows (both non-negative integers )" only if all this holds: 1. its set of locations is the set of all non-negative integers smaller than C times R, and 2. its neighbor relation is the set of all those subsets of its set of locations that have exactly two members and whose non-negative difference of their members is either 1 or R. S3. "A board is a rectangular board with C columns and R rows" only if it is essentially, besides location naming, the same as the normal rectangular board with C columns and R rows. Note that we can't speak of "the" rectangular board of most extensions because it's arbitrary how the integers are assigned to the locations. That's the reason for picking one and calling it "normal". For instance, board ( {0,1,2}, {{0,1},{1,2}} ) is essentially the same as board ( {0,1,2}, {{0,1},{0,2}} ). Each is a rectangular board with 3 columns and 1 row (or the other way round - CxR = RxC if C or/and R = 1). The first board calls its center "1", the second "0". Equalizing renamings of the second are either {0=>1, 1=>0, 2=>2} or {0=>1, 1=>2, 2=>0}. The first board is the "normal" rectangular board with 3 columns and 1 row (as well as that with 1 column and 3 rows). The correspondence between a normal rectangular board and its usual visual presentation is quite simple: Take a grid formed by C columns and R rows, having C x R locations. Start at the lower left corner and give it number 0. Number all locations above it with increasing numbers from bottom to top. After each column continue at the bottom of the next column to the right. (One can do it this way or that way, but: To start at the lower left corner fits best to mathematics, to start with 0 leads to the nice property that the coordinates of location N are X = N DIV R and Y = N MOD R, and going along the columns fits to the sequence of X-Y's after a lexical sort.) Now notice that the location directly above of some location L has L's number plus 1, and that the one directly to the right has L's number plus R. Since two locations only are neighbors on the visual board if they share the same row or column without any location between them, one of them has to be directly above or to the right of the other. So the visual representation and the abstract one are essentially the same. An alternative naming for each locations of the standard board is the algebraic one. The columns are named a,b,c,...,r,s,t (omitting either i or j to avoid confusion) from left to right, and the rows are named 1,2,3,...,17,18,19 from bottom to top. Each combination then denotes one location: a1, for instance, denotes the lower left corner. This certainly serves the purpose better than numbers, but only works for rectangular boards. The location (or integer) on a normal rectangular board that corresponds to such an algebraic combination X Y is ((#X - 1) * R) + (Y - 1) provided #X is the ordinal of X in the column letter sequence. For instance (on a 19x19): lower left hoshi = d4 = (( 4 - 1) * 19) + ( 4 - 1) = 60 tengen = k10 = ((10 - 1) * 19) + (10 - 1) = 180 lower right hoshi = q4 = ((16 - 1) * 19) + ( 4 - 1) = 288
Everything said so far was meant for two player of equal strength. This is defined to be the case if both win on the same rate in a (long enough) color-alternating series of no-komi games. Such a series can be expressed relative to one player as 0 1 0 1 0 1 ... Each number corresponds to one game of the series and represents the handicap that player takes. In other words, the number of his stones already around when yielding the turn to his opponent. Thus, 0 means that he has white, 1 that he has black (without komi, of course), 2 that he takes 2 stones handicap (and has black because traditionally Black places the first stone - handicap or not), and -1 that he gives 2 stones handicap (as if his own first played stone vanishes in a matter-antimatter reaction with his negative handicap stone - puff). Since infinite series aren't very handy, let's only consider periodical ones with a period of, say, 6 games. Further, because we're not concerned with the mixture here, let's sort the numbers in a period. Above then becomes 0 0 0 1 1 1 (even) Player B will use this series when strengths match, but if player A is stronger than player B, A will win a higher percentage of the games in the long run. To adjust for this, B adds 1's to the period till the winning rates match again (traditionally he takes one stone more every time he's 4 games down). The next series to try is 0 0 1 1 1 1 (Japanese 1-pro-dan gap = BWB) (0 0 0 1 1 2 is no series because the numbers in a period shouldn't differ by more than one.) This will continue with trying 0 1 1 1 1 1 1 1 1 1 1 1 (handicap 1) 1 1 1 1 1 2 1 1 1 1 2 2 1 1 1 2 2 2 (handicap 1.5) 1 1 2 2 2 2 ... till the match is found. If it were the last row above, this would mean that, facing A, B takes 2 stones handicap in 4 games out of 6 and only enjoys black in the remaining two games. Another way to express this is simply to say that B takes a handicap of (1+1+2+2+2+2) / 6 = 10/6 = 1 + 2/3 stones against A. This number can be converted back to a unique period for any given length (but only certain ones will yield integers). If A were the (busy) reference player everyone compares to, each player could use his personal handicap against A to denote his strength.
Now let's come to the tricky part. Imagine two players being G stones apart in strength. What handicap would you advice? Did you suggest G stones? WRONG - a common error. The correct handicap is half a stone bigger. Here's why: Suppose the stronger player is A himself, our reference player. His strength is not zero, as one might expect, but 1/2 - this is because A plays an even series against himself (0 0 0 1 1 1 = 3/6 = 1/2). Since his opponent B takes SB stones from A when B's strength is SB simply by definition, the handicap H (= SB) is 1/2 bigger than the strength gap G (= SB - 1/2): _______________________ / H ______________\ / / G \ +---------+------ ... ------+ 0 1/2 SB If this is correct when comparing to A, it must also be correct when comparing to someone else - just shift all strengths till the stronger player ends up with 1/2, and then pretend him to be the reference player: Half a stone has to be added to the strength gap (measured in stone units) to reach the correct handicap! Maybe an analogy helps. If a plane, starting in A, takes two hours to reach B, and the next two hours to reach C, B isn't necessarily midway between A and C. If planes usually had to taxi for, say, half an hour before takeoff, the net time between A and B is just one hour and a half. Since comparing two flights starting from the same origin only yields a net time, a flight from B to C will not take two hours, but two hours AND a half (now taxiing on B's ground). So, if you take one stone from Guru and Dummy takes two, rejoice: you're no half-dummy - you're twice as near to Guru than to Dummy. Let's call this the "handicap paradox".
The traditional Japanese strength names or grades (in other fields as well) in decreasing order are 9-dan 8-dan 7-dan 6-dan 5-dan 4-dan 3-dan 2-dan 1-dan (shodan) 1-kyu 2-kyu 3-kyu ... Note that there's nothing higher than 9-dan. Note further that among dans higher numbers are the stronger ones, whereas among kyus lower numbers are. If you silently try to fix by adding a minus sign to the kyu numbers, you notice another defect: zero is missing. At least one would expect dans to be the masters and kyus to be the advanced players and beginners, but on top of this mess there's another distinction - that between professional dan and amateur dan. Reminds me to tell you that amateur dans actually only get as high as 6-dan (with "of course" some 7-dan exceptions), which might fit to the saying that an amateur 6-dan is about a pro 1-dan [P-WD]. After all - "great", isn't it? Are at least the strength gaps sound? I'm afraid no. Amateurs grades are 1 stone apart. Sounds good, but taking black in all games - the natural step - is taking half a stone more than compared to an even series: the 1/2-stone gap is the canonical choice! What about the (Japanese) pros? Of course, you guessed it - they take their own gap. Everybody will tell you that it's a 1/3-stone gap, but look at this [GW50b]: pro-dan gap series 0 0 1 0 0 0 1 1 1 (even) 1 0 1 1 0 0 1 1 1 1 +1 (BWB) 2 1 1 1 1 1 1 1 +2 3 1 1 2 1 1 1 1 2 2 +2 4 1 2 2 = 1 1 2 2 2 2 +2 5 2 2 2 2 2 2 2 +2 6 2 2 3 2 2 2 2 3 3 +2 7 2 3 3 2 2 3 3 3 3 +2 8 3 3 3 3 3 3 3 3 3 +2 (Mixture dropped, e.g. 0 1 1 instead of 1 0 1. Last 5 rows added.) This is the system of series said to be used in the "Oteai", Nihon Ki-in's rating tournament. I added the last 5 rows (4 - 8) only to complete the picture. They're not necessary because the maximal pairing gap in the Oteai is kept to 2 dans, which only occasionally could become 3 dans due to a meanwhile promotion. Notice that all steps add 2/6 = 1/3 stone - except the first one from even to BWB: it adds 1/6 stone. Nevertheless, since the majority of games played in the Oteai are 0- and 1-gap games (an unhealthy inbreeding in my opinion, by the way), the BWB series dominates in defining the Japanese pro-dan gap: it's 1/6 stone. A Korean pro 7-dan pointed to this irregularity in Baduk-1189 and suggested a system were all steps are the same, 1/4 stone [DGZ0490]: pro-dan gap series 0 0 0 1 1 1 0 1 1 1 2 1 1 1 1 (handicap 1) 3 1 1 1 2 4 1 1 2 2 5 1 2 2 2 6 2 2 2 2 (handicap 2) 7 2 2 2 3 8 2 2 3 3 (handicap 2.5) (Mixture dropped. Last 2 rows added. VVGV's G read as W.) The period is a bit longer than before, 4 games instead of 3, but Kang Chol-Min's system is indeed logical and its handicap of 2.5 stones between pro shodan and pro 9-dan seems to be more reasonable than former's 3 stones because "the margin between a top [pro] 9-dan and an average [pro] 1-dan seems more like two stones" [GW50b]. If this quote really means 2 stones and not 2.5, steps of 1/6 would be even more reasonable. A pro shodan playing a pro 9-dan would then only take (9 - 1)/6 + 1/2 = 11/6 = 1 + 5/6 stones - almost two. The 1/6-gapped system looks like this: pro-dan gap series 0 0 0 0 1 1 1 0 1 1 0 0 1 1 1 1 0 1 1 (BWB) 2 0 1 1 1 1 1 0 1 1 1 1 1 3 1 1 1 1 1 1 1 4 1 1 1 1 1 2 = 1 1 1 1 1 2 5 1 1 1 1 2 2 1 1 2 6 1 1 1 2 2 2 1 2 7 1 1 2 2 2 2 1 2 2 8 1 2 2 2 2 2 1 2 2 2 2 2 The advantage of the 1/6 system over the 1/4 system is that it preserves the traditional Japanese BWB series played for a pro 1-dan gap and that it fits well to a komi of 6 points. The drawback is its lengthy 6-game period for a pro 2-dan gap. Since gaps above 3 don't occur in the Oteai, the other two 6-gamers don't really bother.
But are the original series actually used in the Oteai anyway? What puzzles me is the color distribution in [GW50b]'s example of how Michael Redmond earned his (pro) 3-dan: opp gap Oteai games he got expected str series played black by series ------------------------------------------ 1-d -1 WBW 7 0 2 1/3 2-d 0 BW 4 3 2 3-d +1 BWB 6 6 4 4-d +2 B 7 7 7 Take the first row. Mike, 2-dan at the time, played 7 games against shodans without ever getting black? But the series for a pro-dan gap of -1 is WBW, giving him a 1/3 chance. Then consider the third row. He played 6 games against 3-dans without ever having to take white? But the series for a pro-dan gap of +1 is BWB, giving him only a 2/3 chance to avoid white. Are Oteai series played between individuals? This hardly would make any sense: in the 24 games played (from Nov. 25, 1981, to Sept. 21, 1983) Mike faced not one of his opponents for a second time - let alone for a considerable number of games to create a fair series. On the other side, there must be some series - otherwise Oteai's points-per-game system (distributing 120 points between both players per game) wouldn't have to cover cases where the weaker player takes white. Either I don't understand it, or it fits into the whole mess. By the way, recently the Nihon Ki-in replaced Oteai by promotions due to performance in regular tournaments. The reason seems to be - guess what - money. No public attention, no sponsors - no money. Ryu Shikun, for instance, didn't attend the Oteai for years. So, despite being in the top ten, he still was a "7-dan". [DGZ0103a]
Let's leave Japan's jungle again and step out into the clearing. The Oteai might or might not have used series, but they aren't in use anywhere else. Why then mention them? Because they serve well in explaining the handicap paradox and, to come now, the relation between partial handicap stones and komi. A handicap of, say, 1.5 can be translated to a series with a 2-game period: 1.5 = 3/2 = 1 1 + 0 1 = 1 2, giving the weaker player black in one game and 2 stones in the other. But what if only a single game is to be played? The idea is to convert 1.5 to an integer via komi. But how much komi would Black have to pay to buy half a stone and increase 1.5 to 2? Or should he rather sell half a stone and decrease 1.5 to 1? If you play someone of your own strength, you take a "handicap" of 1/2. This either means a "0 1" series or a single fair game. The latter is either you taking black and paying some komi or you taking white and receiving some komi. One can also put it this way: Before you yield turn, you place your handicap onto the board - in this case it's half a stone. But since you can't play with chopped stones, you either have to buy a second half or have to sell the first one. After this transaction, either one black stone is around and you paid komi, or no stone is around and you got komi. The first case matches an even game with you being Black, the second an even game with you being White - therefore the komi to be used must be that used in an even game: The price for half a handicap stone is the perfect komi Don't confuse this with buying sente. In this case you have no stone on the board and would have to buy two half-stones - costing TWICE the perfect komi. If the "handicap" is 1/2, there's a symmetry between buying and selling. For all other handicaps this is not the case. Since komi should be kept as small as possible (primary criterion), fractional parts greater 1/2 should be completed by buying their complement (to one), and parts below 1/2 should be sold. Fractions of exactly 1/2 should also be sold to favor a lesser number of handicap stones (secondary criterion). For instance, assuming a perfect komi of, say, 5 points: gap H N K ---------------------------------------- -1.6 -1.1 -1 1 (= giving 2.1) -1.2 -0.7 -1 -3 (= giving 1.7) -1 -0.5 0 5 (= giving 1.5) -0.5 0 0 0 (= giving 1 ) 0 0.5 0 -5 (or 1 5 ) 0.5 1 1 0 1 1.5 1 -5 (not 2 5) 1.2 1.7 2 3 (not 1 -7) 1.6 2.1 2 -1 (not 3 9) 2 2.5 2 -5 (not 3 5) 2.5 3 3 0 3 3.5 3 -5 (not 4 5) 3.5 4 4 0 4 4.5 4 -5 (not 5 5) ... with gap = your strength minus his strength H = gap plus 1/2 = handicap you take N = number of stones you place before you yield turn K = number of points you pay before you yield turn (|K| <= perfect komi) It would be more logical to swap the sign of the komi K since more handicap stones are "positive" for Black and putting them into the lid as komi is "negative" for Black. But since everybody is used to speak of positive komi in the normal case of an even game, I left it to avoid confusion. (To make up some "logic": both handicap components count stones of the same color if their signs match. ;-) The "negative" rows may be a bit confusing. What's a handicap of -1.1? It's 1 - (-1.1) = 1 + 1.1 = 2.1 seen from the other side. To convert a handicap to your opponent's view, take its complement to 1 or, for a pair, its complement to (1,0). This is academic. It's clearer to stick to N > 0. This is Black's point of view since always Black puts down the first stone - handicap or not. (This wasn't always so, but nowadays it is.)
By now you should be convinced that a, say, 1-kyu has to give a 3-kyu not 2 stones, but 2.5 stones, that's, 2 stones plus komi paid by White (negative komi). In fact, if strengths are 1 stone apart, there are no games without komi! Either it's an even game and Black pays komi, or it's a handicap game and White pays komi - besides giving handicap stones according to the strength gap. If you don't agree - just relax, you're in "good" company: even the German Go Federation (DGoB) ignores this fact. Recently it invited clubs to take part in the German Club Championship - played with "full" handicap. This was defined as the stronger player taking white and giving N handicap stones to a N grades weaker opponent [DGZ0103b]. "Great". As just explained, negative komi is missing. But can't we just define it this way? No, we can't! It would not be consistent. The step from even game to black is half a stone, but that from black to handicap 2 is 1 stone. It makes no sense to vary the step. If grades are 1 stone apart, and if perfect komi were 5 points, you "take" 1 stone and pay 5 points in an even game. If you are 1 grade weaker, you take 1 stone more, but since fewer handicap stones should be preferred, use 10 points more instead, that's, you still take 1 stone, but now receive 5 points instead to pay them. Each further step adds 1 handicap stone - and leaves komi negative. (Not to minimize the number of handicap stones wouldn't avoid komi. It just became positive instead, in trade for 1 handicap stone more.)
But the German Go Federation should know better. Its former grade system, still around when I started in about 1975 and at least in use until 1993 in the Netherlands [RGG011093], called its grades "classes". The gap between two neighboring classes wasn't 1 stone, but 1/2 stone. This, as already mentioned, is the canonical choice. It recommends itself because the step from even to black is half a stone. Handicap was then defined as follows [P-WD] [RGG011093]: H = (gap + 1) / 2 N = (gap + 1 + E) / 2 K = E * 5 E = 0 for odd gaps E = 1 for even gaps For even (class) gaps that's: gap H N K ------------------------- 0/2 0.5 1 5 2/2 1.5 2 5 4/2 2.5 3 5 6/2 3.5 4 5 8/2 4.5 5 5 ... This was based on the assumption of 5 points being the perfect komi and no synergic effects among the handicap stones. Notice that always Black paid komi. Just trade 1 handicap stone for a komi-sign reversal to get to the negative-komi system I favor: gap H N K ------------------------- 0 0.5 0 -5 1 1.5 1 -5 2 2.5 2 -5 3 3.5 3 -5 4 4.5 4 -5 ... Since the dan/kyu system has full-stone gaps, but the class system has half-stone gaps, one dan/kyu grade matched two classes: dan/kyu class strong 7-dan 6 weak 7-dan 7 strong 6-dan 8 weak 6-dan 9 strong 5-dan 10 weak 5-dan 11 strong 4-dan 12 weak 4-dan 13 strong 3-dan 14 weak 3-dan 15 strong 2-dan 16 weak 2-dan 17 strong 1-dan 18 weak 1-dan 19 strong 1-kyu 20 weak 1-kyu 21 strong 2-kyu 22 weak 2-kyu 23 ... The German class system was a very good grade system: no artificial distinction between dan and kyu grades, canonical strength gaps of half a stone, and sound handicaps. I don't quite understand why it was dropped nor why the former president of the DGoB (1966-1981) and EGF (1967-1969), Karl-Ernst Paech, takes pride in having initiated its removal [DGZ0602c]. Sometimes it's better to stick to your own tradition.
Let's design a new (international?) grade system. First, there should only be a single measurement unit - of course a full stone. Then, each grade or strength should (at least try to) tell what handicap the perfect player would give its owner. This forces us to assign the perfect player the strength 1/2. Then, we would have to guess where to put the best pros. How about strength 2 (perfect player gives pro 9-dan 2 stones and no komi). If pros are 1/4 stone apart (handier than 1/6), pro shodan is of strength 4. If this equals an amateur 7-dan (instead of 6-dan for this nice 9p=9d join), amateur 6-dan is of strength 5. All in all that's strength name ---------------------- 0.5 perfect (= pro 15-dan) 2 pro 9-dan (= ama 9-dan :-) 2.25 pro 8-dan 2.5 pro 7-dan 2.75 pro 6-dan 3 pro 5-dan (= ama 8-dan) 3.25 pro 4-dan 3.5 pro 3-dan 3.75 pro 2-dan 4 pro 1-dan (= ama 7-dan) 5 ama 6-dan 6 ama 5-dan 7 ama 4-dan 8 ama 3-dan 9 ama 2-dan 10 ama 1-dan 11 1-kyu 12 2-kyu 13 3-kyu ... This system actually has no fixed strength gap, since any weird strength is possible. But if used as a grade system, on which handicaps are based, at most missing multiples of 1/2 should be added. This brings down the gap between neighboring amateurs strengths to the canonical gap of 1/2 stone - and is precise enough. If you don't agree to the right side, just take it as defining "nicer" names for the left one. If you think that all multiples of 1/2 deserve a name too, how about using "strong 2-dan" for 8.5, "strong 1-kyu" for 10.5, etc. (avoiding "weak" ;-). But it might be even better to forget all these names again. What's wrong with "My handicap is 8.5" ? Totally plain. ("Once in a while I play with Him, taking 8 stones and komi." ;-) The handicap taken by the weaker player already was defined above: Add 1/2 to the non-negative strength gap and either sell the fraction or buy its complement - whatever brings komi nearer to zero and leads to fewer handicap stones, favoring the former.
There's another way to put it. One can use a price system (or function) P. P(N) is defined as the number of points a perfect payer playing another perfect player gains in the result when he uses N handicap stones instead of none P(1) then has to be twice the perfect komi PK because taking 1 handicap stone (that's, taking black) wins by PK, but taking 0 (that's, taking white) loses by PK: P(1) = 2 * PK Now we know P(1). What about the rest? If one assumes P to be linear, that's having the property P(A+B) = P(A) + P(B), the rest follows easily: P(1) = P(0.5) + P(0.5) P(1.5) = P(0.5) + P(1) P(2) = P(1) + P(1) P(2.5) = P(1.5) + P(1) P(3) = P(2) + P(1) ... P(X) = 2 * PK * X and of course P(0.5) = PK. We could now guess some PK, for instance 5, produce a price table based on it, and calculate the handicap pairs (N,K) by going the opposite direction - from P(gap+0.5) to best fitting P(N), and adjusting the rest in K. This wins nothing - but wait. This price system is linear. 2 stones cost twice as much as 1, etc. But this was just an assumption. Nobody knows if this is the case, but it's very likely that it is not and that a couple of handicap stones create synergy. A table could cope with these irregularities.
In the time of the German class system, a rating system called "Karlsruher Methode" (KM) was around that used such a price table. It was based on a perfect komi of 5 and took synergy into account by increasing the price of each handicap stone, starting with the third. For instance, 6 handicap stones wouldn't be worth 60 points but 10 + 10 + 11 + 12 + 13 + 14 = 70 points (actually all prices were 5 points less to spare increasing the class gap by one before it was multiplied with 5). In other words, a strength gap of 6.5 would only yield a handicap of 6 stones because 6 stones' synergy adds up to a virtual 7th one in KM's believe. [P-BZHZ] KM's price table thus looked like this: N P(N) ------------ 1 10 2 20 3 31 4 43 5 56 6 70 7 85 8 101 9 118 10 136 11 155 12 175 13 196 14 218 15 241 16 265 17 290 ... (Or as formula: P(N) = (N * (N + 17) / 2) + 1, but P(0.5) = 5) To find (N,K) for a gap G, one has to search for the first P(N) with a difference D = P(N) - (P(1) * (G+0.5)) nearest to zero and set K = D. The Karlsruher Methode would therefore advice following handicap pairs (actually its gaps were measured in classes, its K sign was reversed, and handicap fraction elimination could go in either direction): or gap N K N K ----------------------------------- 0.5 1 0 1.0 1 -5 2 5 1.5 2 0 2.0 2 -5 3 6 2.5 3 1 3.0 3 -4 4 8 3.5 4 3 3 -9 4.0 4 -2 4.5 5 6 4 -7 5.0 5 1 5.5 5 -4 6 10 6.0 6 5 5 -9 6.5 6 0 7.0 6 -5 7 10 7.5 7 5 6 -10 8.0 7 0 8.5 7 -5 8 11 9.0 8 6 7 -10 9.5 8 1 10.0 8 -4 9 13 10.5 9 8 8 -9 11.0 9 3 11.5 9 -2 12.0 9 -7 12.5 10 6 9 -12 13.0 10 1 9 17 13.5 10 -4 9 22 14.0 10 -9 9 27 14.5 11 5 9 32 15.0 11 0 9 37 15.5 11 -5 9 42 16.0 11 -10 9 47 [KM used (12,10) for (11,-10)] 16.5 12 5 9 52 17.0 12 0 9 57 17.5 12 -5 9 62 18.0 12 -10 9 67 18.5 13 6 9 72 19.0 13 1 9 77 19.5 13 -4 9 82 20.0 13 -9 9 87 20.5 14 8 9 92 21.0 14 3 9 97
Let's now put the pieces together and codify handicap games: If two players' strengths are equal or if handicap is ruled out, it's an even game and the rules stay unchanged. Otherwise it's a handicap game and the rules are extended by the rules about boards mentioned above and changed by replacing A1 and A2 as follows: A1. "Two players play a handicap game of go on the standard board according to Logical Japanese Rules of Go " by doing - essentially - the following in the given order: (This requires (1) that a strength, given by a rational number, is assigned to each player and (2) that a price function P is defined that maps each non-negative integer N to a non-negative integer P(N).) 1. They call the weaker player "Black" and the stronger player "White". 2. They determine the "strength gap" G = |S1 - S2| (with |X| being -X for X<0, and X otherwise) using their strengths S1 and S2 (two rationals). A handicap game requires G > 0. 3. They determine the "handicap" H = G + 1/2. 4. They determine H's "handicap pair" (N,K) by finding integer N and rational K' that satisfy P(N) = (P(1) * H) + K', favoring smaller |K'| over smaller N ("best table fit"). If K' >= 0, K = round(K'); otherwise K = -round(-K') (with round(X) being the integer nearest to X + 1/2 if X is no integer, and X otherwise). For linear P (P(A+B) = P(A) + P(B)) this is the same as a) to split H into integer I and rational Q that satisfy 0 <= I, 0 <= Q < 1, and I + Q = H; and b) to determine N and K depending on Q: if Q <= 1/2 ("sell"): N = I, K = -round(P(1) * Q) if Q > 1/2 ("buy" ): N = I+1, K = round(P(1) * (1 - Q)) 5. Black must choose a state that's initial for N and K on the standard board. This state is called "current state". 6. While the current state is not final, the player having the turn in it must replace it with one of its successors. 7. When the current state is final, the player with the higher score in it wins. If both are equal, it's a "jigo" (tie). A2. "A state S1 is initial for N (handicap stones) and (a komi of) K (points) on the standard board" only if all this holds: 1. N is a non-negative integer. 2. K is a (possibly negative) integer. 3. S1's board is the standard board. 4. S1's set of black locations is a subset of S1's set of locations having no more than N members (possibly less). 5. S1's set of white locations is empty. 6. S1's set of temporarily marked locations is empty. 7. S1's set of permanently marked locations is empty. 8. S1's black captive count is K for K > 0, and otherwise 0. 9. S1's white captive count is -K for K < 0, and otherwise 0. 10. S1's turn is "white". 11. S1's pass count is 0. 12. S1's history is empty. Both, the strength system and the price system, are purposely left open. The only implied requirement for the strength system is that a gap of 1/2 in it would mean that the weaker player takes black and no komi from the stronger player, because otherwise it wouldn't fit to whatever price system is defined. The price system, on the other hand, is totally free - at first sight. But its purpose, of course, is to bring Black's and White's winning chances as close as possible together.
The most prominent price system candidate is the plain linear P(N) = N * 2 * EK with EK being the (rounded down) komi that seems to be fair for even games. This ignores synergy created by handicap stones. But since synergy is hard to figure out anyway (KM obviously just made a wild guess) and only seems to exist for gaps above two, this is no big problem: up- and down-grading should depend on results made against grades in the neighborhood - not on teaching games (starting with more than, say, three handicap stones). That the perfect komi might differ from EK is neither a problem. It's better to match the winning chances in the real, unperfect world than to have unmanageable high komis. In the same sense I dropped the requirement that P(1) had to be even, as it certainly is in the perfect world. That the komi is an integer was kept to allow jigo. I love jigo as well as seki.
The only problem with a grade system based on handicap is that official handicap games have to be played. Otherwise the system could lose touch and float, letting gaps globally or locally either shrink or grow. Japan is going exactly in this direction by abolishing Oteai (if they not already were on this track by neither using series nor handicap stones in it). Needless to say that a further necessity for keeping up a sound grade system is to permit down-grading or demotion (which the Oteai also failed to do). Since games played in one's home club are done with full handicap, they could (and should) go into the grading process. But solely to depend on them would be like inbreeding. Tournament games too have to be considered, even if played without handicap. If the strength gap doesn't go beyond one, every even game can in retrospective be interpreted as a handicap game simply by adjusting it with the proper komi before the grading process takes it into account. So, for instance, if 1-kyu wins with white by 4 points against 2-kyu in an even game, this would be an adjusted loss by 8 points under a komi of 6 (White returns 6 points and gives further 6). (By the way, the stronger grade should always take white, even if no handicap is used.) In this case each player can choose to look at it positively: 1-kyu made a point in the tournament, and 2-kyu improved his winning percentage in the grading process. Each even game with a larger gap could also retrospectively be adjusted, treating each missing handicap stone to be worth P(1) points for the side that lacks it (ignoring synergy again). But since the character of those games compared to a handicap game has changed, those games should be of lesser weight than the former ones. I'll leave the details of the grading system open. A simple scheme, for example, would be to grade up after 4 wins in a row and to grade down after the same number of losses in a row (adjusted and weighed games, of course). The step for increasing or decreasing strengths would be 1/2 among amateurs and 1/4 among pros.
The traditional locations for Black to place the handicap stones on the standard board are (in this order) bottom being Black's side On a (real) standard board all nine locations used above are emphasized to support orientation. Each is called "hoshi". Black shows awareness if he "colors" them in the traditional order. However, there are two exceptions: 1. If the last handicap stone is to be placed and it's also the first, every location may be used (but see polite start). 2. If the last handicap stone is to be placed and its ordinal is odd and greater three, the center hoshi ("tengen") is to be used. Note that no stone lands on tengen if not last - in contrast to some sources that suggest to always occupy tengen with the fifth stone - and that the third stone avoids tengen even if last. There's no tradition for the case where the number of handicap stones exceeds nine. Let's make up one just for fun. Watch this progression (ONLY hoshis are shown): 1 - 4 5 - 8 9 - 24 25 - 52 53 - 80 Not that anyone cares, but in case you plan to play on a 31x31 and to get up to 81 stones handicap, you now know exactly where and in which (darn) order you have to place them. The first 25 hoshis fit on the standard board (9 traditionally emphasized ones plus 16 in between) and are more likely to be useful. My set of generating rules, as you might have discovered, is G1. Start with 2 horizontal and 2 vertical lines. Their intersections create the first 4 uncolored hoshis. G2. As long as there are uncolored hoshis besides tengen (center), color that one that fits best to following preferences, considering lower preferences only to break a tie: P1. Prefer a greater distance to tengen. P2. Prefer more symmetry. P3. Prefer the right side. P4. Prefer the upper side. G3. If all hoshis besides tengen have been colored, insert new lines halfway between all older lines. Each new intersection is a new, uncolored hoshi. Continue with G2. This generalizes the traditional handicap position and order. Notice the funny coincidence in above's procedure that tengen isn't yet created when the third stone is to be placed, "explaining" why it doesn't go to tengen.
But the first exception, free placement in case of a handicap of exactly one, still is a miracle - isn't it? Wouldn't it be logical also to place the first stone of a one-stone handicap game on the upper right hoshi - only allowing its free placement if Black pays komi? The reason for this inconsistency seems to be that free placement was invented before komi. In ancient times the game started with a fixed pattern of four stones - each player occupied the hoshi in his upper right and lower left corner with a stone. Japan abolished this "zuozi" practice in the 14th or 15th century [P-MK]. From then on they started the game with an empty board. Since there was no komi, all games were in fact one-stone handicap games - with free placement of the first stone. Wouldn't it only be consistent to also "free" the rest of the handicap stones? Even if this spoils my generalization efforts above - yes, it is. That's why LJRG prescribes no fixed pattern. By the way, the play-off between amateur and professional Honinbo, sponsored by the Mainichi Shinbun for now 40 years, uses free placed handicap since 1995. On November 4, 2002, amateur Honinbo Samejima Ichiro made his first appearance and boldly placed his two handicap stones on two diagonal 5-5's. After 282 moves heavy fighting and several large ko fights, Honinbo Kato Masao (returning after 23 years, by the way) had to resign. [SL1] [DGZ0602a] Also interesting is that this event's handicap varies depending on last year's outcome. If Black loses, komi decreases by 2.5 points. If he wins, komi increases by the same amount. Half of the games thus enable jigo. A komi of -7.5 is converted to 5.0, while adding one handicap stone. Similarly, a komi of 7.5 is converted to -5.0, while taking away one handicap stone. One handicap stone's price is thus 12.5 points. Since the 2002 event saw a handicap of 2 stones and -5.0 points and was won by Black, 2003 will see a handicap of 2 stones and -2.5 points (as 2001 did). Had Kato won, the amateur would have gone down to 3 stones and 5.0 points. In the diagram above, I labeled the handicap stones with 1 to 9. This was only to show their order of placement. Usually handicap stones are not labeled. But silly me likes to - know in which order the handicap was placed - always have odd numbers for black and even for white stones (except in variation diagrams, of course) - be prepared for the handicap liberation Therefore I strongly recommend to label handicap stones with 1a, 1b, 1c, etc. Of course, in case of just one the label is 1. (A one-stone handicap game being the same as a no-komi game.)
The placement of stones is free, but not all locations are polite. A remaining chance for Black to show awareness is to keep his first stone, handicap game or not, in the half-past-one-till-three-o'clock sector of the board (triangle k10-t10-t19 on the standard board). [DGZ0994] motivates this with anticipation of where White would like to answer (Black's upper left corner), but I rather think it stems from old Japanese (and, of course, older Chinese) writing direction, which starts in the upper right corner and fills one column after the other from right to left. This preference of right side over left side and - in this order - upper side over lower side naturally selects this sector (and also influenced the handicap sequence, as we saw). Each location on the left side of the board has at least one symmetric partner on the right side (that with the complementary first coordinate - e.g. b3 = 2,3 <=> 18,3 = s3), and likewise each location on the lower side of the board has at least one symmetric partner on the upper side (that with the complementary second coordinate - e.g. b3 = 2,3 <=> 2,17 = b17). According to our preference of right and upper side, no location on the left or lower side of the board will ever be chosen because there always is a "better" partner. Similarly, each location above the diagonal from the lower left to the upper right corner has at least one symmetric partner below this diagonal (that with swapped coordinates - e.g. b3 = 2,3 <=> 3,2 = c2), and, since this partner always is more to the right, we can as well forget all locations above this diagonal: What remains is the sector in question. (Could it be reduced further? No.) One would believe that at least Japanese pros stick to form without any rule, but that's not the case. In 1999's Meijin final between Cho Chikun and Yoda Norimoto, Yoda, after having boldly announced his victory and losing the first two games, placed the first stone of game three in his upper left corner - above the hoshi [DGZ1099]. Hopefully this sets no bad example, even if it incidentally led to Yoda's only win over Cho in this best-of-seven match. Yoda may argue that the sector rule isn't followed strictly, for instance: Kitani Minoru at least once started a game in his lower right corner (1941 in a game against his former teacher Kubomatsu Katsukiyo), and left-handed Osawa Ginjiro (1844-1906) even made it his habit as Black to start in his upper left corner [GMR0469]. But the overwhelming majority of games indeed start in the "right" sector (selected by historic incident, of course). Restricting the first stone to one sector avoids confronting White with unusual and irrelevant symmetric variations without costing Black anything. It's a matter of courtesy (but I wouldn't even bother if some rule would take care). Today, with computers, is takes nothing more than to press a button to mirrow the game record so that its first stone sits in the right sector. Please don't do it. Please tell the truth! Keep it to rotations, and if Black doesn't end up at the bottom, please mention his side.
CYCLE REMOVAL
First some points about detecting a cycle. Imagine some game. The game starts in some initial situation (or state). Both players take turn to manipulate the situation. Only the situation itself and the rules of this game constrain how this can be done - nothing else. Now imagine that one of them comes to you, shows you the situation he is confronted with, and claims that this could go on forever. You have absolutely no knowledge about the game that goes beyond the information given above. What to do? Your only chance to decide on this issue is to ask them to show you all former situations. Then you search for one that is IDENTICAL to the one in question. If you find none, you stay undecided. But if you do, it's obvious that the claim was correct: this could go on forever. Now imagine that it's not you who has to decide, but LJRG. And further imagine that LJRG has some special goodies for anybody that suffers from a cycle, but that it wants to make sure that he or she deserves it. Well, then LJRG has to apply the same test as you did - and that's (almost) exactly what it does. In LJRG's case the game to decide on already includes a treatment of short cycles (ko and double pass) - therefore the treatment of long cycles is the next layer of cycle treatment. This may seem complicated, but enables LJRG to treat long cycles in a different way than short ones. I'm telling you all this to let you understand why LJRG doesn't just compare the stone configurations or additionally the turns of two situations to decide if cycle removal is legal. Even if it's true that a running cycle will necessarily repeat those aspects, this doesn't has to be the only cause. LJRG tries to stay on the save side. So, why are the captive counts totally ignored when testing for similarity? First, because they don't influence what can be done in a go situation in any way. Second, because this allows the removal of unbalanced cycles like the one possible below (no dead bent four - see beast 31): 0 1 W 0 To avoid losing, White could try to repeatedly sacrifice two stones and capture one. This "cycle" can't really hurt Black. He patiently answers till he has piled up enough white prisoners. Then he sticks to passing. This eventually forces White to pass too, since there's no suicide, which ends the game. But why not give Black the means to stop it earlier? Actually it's redundant to keep two captive counts because what matters is only their difference, but since I decided to even ignore that for the reason just given, I kept it more in sync with reality.
Second, to avoid a bunch of diagrams cycles notoriously produce, some abbreviations to shrink each situation to one line: . empty location # empty, but temporarily prohibited * empty, but permanently prohibited x black stone o white stone B Black's turn W White's turn 0 pass count is 0 (implies no #) 1 pass count is 1 (implies no #) pass count is -1 (implies one #) For instance 0 0 B 0 with following 7 locations of interest 0 0 B 0 gets squeezed to ________ neutral is empty / ________ black stone in left ko / / _______ white stone in lower right ko / / / ______ black stone in upper ko / / / / ______ Black's turn / / / / /_______ pass count is 0 / / / / // . x. o. .x B0 If the cycle only runs on kos, as above, each ko is squeezed further to a single letter: . x o x B0 The letter is capitalized if its stone is neighboring a temporary mark: . #o o. .x B . O o x B
Let's now see what the effect of allowing cycle removal is. What if two double-ko sekis are around and the game is still in progress? 1 0 B 0 with following 8 locations of interest Black is behind. What if he tries to reach no outcome by producing a cycle? It could continue like this: S1 xoxo B0 (1 0) S2 xXxo W (1 1) S3 Oxxo B (2 1) S4 oxxX W (2 2) S5 oxOx B (3 2) S6 Xxox W (3 3) S7 xOox B (4 3) S8 xoXx W (4 4) S9 xoxO B (5 4) not similar to S1 (temporary mark!) S10 xXxo W (5 5) similar to S2 (ignoring prisoners) In S10 5 5 W -1 White is allowed to remove the cycle: 8 6 B 0 Notice how the stones in the cycle were treated as if captured, increasing the black captive count by 3 and the white one by 1. What did Black "accomplish"? He lost a stone and he lost sente. Losing a stone is only the case when the number of black and white stones in the set of locations used by the cycle match, but if not, like in a triple ko (beast 8), the disturber "only" loses sente. Losing sente, on the other hand, is for sure if one side "disturbes" by staying in the cycle. His opponent will eventually remove it and nevertheless be allowed to play his stone subsequently. We conclude that Black can't gain anything in playing this cycle: that's exactly what LJRG intends. You may think the story is over now and everything worked out just fine, but there is still a nuisance left. Black may leave the cycle uncompleted and play 9 elsewhere (if the board were bigger). Since after 8 both captured 4 stones, it's as if the whole sequence never happened. Though Black can't stop the game's progress, he can slow it down drastically - disturbing. It would be nice if White could now himself chase Black through the cycle and eventually remove it, but this costs a stone and sente as we've seen. So, this will only work if White can afford it. Even though I'm not totally satisfied, in the long run cycle removal prevents no outcome.
What if no kos are involved like in a "round-robin ko"? In this case the starting situation will be repeated - not the one following it, as above - and Black will have the chance to remove the cycle himself: 1 0 B 0 The first flip produces 3 2 B 0 The next flip results in 5 4 B 0 Black could now remove the cycle since this situation is similar to the first - but he aims for no outcome and continues to 5 4 W 0 Since this repeats the second situation, now White can remove the cycle: Black loses his recent stone and sente. Black would have been better off removing the cycle himself. So again, Black can't disturb forever. End of the story? I cheated a bit. Sly Black could play 9 here: 5 4 W 0 This situation didn't happen yet. So, another flip will be played, repeating the situation after the first flip: 7 6 B 0 Now finally the same arguments as above apply, convincing Black to remove the cycle in his own interest. Believe me: I hate bookkeeping of situations to detect cycles as much as I guess you do. But cycles only happen rarely, and if, I see no way to cope with them without some sort of bookkeeping. In practice we certainly won't draw down situations - please don't get me wrong.
Everything till now comprises the first design of cycle removal. But then I discovered that there are cases where both players try to avoid to pass ("pass fight"), which is silly. The solution was to add a further condition: Cycle removal only is allowed if the pass count is not 1 This makes sense by itself because cycle removal should help the disturbed player, but certainly nobody can claim being disturbed when he could end the game at the same time - which is exactly the case when the pass count is 1. Here's an example for both avoiding to pass first without this rule: 0 0 B 0 If the game ended as above, Black would win by 1 point: he controls 12 locations at the left side, giving him 3 points, White controls 11 locations nearby, giving him 2 points, and nobody controls the rest (see beast 8 for a discussion why) - including that neutral at the left that will be important (but shouldn't). If White removed a cycle from the three kos in a situation similar to above's, he would make jigo by removing 2 black stones compared to only 1 white stone. Therefore White will try to create a cycle. Here's one possible sequence of situations: S1 . xox B0 (the situation above) S2 . xox W1 S3 . Oox B * S4 . oXx W S5 . oxO B S6 . Xxo W S7 . xOo B S8 . xoX W S9 . Oox B * (is similar to S3) White keeps on forcing after Black's initial pass, but Black gets the first chance to remove the cycle in S9. He does and wins: one black stone more was removed by capture, but therefore one white stone more was removed by cycle removal (as a short cut, pretend that Black already removed the cycle in S3 - this works if passes in the cycle are balanced). First it would seem that cycle removal succeeded in convincing White to abstain from "disturbing" - but look at this sequence: S1 . xox B0 * S2 . xox W1 ** S3 . Oox B S4 . oXx W S5 . oxO B S6 . Xxo W S7 . xxo B0 S8 . xxo W1 S9 . Oxo B S10 . oxX W S11 . oOx B S12 . Xox W S13 . xox B0 * S14 . xox W1 ** This time White passes in S6. If Black again (as in S1) refuses to fill the "useless" neutral and passes instead, White forces a similar sequence leading to S13. S13 is similar to S1. Black can remove the cycle, but since an equal number of black and white stones was captured and there happen to be more black than white stones in the cycle's arena, this is of no use for Black - but passing is neither because White would remove the cycle (S14 is similar to S2) and enjoy jigo again. Considering all this, Black will fill the neutral (and win): S1 . xox B0 S2 x xox W0 S3 x Oox B * S4 x oXx W S5 x oxO B S6 x Xxo W S7 x xxo B0 S8 x xxo W1 S9 x Oxo B S10 x oxX W S11 x oOx B S12 x Xox W S13 x xox B0 S14 x xox W1 S15 x Oox B * White applies the same strategy as above, but now S15 is the first chance to remove the cycle and this favors Black again: one black stone more was removed by capture, but therefore one white stone more was removed by cycle removal. Black keeps his 1-point winning margin - regardless if White passes or continues in S14. Now what if it were not one, but two neutrals? If Black takes one, White takes the other and reaches jigo via the 2nd sequence (that was played as if there were no neutrals). Should Black pass instead, White again plays the 2nd sequence to reach S13, in which Black only can choose between cycle removal, passing, or taking the first neutral - each leading to jigo. It seems that Black will only win if the number of neutrals is odd. Anyway, since the number of neutrals should NEVER change the outcome of a game played under Japanese-style rules, above's condition was added to stop this fuss: White is now barred from removing the cycle in S14.
Here's the cause of the next fix of cycle removal: After game end this is a big (dynamic) seki: nobody controls anything. But before game end Black could disturb the ends (continually atari all white groups except that in the center), force White to remove the cycle (suppose White is ahead), and then - backed up by the permanently marked liberties that come with cycle removal - capture White's center group. But this is a dynamic seki and it should stay one. The problem seems to be the exploitation of the permanently marked liberties. To grant stones neighboring a removed cycle immunity shouldn't enable them to become aggressive. Therefore: You may not play a stone if after you'd placed it on the board all stones of your opponent still enjoy liberties but this stone either has none (suicide) or only permanently marked ones (pseudo suicide). This rule prohibits stones neighboring a removed cycle to fill up their last non-permanent liberty. In the example above Black is prohibited to fill either ko in the center after cycle removal.
Here's a historic "cycle" [DGZ1093]. At the end of the initial game of 1993's Honinbo league between Komatsu Hideki (White) and Rin Kaiho (or Lin Hai Feng, born on 6.5.1942 in Shanghai, China), this was the situation (watch the lower left corner): [0 2] W 0 (There are 143 black and 140 white stones on the board and it's White's turn, so I guess Black captured 2 stones more than White.) Rin is leading by 8 points (before komi), but now got shocked by White's attempt to revive the stones in the lower left corner: 1 3 W -1 (4 recaptured at A) Even after Rin played his absolute ko threat at 2 and recaptured, Komatsu continued to "disturb": 2 5 B -1 4 6 W -1 Of course, it would have made no sense for White to capture the next-step ko with 9 because Black would have captured the corner stone and next, since White is without any ko threat, the 3 white pivotal stones. The situation after 10 repeats the one after 4. After some further tries both players agreed to an eternal life: jigo in the league. Under LJRG Komatsu could have removed the cycle after 10 and, still having the turn, would play the last point, after which both would pass: 5 7 B 2 (12 and 13 passed) White would win by 43 - 7 + 5.5 - 31 + 5 = 15.5 points. Rin should have connected the ko earlier under whatever rule set - provided it leads to a cycle. Note that the 2 black positions enclosing the permanently marked locations don't control anything because each can't build 2 eyes on its own, and joining them via the corner wouldn't work either because the permanently marked locations would prevent the 2-eye formation. Therefore the 5 locations enclosed by them don't count. But the cycle is an illusion, as Werner Fabry discovered [DGZ1293]. Rin could have connected the next-step ko with 8 instead of playing his ko threat. White, lacking any ko threats, would then have to approach from the outside, after which Black could have recaptured again with 10: 2 6 W -1 Since White has no ko threats, he only can take the last point. Black will fill or capture, and White will rub his eyes and realize that he just has fed Black with two additional prisoners (the stone Black added to his corner must be added by him anyway - see below). The ko threats on the lower edge have the disadvantage that by using them one produces the next ko threat for one's opponent. Black's 8 above avoided this, but was only possible because of the outside liberty at 9. Rin's agreement to eternal life was an error. Repeatedly he missed the chance to do as explained and win. The best thing for Komatsu would have been to ignore the lower left corner and to take the last point immediately. If both then passed, we'd have this: 0 2 B 2 (2 and 3 passed) Under JRG89 (details below) the game isn't over yet - it only has stopped. Besides filling neutrals, Black would now have to connect the ko (or capture) because his stones around the lower left corner would otherwise be "dead in no territory" after game end (kind of seki). This is because White could capture using the pass-for-ko rule without enabling a new uncapturable white stone. Black would win by 51 - 43 - 5.5 = 2.5 points. Under LJRG there's no (silly) stop - there's just an end. All dependencies with the context have to be detected and removed by ONESELF and BEFORE the end. If Black passes too early, as above, he'll be punished hard and lose: He couldn't claim to be able to lock the lower left corner because in this proof he would neither enjoy his outer liberty nor the absolute ko threat any more - both being buried under permanent white stones.
Notice that there never will be a situation under LJRG where both players keep on playing a cycle because it's always better to remove a cycle instead of continuing it: If you continue, you give your opponent the chance to remove it, but then he has sente and you lost a stone compared to having removed the cycle yourself. But (unfortunately) this doesn't mean it's never wise to start a cycle! In the example below Black shouldn't pass. 0 0 B 0 White would pass too, the game would end, and Black would have lost by 10 points - White controls both corners at the bottom. Instead, Black should force White into a cycle by alternately giving atari in the left and the right lower corner. Even if White has the first chance to remove the cycle, costing Black a stone and sente, White controls nothing after cycle removal and Black wins by 7 points. Under "New Ko Rules" (below) Black wouldn't be allowed to atari a second time in each corner. New Ko Rules establish a kind of local view before the end. This fits well with how things would be ruled after the end, but one can question why other positions aren't then viewed locally too: 0 0 B 0 The lower left corner would be controlled by White after game end. White wouldn't have to capture the single black stone (see beast 10). But the game hasn't ended yet, and if Black fills the neutral White should hurry to capture that single black stone to avoid ko: Black would win it thanks to his (external) ko threat on the right side. If we connect things far away, why should we make an exception if cycles are involved? So, LJRG allows as much as possible during the game. If cycles happen, they are treated as a kind of dynamic seki. The local view only applies AFTER the game end.
At last let me say something about super-ko and the kind. A ko is a cycle with a length of 2: after 2 moves the situation repeats - ignoring ko rule or temporary marks for the moment. Then someone had the idea to prohibit this repetition, producing this fascinating tactical event of a ko fight. So, why not generalize this prohibition and convert all cycles into ko fights? Wouldn't that make things even more interesting? I don't think so because for me it seems unfair. Imagine again the double-ko example. Black is behind and one part of the board looks like this: 0 0 B 0 Why should we disturb harmony and let Black invest his ko threats into killing one of the white groups above? I can't see the point. Now to be fair, Robert Jasiek defined "New Ko Rules" [W-RJ1], trying to nail down Ing's 1991 ko rules. Their idea is to separate the case where one or both players disturb(s) (for instance, in a double-ko seki) from the case where both may fight (for instance, in a triple ko). In the first case, restarting the cycle is prohibited. In the second case, completing it is. I've not yet made up my mind if this definition is clear or complete, but be sure - it's very complicated (Fred Hansen's proposal, risking to go his own way, seems simpler [W-FH2]). In the case above both Black and White would certainly be called "disturber" by "New Ko Rules" if they cycled in it and would be prohibited to do so (if I got it), but in, for instance, a triple ko both would have to treat it as a (super) ko and fight it out. Don't expect me to go into details - I just want to say this: The step from no outcome to fight for life and death in, for example, the triple-ko case is in my opinion a too big one. Let's illustrate this by an example ([P-IK] - this type of triple ko also occurred in a "rating tournament in 1971 between Cho Chikun, then 3-dan, on black and Fukui Masaki, then 5-dan" [GW50a]): 0 3 B 0 If Black connects the upper ko, White will capture the 4 stones in the lower right corner. Meanwhile Black will take one ko and connect it. White will connect the last ko and both will pass, giving: 4 4 B 2 White has won by 2 points. So Black wouldn't want to connect with his first move. He'll start cycling in those kos. Is he disturbing? White certainly has the feeling because it's obvious that Black can't capture him (at least as long nobody has ever heard about super-ko or "New Ko" rules). Black, on the other side, will agree to that, but claim that the purpose of his tactics is not to capture the white stones but to dynamically defend his own stones from being captured. If "New Ko Rules" classify this as disturbing (life) just because there seem to be stable states - those with only one black stone in all kos - then why is White allowed to "disturb" such a stable state by approaching the 4 black stones in the corner? Don't they also somehow belong to the local situation? Under super-ko, Black would get a chance to capture White because both would alternately need to make (super) ko threats. Is this any fairer? Cycle removal instead tries to leave dynamic sekis what the are: dynamic sekis. Imagine this triple ko fight to go on forever. It's getting faster and faster. The stones that come and go can't be seen any more. The rest of the board is clearly visible, but in the part of the board the cycle runs, you only see a flickering. It looks as if gray stones are sitting there. If we now treat those gray stones as permanent liberties and somehow decide who gets the first turn on the rest of the board - the game could continue, leaving the ccycle as a kind of seki. That's exactly what cycle removal is about. Another point in favor for cycle removal is that you don't have to record past situations to avoid making illegal modifications (moves). The only risk you take is to stick to a game forever - but certainly it's never to late to start bookkeeping. Therefore cycle removal will gently prevent you from being forced into an endless cycle by your opponent without committing you to perform bookkeeping in advance: If you start bookkeeping "too late", you only lose the chance of getting out of the cycle with sente, but since your opponent has started it, this shouldn't be a problem. I don't want to give the impression that I'm satisfied with cycle removal nor that it's perfect. For instance, Black will lose his 4 stones in the example above also under improved cycle removal, but he won't if you let the white stone at the right edge neighboring the black corner jump into the 2-point eye. Is that logical? It's nothing but a good try. I don't think that I'll ever change the definition of control, but it's hard to resist fiddling around with cycle treatment.
CONTROL
First a technical note. The predicate "control" applies to ONE location. The predicate "lock" applies to a set of them. Of course we can say that "player P controls location L1 and L2", but this doesn't necessarily mean that P can lock them both together! It could be that one of P's lockable sets includes both locations, but it could as well be that not one does. The only thing for sure is that L1 as well as L2 can be found in one of P's lockable sets. If I hadn't made this distinction, had overloaded "control", the statement above would be ambiguous.
What's a "2-eye formation"? I expect you to know inside out what it means to have two eyes, but let's repeat LJRG's formal definition: A player has made a 2-eye formation on a set of locations if (take your breath) beside the technical properties that - the set isn't empty, - contains no "lonely" (i.e. neighborless) locations (since LJRG doesn't exclude 1x1 (sub)boards), - and is bordered by him (to prevent chains to be torn apart and, together with the other properties, to make sure that at least one of his stones is in the set), - all stones in it are of his color, - each contacts at least two empty locations (eyes) in it, - and no empty location is neighbored by another (minimal eyes). So, roughly spoken and compared to the normal sense of having two eyes, you additionally have to shrink all eyes to their minimal size (of one location) to fulfill the definition. Why? The idea is to throw out all opposing stones as well as to hinder any new ones to enter again - even for the shortest time. To "lock" some locations in this way is part of the process to prove being in control of one of them. In case disputes are broken by a referee, this idea serves him to decide who controls what - nobody will actually need to build a 2-eye formation. But in case disputes are played out and your opponent disagrees to your claim, you really have to build one. Note that it isn't necessary to end with exactly two eyes - a 2-eye formation can have more than two eyes. The name refers to the fact that each stone in the formation contacts at least two eyes. Of course, every 2-eye formation can be converted to one with exactly two eyes, but restricting the definition in this way wouldn't make it a bit simpler and would lengthen proofs. To shorten proofs further, couldn't we at least use D.B. Benson's definition [P-DB]? It allows for larger eyes. Roughly spoken and not using original terms, a stone completely contacts an eye (an area bordered by the stone's color) if it contacts all liberties in that eye, and a stone is statically safe if there are some eyes and this stone as well as every other stone of same color that contacts any of them at least contacts two of them completely. Benson proves that statically save stones can't be captured, even if the defender keeps passing, and that stones of the second sort are of the first. The proof depends on ruling out suicide. Not only that eyes don't have to be minimal with this definition, this even allows opposing stones sitting in them. For instance:
Who controls what in this situation? 1 0 B 2 You think Black controls the right side and White the left? Well, that's certainly true in the common sense, but not in the precise sense control was defined by LJRG. For example, if Black claims he could lock the right side including the bordering black stones, White would simply refute this claim by setting up the worst case for Black: 0 0 W 0 and proceed as follows: After 3 it's impossible for Black to build a 2-eye formation that covers EVERY location in the set he claimed because 1 and 3 are now connected to a permanent stone of their color and thus will never fail to have liberties. Therefore we'll shortcut the proof at this point. Strictly followed it would continue by taking all possible move sequences into account that don't go beyond a final or repeated situation. Black can't reduce his claim because the only other sets bordered by him are - the whole board - the complement of the set just tried above extended by the same bordering black stones In both cases White will easily build a 2-eye formation himself inside Black's claimed set and refute those claims too. A similar argument will refute every claim White could make. It's hopeless for White to claim the whole board, and following tries aren't better: 0 0 B 0 Not much to be said about this one. Now the same as above, but swapping inside with outside, that's, the whole board except one location: 0 0 B 0 Besides that White won't be able to hinder Black from building a 2-eye formation at the right side inside his claim, Black can simply capture the 3 white stones and extend his permanent stone into White's claim.
It's boring to go through all of White's possible claims. All will fail. At least I'll show you how to find them systematically. First remove all black stones: Then identify all separate empty areas. In this case we find three. Let the groups of stones bordering each also belong to each. For instance, the set B would be Now every union of some of these sets in the original situation that - neither is empty - nor falls apart - nor contains permanent marks - nor contains bordering stones without an inner liberty is a claim that makes (some) sense. The empty claim won't lead to points, and the ones having borders without an inner liberty will fail trivially because setting up the permanent stones will already capture those border parts, allowing the refuting player to extend one of his permanent stones into the now cleared area immediately. Most claims with bordering stones having only a single inner liberty will also fail, but of course you know the exception: snapback. But don't the claims that fall apart make sense? No, because if you can prove them, you certainly can prove their parts separately. But if you can't prove them (due to ko threats), it's still possible that proving their parts separately will work. And what about the claims that include permanent marks? Permanent marks during the game only come when cycles go. Every permanent mark always has at least a second as a neighbor because of the nature of cycles. Since both permanently marked locations are empty, either bordering fails or a 2-eye formation is impossible. I'm sure you know exactly what you think you can claim at the end of your games. Only computer programs will have to go through above's trouble, so let's forget about the rest and just take a look at White's natural claim: 0 0 B 0 The defect in White's border now lets Black refute White's claim easily: Black captures 2 stones and extends his permanent stones into White's claim.
What did we learn? That control has to be independent from the outer context and the turn. Even in the toughest circumstances the claiming player has to be able to fill up his claim with a 2-eye formation. Neither Black nor White were able to do so above because their borders each had a (trivial) defect. Suppose Black had fixed his defect before game end: 1 0 W 2 Now Black could claim to be able to lock the right side without fearing a refutation because his worst case would now be 0 0 W 0 and you certainly agree with me that White can't prevent Black from building a 2-eye formation on Black's claimed set this time. (White can fix his defect equally simple, of course: just has to capture the single black stone before end.)
Let's look at another example: 0 0 B 2 Black now claims that his stones on the left side are not dead because he could atari 2 white stones as a ko threat. How about that? Indeed, this possibility refutes Whites claim of being able to lock the whole board exclusive the upper right corner. After we fill up the rest with permanent black stones to serve the rules, Black - having the first turn - will proceed as follows: 4 recaptured 5 threatens the 2 white stones and thereby White's whole claim, but if White answers it, Black will win the ko and live in the corner - refuting White's claim again. Does this mean that those black stones are not dead? No. Sly White can prove his control step by step. In the first step he excludes the 2 white stones and their liberties from his claim to get rid of the ko threat. Notice that this claim is still bordered by White and that Black can't win the ko any more: After 3, White recaptures in the ko and Black finds no ko threat. Does this mean that White can't count the 2 empty locations at the right? Again no. Sly White delivers his second punch and claims to be able to lock the "diagonal": 0 0 B 0 It's obvious that White will complete his 2-eye formation here, even taking second turn. So we find that each labeled locations below is in a set White can lock - the B's even in two. Therefore White controls each of these locations, and the black stones sitting in the A area are dead. White has shown by his 2-step proof that the ko threat and the ko are independent from each other, that they don't belong to the same local fight. (Ever searched for a definition? Now you've got one.) Just to serve perfection, Black could have lost by 1 point less if he had started the ko before letting the game end: 2 1 W 1 (4 recaptured at A, 5 passed) Now the ko has become direct, without Black having invested more stones than White. Since Black's pass with 5 is a (trivial) ko threat and White has no reasonable ko threats, White must give up 1 point by connecting the ko. (Even if passes didn't serve as trivial ko threats, that's, if the second pass in succession always ended the game, White would have to connect since direct kos spoil control.) This example showed that two lockable sets of the same player can indeed overlap. But I'm confident that this never will happen if they belong to opposite players. I don't have a proof, but consider this: If a location is controlled by both players, both at least have one lockable set that includes it. The first player can lock his set even under the worst circumstances: its outside filled with permanent opposing stones and him taking second turn. If now the second player makes his lock, the first player's set's outside as well as itself partially stays unchanged and partially becomes filled with his own permanent stones. On top of that, the first player gets the turn. Everything just turned in his favor. Why shouldn't he be able to lock his set again, including the location in question and spoiling the lock of the second player? Because of symmetry, the second player can spoil the first player's lock likewise: contradiction. (Again: this is NOT a proof!) But please note that LJRG doesn't depend in any way on the property that a single location at most can be controlled by one player (or that a stone can't both be alive and dead at the same time). If it happened it wouldn't prevent us from scoring since LJRG scores without removing dead stones! Either such a pathological location is empty and both players earn one point, or it's occupied and one player earns two points and the other just one. As simple as that.
What if we shift the white stone from A to B? 0 0 B 2 Things would change dramatically. With the same argument as above, White can't lock the whole board exclusive the upper right corner. But worse, now White neither could shake off the ko threat. If he reduces his claim by excluding B and all white and empty locations contacting it 0 0 B 0 White would have lost too many liberties to win the ko and prove his claim. Since White can't separate the ko from the threat with the divide-and-conquer strategy as above, they are not independent from each other. The only thing White can claim to be able to lock is the diagonal: 0 0 B 0 But this is a cold comfort for White because now he would have lost by 1 point. So in the shifted-stone case White should have connected the ko. (Eliminating the ko threat or capturing the black stone in the upper left corner would work as well.) Note that there's no need at all for Black to continue the ko in this case. He rather should leave White the chance to fail. If White can't claim the left side now, does this mean that Black can claim something there? No, Black still can't claim more than the upper right corner - try it out yourself. The whole left side (we labeled with A, to be precise) would be controlled by nobody, would be sort of seki.
BEFORE END
LJRG's definition of control has some consequences on what to do before the game ends because there's neither a discussion if the game should be continued nor a chance that it will: The result of the game is fixed in the very moment the game ends! (At least if LJRG's ideal form is used, that's, diputes aren't played out - but even then the consequences remain the same.) Any following method to count the game is only a method and is not part of the rules. We won't care how the game actually is counted at all. We'll be satisfied to know that its result is precisely defined - even in unlikely situations too complicated for humans. Let's follow an example game [P-JDRB]: resulting after move 17 in the already known situation 1 0 W 0 Even though the authors now tell you that only neutral points remain to be taken - this is a bit misleading. Location A may be neutral technically, but it matters who plays it. Not being able to surround something doesn't mean one can't manage to make points: Black can destroy a point by playing at A, White can save one. They then let the game continue beyond A, treating neutral fill up and defect elimination (connecting both hanes) as part of the game. But Japanese style of ending is that White would play 18 at A, and then both players would agree that the game has ended because nobody can gain anything more: 1 0 B 0 This would be the last diagram in the newspaper. What remains is counting. But if both players had passed in the situation above, according to LJRG nobody would control any location on the board because any set of locations a player claims he can lock must be independent from its outer context. We've gone through this in detail in the last chapter. So, the conclusion is that under LJRG self-interest will lead both players to continue with giving 2 0 B 0 and NOW both players may pass without being punished by LJRG: Black can lock the right side including the black stones, White can lock the left side including the white stones, and nobody controls the lower left corner location. (Proofs left to you.) Everybody gets what we expect him to get: B = 11 + 0 + 0 = 11 W = 6 + 0 + 2 = 8 ---- Black wins by 3 points Isn't that great? Both have to fix their defects BEFORE the game ends. Their opponent is relieved from having to force them to do so by filling up neutrals at the outside. This isn't a big deal when considering the number of stones you have to handle because with the common counting method neutral locations are filled anyway. But in official games filling up before the game ends is a nuisance because those stones would belong to the official game record. LJRG induces exactly the right number of moves to be done and recorded - (extra) trailing moves explicitly proving awareness of defects. Detecting defects may be trivial in most cases and one assumes the opponent knowing about them - but you never can be sure. So, if no punishment existed, it would end up in filling all neutrals, no matter what, just not to give one's opponent a clue in those rare cases he might not be aware of his defect. Shifting defect elimination into the game is "only" a side effect. The real purpose of defining control as LJRG does is to be sensible about internal ko threats without giving up localization and to fairly deal with situations like "one slips" (beast 4), where one player can't be prevented from capturing either of two groups, but isn't able to capture both. Following, two famous teire incidents:
Iwamoto's refusal At the end of the first game of a 10-game match between Go Seigen (born in China as Wu Ch'ing-Yuan) and Iwamoto Kaoru in June 1948, Iwamoto (Black) refused to eliminate the ko by capturing at A (or filling above 1), arguing that he leads in ko threats. last two moves shown A Nihon Ki-in bylaw from Shusai's time was dug out and Iwamoto got his way. White still won by 1 point - but pros were alarmed. This triggered the first rules written down by the Nihon Ki-in and published on October 2, 1949. It required all direct kos to be eliminated before the end - contrary to above's decision. So far Ing Chang-Ki's story in [GW72]. You get the impression that Go Seigen wanted to convert his 1-point win into a 2-point win by having Iwamoto add a stone. But according to [GW45a], Go Seigen actually agreed with Iwamoto and argued that "White cannot possible win this ko and has nowhere left to play". Note that Black has two ko threats in the lower left corner and one ko threat on the right side (connecting his two single stones), but White only has one ko threat on the upper side. According to [GW45a] the "game was declared a 1- or 2-point White win". Well, that certainly should trigger some work on the rules. Go's "nowhere left to play" is interesting. It seems to reveal Go Seigen's view that for him only neutrals can serve as last resort for (trivial) ko threats - that for him a pass play never makes up a (trivial) ko threat because the opponent may pass too, ending the game. With their 1949 rules the Nihon Ki-in didn't follow him in this. But instead of allowing passes as (trivial) ko threats, which would naturally lead to the solution, they added their direct-ko-removal obligation. Let's now see how JRG89 or LJRG would handle the case. Under JRG89 Black would eliminate the ko before the game ends (possibly AFTER two successive passes) because otherwise the single black stone at 1 would be called dead. This would make the location above 1 a dame and infect all of Black's stones and "territory" on the right and upper side with seki. Under LJRG Black would also add a stone before end (and BEFORE the ending passes), but his punishment if not wouldn't be that big - he would lose control of only four locations: A, 1, the one between them, and the one above 1. This would cost Black three points compared with capturing at A (the one above 1 no more counting one point, and the one to his left no more counting two points). The reason for losing control is that Black can't use his stone at 1 as a border of a lockable set - White would capture it and couldn't be prevented from extending his permanent stones into Black's claim.
Go Seigen's refusal This example is from [GW72] and [GW45a]. According to [GW45a] you find the game's record in Go World 41. It's also in [GMR1069]. At the end of the second game in a 3-game match between Go Seigen and Takagawa Shukaku in 1959, Takagawa insisted that Go Seigen (White) must connect at A to eliminate the possibility of a ko. Go Seigen refused. The dispute was undecided for some MONTHS. Finally Go Seigen - lacking support - connected and lost by half a point. 19[+4.5] 12 (244 moves) First a detail. [GMR1069] wrote "Komi: None", but this can't be true. I counted the game and came to 123 (=9+65+37+12) points for Black and 119 (=32+47+21+19) points for White. I double checked it with area-style counting: 181 for Black, 177 for White, 3 neutrals. This fits to the figures above (244 moves or 122 stones each, 16 dead black, and 17 dead white stones): Neutral 3 = 3 Black (122 - 19 - 16) + (123 - 12 - 17) = 181 White (122 - 12 - 17) + (119 - 19 - 16) = 177 ------ 361 Black leads by 4 points on the board. If Black won by 0.5 points after White added a stone, the komi must have been 4.5 points. Now to the ko. The aji in the center is as follows: If Black could win this ko, he would capture White's center group. White holds back the A-for-B exchange as a ko threat. Go Seigen's reading, Takagawa agreed to, was as follows: 9, 12, 15, and 18 took the ko - 14 passed 8 is better than passing because it removes a "threat". Remember that, as explained in Iwamoto's refusal, for Go Seigen two passes in a row end the game. Therefore neutrals are valuable ko "threats". White started the ko and continued it as long as he found internal ko threats (10 and 16), but after 19 he had none and had to remove the ko with 20. This reduced his territory by 1 point, but Go Seigen argued that he would get 19 as compensation because he wouldn't need to connect this second ko: 24 recaptured ko After 24 Black has no ko threat - not even of the smallest kind: neutrals. Therefore Black would pass, letting White pass too and end the game without connecting the second ko. Go Seigen [GW45a]: I think it best not to create intricate provisions to the game of go. If all the liberties of a group are filled the group is taken off the board, a ko may not be retaken until a move is first played elsewhere, the side with the most territory wins; fundamental principles such as these are sufficient regulation. One desires simplicity in the rules. This will also aid in increasing the go population. Intricate rules are only manifestations of elaborate technique. The Chinese rules play everything out to its conclusion; there is no perception of irrationality. The Japanese rules produce situations such as a seki on the same board as a 'bent four in the corner' ... or the provision that White must add a stone to his center area in [the current game]. These problems do not stand to reason. If a one-move ko is thought to demand a preventative move, then the shape must be incomplete [in the sense that the game has not yet ended]. Completing the shape, in case of a yose ko also, is the necessity here. Stones are alive not only because the can not be captured ... I hope that irrationality in the rules is corrected as soon as possible. This sounds well, but is a bit cloudy. I'm curious how Go Seigen would argue that his stone to the right of 19 is alive. If, for instance, he would define stones that can't be captured if they possessed the first turn to be alive, then 19 would be alive too, spoiling his territory. But maybe he would argue that the history still is alive and that trailing passes are to be ignored in the post-end analysis, which would prohibit capturing 24 immediately and give 19 no chance to avoid capture. Another advantage of such a view would be that a single double-ko seki couldn't be used to cycle. The drawback, of course, is that the outcome of a game, even under Japanese-style rules, could depend on the number of neutrals - something LJRG manages to avoid. Under either JRG89 or LJRG White can avoid the connection at A, because if Black starts above's sequence after the end, White captures in the ko first and will win it. Under JRG89 this is because Black would have to pass for that ko. Under LJRG because Black doesn't find enough internal ko threats in White's claim: 9 and 12 took the ko, 14 connected it Does this now mean that under JRG89 or LJRG White omits the stone at A and wins? Only if Black lets the game end too early. But if he continues (Go Seigen's sequence) to a certain point - under JRG89 till 6, under LJRG till 12 - White will again have to add a stone and lose by half a point. In both cases Black managed to force White to take the ko before end, allowing Black to take the ko back after the end. Under JRG89 Black doesn't has to fear internal ko threats because only a pass can open the ko again. Under LJRG Black has to take care that White used up all his internal ko threats before the end - that's why it takes a bit longer. White's threat with 16 is no internal ko threat under LJRG because it will be covered under the permanent stones. So if White switches the order of his threats and plays 16 before 10, Black has to continue until White finally has used up 10. So if the game proceeds until this certain point and White lets the game end without connecting the ko, White will lose by much more than half a point. Under JRG89 White's stone that took the ko would be dead and the empty location above it would be dame, infecting White's whole claim shown above with seki. Under LJRG the argument isn't that weird. White simply won't be able to lock above's claim because Black will refute it: Black, playing first in the proof, takes the ko and, since White finds no internal threat, gives atari and captures.
What do you think about Black playing at A? 0 0 B 0 (It threatens to throw-in at C and to capture four stones, of course.) According to Iwamoto Kaoru [GR-Sp74], Black's A lacks "kihin", which "means etiquette shown in a good game fought by the rules of knighthood". "In days gone by [...], if a player lacked this quality of 'kihin', he would never have been allowed the degree of shodan." (I suppose "kihin" to be the same as "ki-in" and "kiin".) Likewise, White starting with B lacks kihin. There's no doubt of missing kihin if A is accompanied by a statement like "there seems to be no other place for a move". But why is A by itself nasty? Well, having the turn has no meaning at this point, and present custom would indeed be to leave it as it is, but under LJRG Black at A incidentally still belongs to the game because it secures control, as does B. So under LJRG, Black's A as well as White's B have good reasons beyond tactical tricks - neither is nasty. Maybe one could call answering A with C nasty: to keep sente is pointless in this situation and, under LJRG, White still needs to reinforce at B. To catch the spirit, let's transform Iwamoto's example (I shrunk, by the way) to fit LJRG: 0 0 B 0 A move at A still threatens the same, but now it's not even under LJRG necessary any more. If you can expect your opponent to answer correctly, then to play it only prolongs the game and is pointless. We shouldn't condemn Black if he dares to play A, especially among double-digit kyus, but among, say, amateur dans I would agree that Black lacks kihin if he can't resist A. On the other side, we as well as the referee must accept if Black ignores kihin and nevertheless plays A - he's perfectly obeying the rules. Rules are one thing, social conduct is a different. Referees have to judge rule obedience, not social behavior (provided it violates no rules). So, if Black plays A, he may do so, but he shouldn't be surprised to end up in the (social) pillory afterwards. Likewise we must accept if our opponent starts filling neutrals before the end. Viewed strictly, unfortunately, he can even give a sound reason to stick to this practice: He keeps the option to exploit defects BEFORE game end, capturing an entire group instead to just let its "territory" be spoiled. Does this now mean that we end up filling neutrals, contrary to what LJRG was praised for? Well, since in most cases the capture will only be partial, spoiled territory will be the better option. Therefore, whoever refrains from neutral fill-up on principle will only pay a tiny price for keeping his membership in the "I'm so clever to recognize the end" club. The focus here was on not to drag on a game when there is not even a technical reason to do so. If we wanted to force this by rules, we would have to refer to perfect play. In fact, LJRG already does refer to perfect play in its definition of control. But to now also define to stop as soon as possible would go a bit too far in my eyes. I'm satisfied that LJRG excludes any technical reason to fill dame. Let social pressure take care of the rest, but don't let it get too strong: If everything would be forced by rules (of whatever nature), it would become impossible to demonstrated kihin - you only can show kihin VOLUNTARILY. For instance, when your opponent captures a ko immediately, it would show kihin to let him redo his move - but of course he has no right to expect you to do so.
Here's an example of a professional missing his chance to show kihin (compiled from [DGZ0102] and [RGG220202a]): The 5th game of the 26th Kisei, played on February 20 and 21, 2002, between O Rissei [9d, born in Taiwan as Wang Licheng], and Ryu Shikun (7d, Black) was almost finished. Doing move 293, Ryu asked, "It's over, isn't it?", but got no reply from O. They continued filling neutrals. As O filled a neutral with 298, 6 stones of Ryu went into atari. Only after Ryu filled an unrelated neutral, he noticed this and tried to redo his move, but O declared, "I didn't say anything", meaning that he had not yet agreed that the game was over. Ryu didn't understand. O repeated his statement and asked the game recorder to confirm, but the recorder wasn't able to. O called the referee, Ishida Yoshio, and explained the situation. Either before or after Ishida's arrival, O complained that Ryu already had redone a move ("matta" - 285 according to Michael Redmond) without a protest by him, but that he wouldn't permit this for a second time. Ishida Yoshio and representatives of the Nihon Ki-in and the sponsoring newsletter Yomiuri Shinbun discussed the issue and looked at the video tape for about an hour. Since there was no evidence on the tape of both players agreeing to an end [a stop, technically] - in fact, not even one of Ryu offering end - O was allowed to continue. O clearly felt bad about the situation, not just Ryu, and there should be sympathy for O - said Richard Hunter. After O asked Ishida, reassuring that it was his turn, he captured the stones. Ishida didn't refer to the alleged matta when he resumed the game. After O's capture Ryu drew some deep breaths and stopped the game for the second time by asking Ishida about it. Ishida admitted that Ryu's move in question (285) was close to matta, but finally concluded that no matta had occurred - said Hisashi Fukui. The camera angle didn't reveal if Ryu released 285 twice or not. O insisted that, nevertheless, 299 had been released (on the wrong spot). So finally Ryu gave up. Two weeks later O Rissei also won the 6th game and the 26th Kisei [DGZ0202a]. Sorry, Richard, if I hesitate to congratulate. Let's take a closer look at the situation after 283: 13 21 W 0 (1-3 = 281-283) The only things left are the 2 kos (at both sides beneath center). Since it's White's turn and he can capture in both, White will win one for sure - and that he can't win both should be understood. The normal sequence would therefore be that White takes one, Black connects the other, White connects the first, and both then agree to game end (capturing 283 and fellow is useless since White had to invest 2 stones), giving Black a win by 9 - 5.5 = 3.5 points and a 3-2 lead in this best-of-7 match. But White's 284 filled the false eye beneath center instead: 20 24 B 0 (4-20 = 284-300) (According to Richard Hunter, 297 and 299 were played in reverse order - playing the more "important" dame first.) 285 is the alleged matta. Strange - was this Ryu's second thought? Why not answer 284 at 286? 285 lets White gain a point in sente with 286 and, after coming back with 288, still having the chance to win the remaining ko - even if this now depends on ko threats. But anyway, White didn't try to win this ko. Strange again - what then was his purpose to continue? If 285 really was matta, a redone move, then Ryu already must have believed that the game was over after 283 (or 281). How can this be? Did Ryu already offer end before 293? Or was he using the silent gentleman agreement that a game is over when having the turn got meaningless? If White had more ko threats, the game would indeed be over in this sense after 283 (or 281) because White wins one ko no matter who starts - but it seems to me that Black leads in ko threats. Black may not care if he wins by 4.5 or 3.5, but in above's sense the game wouldn't yet be over. Anyway, after Black connected the second ko with 293, it's kyu-obvious that turn possession became meaningless. O Rissei may have troubles with his ears (since 1998 they say), but he isn't blind. One therefore can understand that Ryu, after expressing the obvious (again?), on which O didn't oppose (to put it in Ryu's favor), was convinced that (sloppy) preparations for counting were on their way. Isn't this the beauty of omission, Japan is so proud of? I would be very curious if O always fills dame before he agrees to stop, or if he only did so in this game. In the latter case I'm afraid that O, being aware of Ryu's false belief since 285, exploited the situation - sorry to say. Another thing that annoys me is that O was tolerant as long it didn't matter - provided talking during the game or undoing moves doesn't lose - but went strict as soon it did matter. Rules shouldn't depend on kihin, but if it's custom to ignore their technical details - in this case not to express one's opinion that the game is over by PASSING, as JRG89's Article 9 calls for - then nobody should suddenly insist on technical details either. That Ryu asked about the end instead to pass indicates that this is common (bad) practice among pros. Why else would Ryu have done so in an important title match? Further questions: Is it also common practice to say nothing if you disagree? Did Ishida consider local custom in his decision? Don't get me wrong - I prefer a more formal conduct during "game". Generally it should be possible to play the game without having to utter a single word. You may not like pushing marks around, fine - even though nothing could be more transparent for spectators - but actions should be formalized in some way or the other. If players operate the clock themselves, switching it without playing a stone would be a clear way to pass. But since pros in Japan don't operate the clock themselves, how about letting them grab a stone even in case they're about to pass, aim at the recorder, time keeper, referee, or whatever official is hanging around and seems to be a good target - and "deliver" him the stone (and maybe kensho). Ok, let's get serious again. The problem that caused this embarrassing incident isn't one of when or when not to fill dame. I would neither want rules that prohibit me to fill them nor rules that force me. The problem to solve is how to clearly end the game and, additionally, how to make this state of the game transparent. Maybe this example would fit better into the chapter about ending. The "ko mark" introduced there (no joke at all), combining the temporary mark with the pass count, would solve these problems instantly. On the other hand, the topic we're talking about is exactly what O had the chance to demonstrate, but missed: kihin.
Japanese style is to pass as soon as it becomes meaningless who possesses the turn. This sometimes even leads to incomplete borders: 0 0 W 1 Black just has passed because he can't reduce White's territory any more. Japanese style would now be for White to pass too since he neither can increase his territory. You don't believe it? See the 4th game of 1973's Honinbo (final) for this example [GR-Au73] (I made up the seki at the left just to shrink it). Under LJRG White needs to play A to count 6 points. More (shrunken) examples: Inspired by the 5th game of 1975's Meijin [GR-Wi75]: 0 0 W 0 White would pass under Japanese style because Black can't make any use of sente. But under LJRG, White would have to add 2 stones at A before game end. The first stone will close White's border. The second will make his claim independent from the context. The 7th game of 1975's Honinbo [GR-Au75] molded this one: 0 0 B 0 Black would pass under Japanese style. Under LJRG he should connect at A to close his border and gain control before game end. (White will play B, of course.) Playing above A wouldn't establish control. This type happened in the 7th game of 1975's Meijin [GR-Sp76]: 0 0 W 1 Under LJRG White should continue at A instead to pass (because he has to imagine permanent black stones crowding the outside). Game four of 1987's Meijin ended with this sort of gap in the center [DGZ0687b]: 0 0 B 0 Under LJRG Black should play A instead of omitting it. (He gains nothing by playing to the right of A, of course, because of the double-atari threat that pops up when dame is filled.) This kind of gap was left in the second game of the first Bohae-Cup ("World Women's Go Championship") [DGZ0395]: 0 0 B 0 Under LJRG Black has to capture the two white stones before the end if he wants to count anything - not matter if White approaches or not. The first game of the 50th Honinbo featured this one [DGZ0595]: 0 0 B 0 The only move missing is A. Black is justified and urged by LJRG to play it before game end. (Playing left of A, of course, gains nothing because of the seki threat produced by dame fill-up.) So, since LJRG provides no "confirmation" phase in which missing stones could be added, the habit of uncomplete borders would have to be dropped (and no one should miss them anyway): If you want to count points after game end, close your border BEFORE game end!
We've seen that you'd better eliminate defects before game end if those defects spoil your control, for instance, 0 0 W 1 White shouldn't pass here. He wouldn't be able to claim any control. He should connect at A instead to anticipate the worst case: the rest filled with permanent black stones. But, as it turns out, not all "defects" affect your countable control. In all of the following situations Black could indeed pass without loosing any point: 0 0 B 0 White controls the 10 locations on the upper side. Nobody controls the rest - even if Black connected the bamboo. 0 0 B 0 Black may leave his single stone unconnected. He controls the 9 locations in the lower left corner. The location occupied by the the single black stone and its 2 liberties are controlled by nobody. The rest is controlled by White. 0 0 B 0 White shouldn't pass because he controls nothing in the strict sense. He has to capture at least one black stone to gain control (of what should be obvious. Black will then, of course, save the other). Black may leave it miai ("one way or the other"). He already controls the 4 center locations, the 2 locations below them, and the 4 locations in the lower left corner. 0 0 B 0 Black may omit to fill his false eye. Black controls the 4 empty locations he has surrounded plus the locations of his surrounding group. White controls nothing in the strict sense because no matter how small he makes his claim always a white border stone is ataried, enabling Black the refutation. White should fill his false eye at A. Viewed superficially this last example may seem illogical: one side has to connect its false eye - the other not. The difference, of course, is that White's territory isn't yet independent from what's going on beyond its fence - Black's is. Eliminating Black's harmless defects in any of the above cases wouldn't increase Black's countable control nor would it reduce White's. Not claiming something or - to be precise - not being able to lock something doesn't mean that your opponent can lock it. And even if - he may not be able to turn it into points. Players will only care to eliminate defects that harm their territory, which is always the case if that territory depends on outside liberties.
Test yourself. Expect LJRG in effect in all examples. Black just has passed. You're White. What would you do in the following - not totally symmetric! - situation: 0 0 W 1 You connected on san-san (3-3) in the upper right corner? Right - after 2 passes the result is a jigo. You passed? I'm sorry having confused you - you lost by 2 points. You should have connected as mentioned because otherwise White doesn't control anything on the diagonal. No matter how small you make your claim there, always one of your border stones will be ataried by the permanent black stones crowding the rest of the board. You think neither does Black control anything on the diagonal? Wrong. Black's 6 stones including their 2 eyes in the lower left corner are independent from the context. Therefore Black controls them. Only the rest of the diagonal isn't controlled by Black. He could, of course, extend his control by filling some false eyes, but this wouldn't entitle him to count more points. After this made-up example a realistic one [RGG190202]. Black just has played 1. Figure out where both sides should add further stones before they pass: [8 0] W 0 (I assume that White was leading with 8 prisoners because there are 145 white but only 138 black stones on the board. I don't know what komi was used. Let's pretend that it was a no-komi game.) Only another four stones are needed to complete the game under LJRG: [8 5] W 2 (6 and 7 passed) That's it: 2 and 3 each reinforce a border, 4 may look silly but is technically necessary because it makes the 9-point eye as well as the 2-point eye independent from the context, and 5 prevents seki if White enters here after dame are filled. Each side counts 41 points: jigo. Needless to say that neither Black's false eye on the lower edge nor on the upper right edge is controlled or counted. But actually the (IGS) game dragged on much longer. After 1 White noticed that Black had to reinforce at 5 to prevent seki. Not to hint Black (otherwise he could have played 5 himself to make it obvious), White played neutrals here and there. As soon as he could afford it, Black kept on passing. Eventually Black asked White very polite to (quote) "please pass as it is game over". White answered, "I think you need to play one more move", and continued. Only after the last dame was played, Black made the necessary defensive move, leaving White with the impression that Black hadn't noticed his problem till the discussion about the end had alerted him. Under LJRG White would simply pass when Black passes with 5. If Black then claims anything in his upper right group, White could disagree and the dispute would either be decided by a referee or played out (see chapter "After End" below). In either case, and in a perfect world, it would be White who wins. Here's another test (not easy). You're Black. Would a pass lead to your 1-point win? 2 0 B 0 No. You should add a stone inside your territory and be satisfied with jigo. If you pass instead, White will pass too, the game will end, and White will refute your claim: (2 at 8 won't do better because of again 3, and 2 at 5 will also fail: 3, right of 6, 8, 7, 4.) This actually is a slightly adjusted tsume-go problem from [DGZ0198b]. Under JRG89 Black risks nothing by passing. He waits if White sees the aji (weakness) and only adds a stone in that case. Under LJRG he could try the same, but risks losing the game. Some people think that area scoring relieves Black from deciding if aji exists or not. Black could simply add a stone without losing a point, they argue. But this is only true if nothing else but an even number of neutrals remain - not the typical case. If not, White will at least get the last neutral. You're certainly suspicious by now. You're Black. Would you pass? 0 0 B 0 Well, since you need the outside liberty to live unconditionally you shouldn't pass under LJRG. Black hasn't yet secured his control. Kudo Norio [GW45b]: By the Japanese custom the game has already ended before the liberty [...] is filled. [...] If the shape [above] appeared, the stronger player would instruct his opponent to add a move, in the spirit of counselling a family member. But it would be funny for this kind of advice to be given among professionals. Well, for me this kind of advice is funny in ALL cases, and under LJRG you'll never need to give it. Instead, Black won't be able to count 8 points if he omits to add a stone BEFORE the end. His lock will be refuted either by seki or ko:
So, with LJRG we get the almost ultimate solution: 1. Defects affecting countable control will be fixed during game 2. There is no need to fill up neutrals before the game ends This is fully in the spirit of Japanese-style rules.
ENDING
Why on earth don't we simply end when two passes in a row occurred? Well, look at following situation: 0 0 B 0 If Black connects, White will do so too and nobody has won: nothing can be claimed on the board and nothing has been captured. Now, what if Black captures instead? White can't recapture due to the ko rule, and filling one of his two liberties would atari himself - so he must pass. Black would now love to pass too and end the game: 0 1 W x This would be a win for Black if x is 2: nothing can be claimed on the board, but now Black leads in the captive count: not very fair. That's the reason for having this seemingly odd pass count of -1 after a ko capture. The effect is that 3 passes in a row are needed after a ko capture instead of just 2 - leaving the chance for ko recapture. Under LJRG the game would continue after Black's pass: White would recapture, Black would be forced to connect his stones, and White would also connect (since giving atari would lead to disaster). Then both would pass and the game would end in jigo: 1 1 B 2
Another example: 0 0 B 2 The game has ended. White claims that he can lock to lower side. The proof would go like this: 2 passed After 3, White can recapture the ko and Black would have nothing better than to pass. White will capture again and proceed building his 2-eye formation. But the whole proof depends on the fact that after White's pass a pass of Black won't end the game since the 2 passes are preceded by a ko capture. White's pass wasn't intended to end progress but to remove the temporary mark preventing ko recapture. So, it's not a pass in the sense of doing nothing. But to avoid confusion, we'll nevertheless continue to call it a "pass" and count it. So again, the pass count must be -1 after the ko capture. LJRG keeps things before and after the end equal. There are no special rules that only apply after end.
An even smaller example [RGG281102]: 0 0 W 0 Originally designed for area scoring, it also works for territory scoring (here a la LJRG). The game result depends on how game end is defined: area scoring territory scoring -------------------------------------- two passes end | Black wins by 4 jigo three passes end | Black wins by 10 Black wins by 7 The results in the first row seem unfair. The problem is that the plain sequence only makes sense for Black if he now can use a pass as a (trivial) ko threat. (Note that 5 makes no sense under territory scoring combined with "three passes end".) But if two passes end, this isn't possible. He better had answered 1 at 4. After White answers at 2, we end in seki. Answering 4, White can again choose 3. Black will now have to pass to keep 2 as ko threat in reserve - a silly consequence of "two passes end". This enables White to end the game with a pass: 0 0 B 2 Area scoring counts the same as in case of "normal seki": 6 - 2. But why is it jigo under territory scoring? Doesn't Black control the whole board? Well, not if two passes also end the proof of control. In this case the trick for White is to start the proof with a pass! As above it's fruitless for Black to connect in the center, since after White takes the ko and Black passes, White ends the proof with a pass - without Black having formed his two eyes yet. By now you should agree that "two passes end" (game or proof) just is too simple. "Three passes end" is simpler than "two passes end, provided the first removed no temporary marks", but the latter is more accurate and fits perfectly to a "ko mark" (to come).
One argument against the need of 3 passes after a ko capture to end the game is that a single double-ko seki could prevent the game to end. I myself was blocked for a long time by this argument, but I changed my mind. Even if I hadn't invented cycle removal I would now stick to this scheme: it's absolutely logical. You don't need to play a stone to give your opponent a chance to fix a ko. He gets it as well if you do "nothing". So, after his answer and regardless if it was a pass or not, you are in a NEW situation and should be allowed to recapture. A pass is a move - just like zero is an integer. Should I give up this logical scheme just to bar a few cycles from the theater while a big, noisy crowd of them already took seat and is waiting to disturb play? Add just one double-ko seki to the first - all efforts to stop cycling by "two paasses end" were in vain. Needless to say that double-ko sekis are no practical problem If you know about a game where one occurred, please inform me. We shouldn't take special measures to cope with them and, as a side effect, corrupt something else. Instead we should let them be what the are - potential cycles - and handle them like the rest of the gang.
As already mentioned, the pass count of -1 has another advantage in case we don't keep temporary marks in our minds: you can use a single mark either to mark a ko or the current pass count. (How about the cuplike base of an acorn? ;-) If it's on the board (marking a ko), the pass count is -1. If it's off the board, the pass count must be either 0, 1, or 2. This suggests 3 fields labeled 0, 1, and 2 beside the board. Since the whole board would stand for -1, field 0 would be positioned nearest to the board and field 2 farthest away from it: If you now capture a ko, you would mark it. And after a pass you would push the mark farther away from the board - getting nearer to the end in a sense. In all other cases you would put the mark back to field 0. Another mark on either field B or W would indicate whose turn it is. Of course, if a clock is used, it would replace this mark and cover those fields. The minimal requirement for the clock is to always give a clear visible sign to everyone about who has the turn - some tiny dots pulsing on a digital display won't do, and neither should it be necessary to take a certain angle to observe this sign. The empty fields at the upper and lower side would be used to line up captured stones - letting everyone see their number easily. Ok, I admit this all being a bit eccentric - but isn't it also pretty neat and logical? The idea should be clear: let everybody, especially both players, visibly perceive the whole situation without having them to refer back to the game's history (which, remember, isn't part of the "situation"). Some cases where a professional captured in a ko prematurely already were mentioned. There are even cases, where the pro didn't seem to know who had the turn: - Rin Kaiho lost the 3rd game of the 1987 Meijin (final) because he made two moves in a row (first time ever in a title match). There was a (evening) dinner break, and Rin sealed move 188 while in byoyomi. It was a forcing move, leaving only one response to Kato Masao. The game seemed to be won by Rin. After dinner referee Iwata restarted the game (by placing 188 and restarting the clock, I guess). One minute later Rin played move 189, skipping Kato's obvious response. [DGZ0687a] [RGG150293] [W-GB] - Cho Chikun lost the 2nd game of the 50th Oza (final) by time (first loss by time in a title match ever) because he kept waiting while, as he believed, the byoyomi ("second reading") was counted for his opponent, O Meien. But in fact it was being counted for him. The game was his, and he already had decided on move 145, but he missed O's 144 while staring into his lap. When the time keeper said "ten" as the last second of the last ten seconds elapsed, referee Sakaguchi Ryuzo declared with Japanese "determination": "Black has run out of time, and so we have to assume White wins". [DGZ0602b] [W-Cho] I don't know how clocks and byoyomi are handled in Japan exactly, only that pros there don't operate the clock themselfes. However, according to LJRG there has to exist a visible sign that tells (at least) both players whose turn it is. If a (reasonable) clock is used, it naturally gives this sign. If one player is in byoyomi, the clock still will be in use to time his opponent. But even if both players are in byoyomi and are timed by two time keepers, each using his private watch, for instance - the clock has to be operated to preserve this sign! I guess you won't object against wanting a computer screen to show all the information making up a situation as defined by LJRG (and additionally easing the task by marking the last stone), but you might absolutely refuse to use marks in the real world. The only compromise I'll offer is this: The only aspect of the situation as defined by LJRG that may miss is the information given by the ko mark. All other aspects have to be visibly obvious, that's, how locations are colored, which are marked permanently, which are marked temporarily (in the initial situation), how many prisoners each side has made, and whose turn it is. Otherwise the game isn't played according to LJRG. If the game is played with a ko mark, it has to be used throughout. If the game is played without one and it's your turn in a situation other than the initial one, you may once ask your opponent (or a designated person) which move was made last - with the right to get an answer. He has to list all locations that changed their color due to this move (for instance, by pointing to them one after the other, or pointing beside the board for a pass). However, empty (uncolored) locations that contact an already listed empty location may be skipped (since they necessarily also changed their color). Your right to ask does not depend on having been absent. Regardless of using a ko mark or not, you may only leave the board if it's not your turn, but if your opponent is absent and no answering person is designated, you additionally have to leave behind the answer about your last move (for instance, by writing down the algebraic coordinates of the locations in question). With a ko mark in use, you have to remember absolutely nothing (missing a cycle removal isn't illegal). Without one, you have to remember at most the last two moves when you return to the board. Given the third, you're able to complete the situation in your mind. (In the worst case, he has passed just after you did. To know if the game is over and if you may stop the clock, you have to be certain that his move before was no ko capture.) Remember Cho asking the scorekeeper (in game 3 of the 1980 Meijin final) if he may take the ko? Under LJRG either there's a ko mark around or Cho would be allowed to ask the sorekeeper what exactly the last move was - both serving his needs. And if the answer given is wrong? To me it seems fairer to undo the illegal move instead of nullifying the game. The number of prisoners has to be visible, no matter if they are placed directly on the table or, as usual, stored in the flipped lids of the stone supplies. There's a funny photo in [DGZ0598], showing one guy standing up, bending forward, and almost tipping his nose on his opponent's forehead to check their number, hidden by a 2-inch board. Apparently his opponent is in overtime and has dumped the lid's contents in front of himself to shut the supply. (Under the popular "Canadian" overtime, see [W-BGA2], a counted number of stones has to be played in a certain period of time. Not to accidentally increase or intentionally decrease their number, one shuts the supply.) He should have shut it with the lid still holding the prisoners or at least dumped them beside the board (into his "prisoner zone" ;-). And what if, more likely, rather the number of stones remaining to be played in the period were to be checked? Neither overtime nor overtime stones are covered by LJRG, but their number should be visible too by analogy. One should keep them somewhere beside the board if it's too thick. At last it should be mentioned that if physical devices like board, stones, marks, etc. are used, they ought to be uses in the rules' sense. For instance, if you push the ko mark over to "2", the game isn't yet at an end - you also need to switch the turn (via mark or clock). If you instead leave your clock running, you risk losing by time since it's, technically, still your turn. If disputes aren't played out, the game would now be over, but since the clock knows nothing about that, your opponent should now stop both clocks. This may seem strange, but it enables the simple rule that whose clock runs out of time, loses by time. Otherwise it could happen that we had to decide which was faster, the ko mark reaching "2" or the clock running out of time - not very practical. Or, if you forget to put the ko mark back onto "0" after making your ko threat and then switch the turn, you committed an illegal modification of the situation just as if you had removed one of your stones to create a second eye. If we look at it strictly, you would have lost in both cases, even it the latter obviously is more intentionally than the former. Practical rules, LJRG isn't concerned with, could try to soften this by letting your opponent undo your illegal modification and continue the game as if you'd passed.
AFTER END
To prove control mathematically, we would have to go through all possible move sequences that don't go beyond a final or repeated situation and allow the claimant to cut off all but one branch in each node he has the turn. If this tree then always ends in leafs with the claimed set filled by a 2-eye formation of the claimant, the claim would have been verified. This certainly is of no practical use because it would take almost forever. So, the two players would have to agree that a claim holds instead. But what if a player doesn't agree? Maybe you think this isn't a problem because we practice this agreement every time we play go - without thinking much about it. But everyone designing rules has to consider the worst case. The simplest dispute breaker would be to designate one or more wise referees who would have to rule those disputes - thereby bound to keep as close as they can to the ideal solution explained above. Another possibility would be to set up a test for each dispute. If, for instance, Black didn't agree in White having control over a location, White would have to identify a set he thinks he could lock which includes the location in question and set up his worst case for that set on a second board. Black would then start and the test would continue until either White reaches his goal, the pass count reaches 2, or the situation becomes repeated. Black only refutes White - not in a mathematical sense, of course - if the test ends without White having reached his goal. White's goal is having build a 2-eye formation on his set. This can easily be checked. To shorten the test, we would also let Black succeed as soon as he extends his permanent stones into White's claim or covers any part of it with a black 2-eye formation. Not to give one player an edge, both would have to fix their claims (write it down, for instance) of what they believe to control before they exchange this information. To shorten this list (or the number of clicks), one (empty) location for every "hole" one believes to control is enough. Each such location is understood to identify the claiming player's smallest bordered set that includes this location. Each player then may mark - privately again - one location claimed by his opponent in case he disagrees. If both agree, there's no dispute (even if claims overlap) and normal count based on both claims decides the score. But if not, each dispute is played out as explained above and the player winning more disputes also wins the game (if both win one, it's a tie). In case there are 2 disputes and one player asks for, both disputes should be played interlocked. Black starts in the first dispute (the one he's the refuter in) after which both players, now starting with White, alternately play in both disputes, each playing first in that dispute his opponent has played in last: B1, W1,W2, B2,B1, W1,W2, B2,B1, ... This was my first version. Here's a maybe more practical second one: After "game end" the players alternately either point to an empty location or pass, starting with the player who didn't pass last. To disagree, a player points to the same location his opponent just has pointed to. In this case a dispute is played out and decides the winner (of the dispute AND the game). In case of two passes in a row there is no disagreement (even if claims overlap) and normal counting based on both claims decides the score and the outcome. Since at most one dispute is played out and passes don't give up the right to claim later, the sequence and timing of claims now may play a role - a (small) drawback of this unsymmetric scheme. If there are lots of small territories, both schemes can take quite a number of pointing. To reduce this, one could let the players identify dead stones and neutrals instead. Both schemes could be modified in this way. Let's modify the second: After "game end" players alternately either point to an empty location, point to one occupied by an opposing stone, or pass - starting with the player who didn't pass last. Pointing to an empty location claims that it is neutral. Pointing to an opposing stone claims that it and all opposing stones sitting in the claimant's smallest bordered set that includes the claimed stone are dead. To disagree, a player points to the same location his opponent just has pointed to. In this case a dispute is played out and decides the winner (of the dispute AND the game). In case the location is empty, the disagreeing player has to prove that he controls it. In case it is occupied, the claimant (opponent of the disagreeing player) has to prove that he controls it. The "proof" is done as usual. In case of two passes in a row there is no disagreement and normal counting decides the score and the outcome. This is done by treating all locations that, suppose all claimed dead stones had disappeared, are empty, neither are nor contact claimed neutral locations, and contact only stones belonging to one player as being controlled by this player. The third scheme seems to be very practical (even if the control claiming schemes mathematically appeal me more). It inherits the unsymmetry from the second (no one wanting to point to dubious locations first), but no overlapping can happen any more. Instead, a new oddity pops up: it's possible to neutralize one's own territory. The opponent can't disagree (because he can't prove control), but he won't bother to do anyway. Claimed dead stones in a neutralized territory don't count because, as defined above, their locations are not controlled. Note that only neutrals in a seki's eye actually have to be claimed. So if there are no sekis with unbalanced eyes and no dead stones around, and no defect elimination is missing, the claiming phase can end immediately with two passes. Nice. The third scheme is slightly gentler than the first two. If you missed a defect eliminiation and your opponent claims neutrals where you believed territory, you can reconsider and avoid losing by a failed proof. Of course, this will only help you if your lead is big enough and no dead stones are sitting in this "territory" (which would let your opponent avoid to claim first). Good rules always have to anticipate extremes. Obstructer will claim whatever gets into his mind, regardless how unsound. Obstructer will disagree with whatever you claim, regardless how sound. Not to drown in disputes, each player at most can lodge one. To compensate this restriction, the second principle is that whoever loses a dispute can't win the game any more. This will prevent unsound claiming and unsound disagreeing - with one exception: Obstructer will do so when he's behind. So, if disputes are played out, you better watch your claim since rules have to treat you as a potential troublemaker. Try this one [DGZ0502b]: Disputes are played out. Control is claimed. The game is over. What should White claim? 0 0 B 2 White certainly can claim control of 8 locations on each side, giving him 4 points. Since this is enough to win, White should refrain from claiming more. If he nevertheless does, that's, if he claims the whole board, he could lose the game (if his opponent decides to kick kihin and stick to the rules). White may think that his proof will succeed via ko since he starts the ko without any internal ko threats around: 7 passes, 8 connects, etc. But Black can do better: 0 0 B 0 If White now expects Black to continue in the center, he'll be quite surprised by Black's pass. Finished? Yes. Got it? It's seki - the most astonishing seki I've ever seen! As always, since I don't mention it in the rules, if a clock is used and disputes are played out, actions after the "end" are to be done while each clock is running. It should be obvious what this means in each case. I won't discuss this further - already went too far. I'm satisfied having precisely defined what it means to "control" a location. Nevertheless, if asked to choose a dispute breaker, I would prefer a referee (or better three of them) because after game end no skill on part of the two players should be asked for any more (ignoring their skill in convincing the referee). Note that if disputes aren't played out, disagreement (intentionally) risks nothing. On the other hand, if the game is played via Internet, playing out disputes recommends itself - at least as far as no program is able to be the perfect referee. This also puts an end to disagreeing escapers. Under Yahoo, for instance, it's possible for the player who passed last to force his opponent to play another stone by disagreeing to game end - three passes in a row are prohibited (to prevent endless resumptions I guess) [RGG090303]. This effectifely implements no-pass go (or nim go - German "nimm" is "take!" ): who runs out of legal moves loses. Some claim this to be "Mathematical Rules of Go" [W-JCC], but we shouldn't regard it to be in the spirit of go. Here's a nice example why [RGG010997]: 0 0 W 0 White wins by repeatedly sacrificing stones in Black's eye, despite losing under every other rule set I know. This especially refutes a claim that nim go is the same as stone scoring: it is NOT. In case you want that, you additionally have to allow to return (or destroy) a prisoner as a move (and treat jigos under stone scoring to be lost by who passed first), as I believe. But the finish remains dull. Preferable, Yahoo should either implement the perfect solution given here or at least the simpler, but less perfect, "cleanup" phase solution. In this case disagreement starts a second phase, giving turn to the player that didn't pass last. The cleanup phase ends in the same way phase one did, but without permitting a further phase nor any agreement about dead stones. Since only empty locations surrounded by one color (i.e. contacting one color) are counted at the end, all believed dead stones have to be captured explicitly. Not to lose points in doing so, each stone played in phase two (no matter if it gets caught or not) generates one extra point (draws a prisoner) for the player having played it. (Equivalent ways to put it: pass-stones plus even number of moves a la AGA, or prisoner recycling plus balanced prisoner fill up [RGG090895]). The cleanup phase solution isn't perfect because - all neutrals will have to be filled in phase one (to avoid counting if their number is even, to avoid defect elimination for free, and to avoid giving a hint about defect elimination) - potential kos have to be uncorked in the global context (e.g., bent four in the corner isn't unconditionally dead any more) - some sekis produce extra points in phase two (those with single-sided dame and - provided seki "territory" is ignored in the case of agreement - those with an unbalanced number of eyes) Point one only means extra effort, and point two and three are admittedly rare - but why settle with second best? (Note that the reasons for filling neutrals can't be overcome by both players' good will to agree on game end and dead stones.) What annoys me about cleanup phase solutions is that most of them just don't treat seki as it should be treated and that they give no real reason for their peculiarities. Take the one above, for instance. After a while you ask yourself, "Why don't we skip phase one and start with phase two immediately?" since, as it turns out, this is equivalent to area scoring, which then can be explained far more simpler.
We already saw this position above: 2 0 B 0 The question was if Black should pass. If he, eager to win, does, he missed to remove the aji that crops up when all outer liberties would be filled, spoiling his control. What if White doesn't recognize this aji and accepts a 1-point loss after both passed? For me this is comparable to any other error during counting. It's a practical matter LJRG doesn't address. LJRG neither deals with dropped stones, shifted stones, manipulated captive counts, graphically recording in advance (I can't share van Diepen's opinion to tolerate one move [P-Prag93]) clicking fans (Rin Kaiho's bad habit [GR-Su74]), rattling stones, humming (Cho Hunhyun's bad habit [DGZ0794b]), talking ("It's over!?"), eating, smoking, etc. A practical solution could be that the result is fixed after both players agreed to it. Would a 3rd person be allowed to correct an error before the result is fixed? In the second week of the 1969 European Go Championship Juergen Mattern and Anthony Goddard agreed to end their game and stopped the clock. Mutabzija, watching the game, intervened and showed that there was a sente-point for Goddard, a gote-point for Mattern, still on the board. Mattern would win with this point. Without it the game would be a jigo. I don't know the game record, so I made up an example: 0 0 W 0 The rule committee decided to play a second game: Goddard getting jigo in case he wouldn't lose. Goddard won by 9 points and got a jigo. Mutabzija was first punished with losing 1 point. Later this was converted into a fine [DGZ0669]. The sad thing isn't that both player overlooked that 1-point play - mishaps remain - the sad thing is thatt both had to play a second game. Since I'm not sure how 1949 rules, effective at that time, define game end, I can't comment on this decision. We only can learn from it that the end of the game must be defined in an unambiguous way. If the (absolute) end wasn't reached by stopping the clock, Mutabzija's intervening would be as if commenting on the game loudly while it's still in progress, but I hardly can imagine that this was his intention. How to handle this, again, is a practical matter LJRG doesn't cover. According to it the game would have reached its end. Everybody would then be invited to take part in monitoring the discussion of control and the counting process. This can't do any harm - can only help to reach the correct result. So, if a 3rd person witnessed counting in our first example, he could, without feeling bad, inform White that Black has missed to add a stone and isn't entitled to count any territory there - in fact, he should inform White. If, of course, disputes are played out, nobody may intervene - as long as it concerns the question of control - till dispute breaking is over! In this case White would have to recognize the aji and find the correct sequence by himself. The example also demonstrates that simply counting everything that's surrounded by a single color after dead stone removal wouldn't always be correct. In practice one could fill all uncontrolled empty locations before counting, but remember that this isn't part of the game any more. If, for instance, Black has missed to add a stone, as in the situation below: 0 0 B 2 then he can't make up for it after game end. Black controls not one location above. Under LJRG Black should have added a stone either above or below the center before end. If uncontrolled empty locations are filled to ease counting, ALL 5 locations at the left would have to be filled - no matter with what color. Here's another (funny) example [DGZ0502a]: x y W 0 White suspected there to be aji and continued at A. Black "oh"ed and took his time. Then, with lots of "oh"s from both sides, it went on like this: After the end Black happily started taking out the white stones - without White opening his mouth. They seemed to agree. But some spectators, of course, raised their eyebrows. I don't know it for sure, but it seems that they counted the game as if the white stones on the lower side would be dead. (The only clue the source gives is that "White nevertheless won" - on a 19x19 board, of course.) If the game is played with play-it-out dispute breaking, spectators ought to keep their mouths shut till the players agree on who controls what - after which they may then burst out in laughing. But if this isn't the case, the spectators should notify the players that Black lacks control on the lower side. The players can't insist on their wrong counting (even if it wouldn't matter) - tough luck for Black. LJRG not even grants him the option to continue and to squeeze out 3 white captives: the game is over.
How should one count? After determination of who controls what, the score must be counted. Traditionally each player removes dead stones from his territory and fills them together with captured stones of the same color into his opponent's territories. Each player additionally moves stones around to shape his opponent's territories into plain forms, of course without affecting their total area. If the only drawbacks of this method were tangled arms and not being able to monitor what one's opponent is doing, this method weren't that bad. To overcome: just let the players take turns. But its main drawback is that the final situation is massacred. This is very unpleasant, especially if the game is close. After counting out game 3 of the 40th Oza, 1992, both players appeared quite surprised to learn that Black (Fijisawa Shuko) had won by half a point. Kobayashi Koichi requested a replay, which is very uncommon, and poor game recorder Endo Yohifumi had to replay the whole game to confirm the result - 230 moves. [RGG100702] Needless to say that the normal folk enjoys no game recorder, and that it either doesn't bother to record at all, or omits to record at least the final stage. A complete game record is the exception. Therefore I recommend not to modify the final situation at all. Instead, both players should count both scores and then compare. To enable comparison, both have to agree on how to treat dead and captured stones. I suggest to avoid subtraction (and negative numbers), contrary to what was done above, and to add those numbers to the score of the reverse color. For instance, one could use following (score) chart: TB DW PW | SB TW DB PB K | SW with T for territory, D for dead, P for prisoner, K for komi, and S for score (and B and W for black and white, of course). Needless to say that SB and SW each is the sum of what's to its left. If the number of moves (M) (including handicap, so it's actually the number of stones) are known and one additionally counts the neutrals (N), one can extend the chart to make it self-checking: TB DW PW | SB TW DB PB K | SW M L N -- ------- X X with L being the number of locations. Needless to say that each X is the sum of what's above it, and that those sums have to match. In case opposing controls overlap (which I don't believe can happen, but anyway), those locations have to be accounted for twice in L, and stones on them twice in M. Here's the (simple) proof that both X match: kind of location increase on control occupied alive left side right side ------------------------------------------------- 0 0 N L 0 1 M L 1 0 T L 1 1 0 T M D L 1 1 1 M L 2 0 TB TW L L 2 1 T M M D L L and, of course, each increase in P is matched by one in M.
To all who prefer to play things out: This certainly leads to simpler rules, but I don't think they then deserve to be called "Japanese" rules because they will fail to treat the question of life and death locally. If, for instance, there's a bent four in the corner on one part of the board and a double-ko seki on another, then playing things out will only result in the unconditional death of the bent four if you modify the ko rule - for instance, prohibit ko recapture till a pass was invested in this ko, but this rules out internal ko threats. Playing things out will also fail to naturally treat sekis as neutral - a characteristic of Japanese rules. The argument that this is a strange exception anyway that should be removed no longer holds: LJRG proves the opposite! I don't have any big problem with playing things out at all. For instance, it would be pretty easy to convert to rules that "punish" passing with a prisoner to be given and to end the game after two passes in a row - provided no location was temporarily prohibited when the first pass was made and White passed last. This would guarantee an equal number of stones used by both sides, and we could count in the Japanese or in the Chinese style - both giving the same result. Now, wouldn't this be a good candidate for international go rules? An existing proposal [W-RJ2] takes this view (see [RGG140998] for announcement and discussion). It includes above's pass-stone method as an optional scoring rule. Since this produces the same outcome as area scoring, it was called "Equivalence Scoring" (which is a poor choice since it's a method of counting - it should be called "territory counting for area scoring"). It differs only slightly from what was said above in that the first stop (double pass) only ends the game if an agreement about dead stones can be made. If not, the game continues (of course, with that player that didn't pass last) and ends as soon as the second stop was made (and all stones left being alive). An equal number of stones is reached by forcing White to add an extra pass (stone) just before scoring if Black passed last. The whole thing is practically equivalent to AGA rules [W-FH2]. AGA rules also use pass-stones (but not as an option). As above a stop followed by an agreement ends the game, and as above White must add his extra pass after game end if Black passed last. But different from above the game doesn't end with the second stop after a failed agreement. Instead, each further stop again gives agreement a chance. In case agreement always fails, a double stop (four consecutive passes) ends the game without agreement (and all stones left being alive, of course). Since the proposed "International Rules" and AGA rules both use super-ko (positional the former, situational the latter), neither allows passes as (trivial) ko threats: after a double pass the ko still is taboo. (However, if the "Basic Ko and Exceptional Game Ends" option of "International Rules" is in effect, one's first pass could be a (trivial) ko threat.) Before you now vote for one of the three alternatives given above (zero, one, or multiple chances for agreement - to coin them), please be aware that they all share one property - they are area scoring effectively. Is this the simplest rule set possible? I don't think so. There's another "play things out" candidate out there - called "stone scoring" (or "stone counting", but I like Robert Jasiek's idea to reserve "counting" for counting methods) - and every child will instantly grasp what's the game about: To get more stones of your color onto this board than your opponent Stone scoring rules seem to be the most natural thing on earth. Why not make THEM the candidate for international go rules? Ok, under the various equivalent counting methods applicable to area scoring everybody finds one he's used to - more or less - but for someone unbiased, stone scoring is absolutely plain (and has the older rights anyway - see below). The scoring rule couldn't be plainer: A player's score is the number of locations that have his color If you look at it this way, it's not very convincing to additionally count eyes. You surrounded one? So what. If you can't occupy it with one of your stones, it doesn't seem to be yours - any toddler will understand that, and Sesame Street's Count von Count would create quite some confusion if he mixed stones and holes in one count. In this text I try to make Japanese-style rules plain. If my aim were to propose an international rule set, logic would sleepwalk me to rules of the "stone scoring" type. And somehow I have the feeling that if the big global rule election would be made, and children (unbiased as they are) would participate (and why shouldn't they?), the vote would be a clear "stone scoring". Maybe they're right. Whatever the current rules are, when introducing the game to kids or beginners, stone scoring would certainly be my favorite rule type (example rule set at the very top). In my opinion, beginners should play lots of games on SMALL boards (say 9x9 or even 5x5) right from the start, and not be taught tactics or elaborated concepts at all. Why not even keep our mouths shut and let them detect the "trick" with the territory ("filling can wait") or that with the two eyes ("don't fill too much") on their own? Japanese-style rules (including LJRG of course - I'm not blind) are spoilers in this respect and absolutely unsuitable for beginners: to let them depend on a referee when questions like "Is the game over?" (without some "two passes end" rule) or "Is this dead?" arise is ridiculous. They should be able to walk off and play with each other. Therefore I have mixed feelings about the "greatest" go event on German TV in the year 2002: our child program "Die Sendung mit der Maus" - famous for bringing things down to simple terms - explained go! That's the good news, but the bad one is that they did it via Japanese rules. They explained capture (but neither suicide nor the case when it just looks like one), territory (empty "crosses" surrounded by one color, but ignoring the symmetry between inside and outside), and that each prisoner and each empty cross in one's territory counts for one point, but ko was never explained (nor distinguished from suicide in an eye). Then a 9x9 game was played and ended as "no more" moves were available (leaving the impression that entering an already surrounded area isn't allowed). Stones surrounded by opposite color were removed (too bad that those stones themselves never surrounded some "territory" - we would have experienced their first rule debate). To top it, they managed to count 6 points in a 3x2-shaped corner. After 66 moves White had won by 24 - 13 = 11 points: 5 2 (66 filled 17) (B sat at the right) No one depending solely on that information will really know the rules. Worse, he'll think he knows them, but probably got'em wrong. Ok, it was a good appetizer and it seemed simple - but it just was incomplete and misleading. I'd tolerate this if go rules couldn't be squeezed appropriately, but this definitely isn't true as, for instance, stone scoring rules given above prove - in less than 25 lines and without any "abstract nonsense". It's better to start with rules that are simple as well as complete than to start with the real thing and omit to define ending or scoring only to simplify or because oneself lacks a complete understanding. I neither recommend crippled rules like "atari" (first-capture-wins) go. Whether the initial rules actually are used anywhere on earth or not is irrelevant - as long as they preserve the spirit of go. But before you now vote for stone scoring, let's look for something else to be considered. There seem to be two conflicting goals: - simple rules (like stone scoring) on one end, and - simple practice (like Japanese-style) on the other. Both, stone and area scoring, have in common that they "play things out". Very appealing - especially when introducing go to beginners. But playing things out also has its disadvantages - especially for experienced players (which one happens to be for the longer time). Experienced players are dealing with the practical consequences of the rules, not with the rules themselves. They want an early end - without any fuss. They don't want to - count groups to see who will need more eyes - make superfluous connections to avoid some eyes (this two drawbacks, of course, only come with stone scoring) - count neutrals to check if having the turn got meaningless (we have to fill'em anyway? - not under LJRG) - let the outcome of a ko or the game depend on the number of neutrals - start silly kos about one neutral more or less (see below) - uncork potential kos (like bent four) in the global context - be forced (by a disagreeing obstructer) to capture dead stones All this would only prolong the game without making it much more interesting - just fussier. Of course it's a matter of taste, but if you prefer the fussy style then consider being consistent and also divide shared spaces in sekis minutely (as Ing rules once did [P-Ing86], but seemed to have dropped). If not, you naturally end up with territory scoring (which is more than just a method of counting). This has nothing to do with stubbornly sticking to some weird tradition. It just shows that once in a while there's a grain truth in tradition - if not a boulder here. The non-fussy practice lets this 0 0 W 2 (suppose the center was prohibited in the first turn) be a jigo, instead to count Black's eyes in the seki. Counting points in sekis wouldn't prolong the game and might not bother anybody - that's why I excluded it from above's list - but nevertheless I like how LJRG treats seki: no control - no points. The non-fussy practice doesn't care about neutrals. You need a definition? I'll try one. Look at board extensions of this kind (LJRG nowhere excludes boards that fall apart, by the way): plain neutral Black's silly ko White's neutral If the main board's "orbit" could be extended by whatever finite collection of such "satellites" (including their color-reversed variants) without changing the game's outcome, we can qualify the underlying rules as being neutral-indifferent (which LJRG is). Some words about the silly ko: 0 0 B 0 (5 stones each) Under Japanese rules both players would now pass and the score would be even, but under stone or area scoring Black will start a ko at A, exploit his ko threat below the single white stone, and win by 2 points. Normally there are "neutrals" around, like here: 0 0 B 0 (16 stones each) Black has to be armed with enough ko threats to keep the ko alive till all neutrals are filled, investing one threat after each pair got filled. He has enough here, and he wins by 2 points (under area or stone scoring) if he starts the silly ko. If not, White ties. In the situation below Black doesn't have enough ko threats to keep the ko alive this long: 0 0 B 0 (14 stones each) But Black wins anyway because the number of neutrals is odd. He'll take the last one even without going through the silly ko. However, Black risks nothing starting it. As soon as he notices that he has exhausted all his ko threats, he can return to the plain sequence by filling the ko. There's a variation of area scoring that deprives Black from the extra point [W-IT]: If the [very] first pass was made by White [...], 1/2 point is subtracted from Black's score and added to White's score [to] eliminate the one-point difference between area and territory rules that arises about half of the time in even games from Black's having played an extra stone. An alternative but more symmetric way to eliminate the one-point difference is to allow a single half-point button beside the board to be taken as a move and additionally to increase komi by half a point [RGG170101]. Either Black takes the last neutral, but his extra point is compensated by button and increase, or White takes it, and Black makes up for the increase by taking the button. Again, if the number of neutrals is odd it makes no sense to fight the silly ko, but in the even number (neck-to-neck) case Black still fights it, even if now "only" for a 1-point win. So, the deprivation amendment fails to make neutrals meaningless in all cases. By the way, it's not "if the last pass was made by Black..." because this invites pass fights. For instance, Black would tie 0 0 B 0 after he filled the last neutral by answering White's pass not with a pass, but with a throw-in (in White's 2-point eye). White can't help but to capture (under any play-it-out rules), letting Black avoid the last pass. For a hyper-complicated treatment of a silly ko see [GW71b]. I'm far from being sure, but it seems that Japanese rules don't enable such a fuss. Above, the ko was fought as soon it was set up. Is this always right? Choose Black's move below (area scoring): 0 0 B 0 (12 stones each) If Black takes the (center) ko, it ends in a tie: Sly White doesn't atari (error), but fills the (bottom) neutral, Black fills the center ko, White ataris, Black fills at the top, White takes the corner ko, Black passes, White fills the corner ko (works in all ending schemes), and both pass. Both captured one stone, and Black's territory is one point larger, but Black suffered from an extra pass. If Black instead fills the neutral, he'll win by 2 points: White ataris, Black fills at the top, and - since both kos cancel out each other - White passes, Black passes, and White passes again (for an even number of moves). Black's territory still is one point larger, but now White suffered from an extra pass. This example is a shrunken version of a game between Seto Taiki and Liu Fan, played in the 2003 National Weiqi B League. Ironically the Chinese (Liu) took the ko and lost by half a point instead to win by 1.5 [RGG040403]. Note that, to be fair, taking the ko isn't wrong per se. If Black had enough ko threats (somewhere else), he could win by 4 instead of by 2 (and overcome komi, for instance): White fills the neutral, Black fills the center ko, White ataris, Black fills at the top, White takes the corner ko, Black retakes it after threat and defense, White passes, Black fills the corner ko, White passes again, and both pass once more. Black is ahead by one point territory, one prisoner, and two white extra passes. Now to the obstructer (plus a rule debate under play-it-out rules - you wouldn't believe it): In the second round of the 46th European Go Championship (Zagreb, July 20 - August 4, 2002) the Hungarian 6 dan Csaba Mero (White) was pitted against the German 5 dan Robert Jasiek (Black). The game was played under Ing rules (area scoring). At the end of the game, Robert was behind with about 25 points. Both passed in succession (first "stop"), but no agreement about dead stones was made (no idea if one was tried - Robert continued). The game went on with Robert capturing "dead" white stones while Csaba kept on passing (and maybe smiling). After having removed all "dead" white stones, Robert finally passed too, leading to the second stop (since Csaba must have passed before). After a third stop, immediately following the second one, the game was over. [DGZ0402] The real "fun" started now - they didn't agree about the "dead" black stones: Csaba wanting to take them off, Robert insisting that the game was over and those stones thus had to stay (giving him the win). The referee decided against Robert. The appeals commission agreed (deciding that "the game is in a pause", but failing to underpin this with rules). Weeks later Matti Siivola, president of the Finnish Go Association and chairman of the RRC (EGF's rules and ratings commission), wrote Robert that the RRC "agreed that the decision of the appeals commission will not be changed" (six members out of seven took part - Robert, of course, not) - with "slightly varying reasons", but not giving the slightest hint [RGG120902]. The Ing Foundation itself didn't answer any of Robert's queries. In an org-e-mail Christoph Gerlach, German 6-dan, also agreed to the appeals commission's decision, arguing that the game doesn't end in case there still are dead stones around. I honestly was stunned. Aren't Ing rules [W-Ing91] of play-it-out type? Or am I mixing up Ing rules with AGA rules [W-FH2]? Under AGA rules (area scoring as Ing rules) the game either ends with a stop followed by an agreement about dead stones or with two stops in succession (making it impossible to block game end by endlessly disagreeing). This would clearly support Robert's opinion. I guess Christoph draws his opinion from [W-Ing91], quote, Article 1 [...] After the neutral points have been filled, both players pass and play pauses. After the dead stones have been taken away, both players pass again and play ends. When you first read this, it doesn't seem to fit to, quote, Terminology [...] 19 "Play ends" when each side passes twice, making four consecutive pass plays. Play cannot resume for any reason, so that game ends. Didn't the former let the game end after one stop, not two? But then you realize that "taken away" refers to agreement and not to capture, and that therefore taking stones away doesn't insert any moves between both stops. For me Article 1 is an example where a rule of practice gets confused with a legal rule: "stop, agreement, stop" might be the normal case (adding a superfluous trailing stop, compared to AGA rules), but of course "stop, no agreement, stop" is also a game end - else we could forget the whole idea of the trailing stop. But nevertheless Christoph wants to think that the game ending stop only qualifies as one if it not only immediately follows another stop, but if additionally all dead stones are "taken away" between both stops. Obviously Christoph (and who not?) disapproves Robert's conduct and tries to interpret the rules in his way. If he is right, he would have to define what "dead stones" are - because depending on agreement will certainly not do. This definition must also be independent from their capture in the "cleanup" phase (after the first stop) to avoid a vicious circle. Suppose we would use "stones are dead if they can't avoid capture (even if they start)" to accomplish this. Of course, this doesn't mean that "dead" stones can simply be taken off after a stop - as "one slips" (beast 4) demonstrates. In its case the game would have to continue (since both groups are "dead"), one group would have to be captured, and the other would be allowed to make life - fine. But rule design is a delicate job. What if the opponent is behind, refuses to capture, and blocks the game from ending? (Not very thankful of him - he's the one we actually wanted to help not to forget his capture.) We could additionally prohibit passing if there are opposing dead stones around (and define "end" without referring to dead stones again), but counter-examples remain: First, the stones in a double-ko seki's kos are "dead" according to the definition, but there's no way to get rid of them: the game would never end (and neither before). Second, it's sometimes wiser not to capture: 0 0 B 0 Each side has 21 stones on the board. 10 locations are empty (21+21+10 = 52 = 13x4) - of which Black has surrounded 3 and White 2. The other 5 are neutral - 4 of them in seki. If Black just takes the last neutral not in seki, he'll win by 2 points. But according to our definition the white stones at the left side are dead (of course not because of bent four) and Black would have to continue after White's pass. After Black starts the ko in the bent four, White will make a ko threat in the seki and, whatever Black does (ignoring the threat or answering it), it will end in a tie (under area scoring). Considering this, we may now come up with the idea that a player is allowed to pass even when opposing dead stones are around, if he only renounces to capture them - but, guess what, now we're almost back to where we started from. We only have to let the renunciation be understood with passing to reach home plate again. I don't think that it's worth the effort to prevent games to end "too soon". If both players know that the game ends with two stops in succession, they should have no problem to capture whatever they feel can be captured before this happens (since this costs nothing but time under area scoring). It's of course the organizer's responsibility to make all players fully aware of this ruling. We should learn this: Either we use play-it-out rules, benefit from their simplicity (though Ing rules aren't the best example), but suffer from having to play it out in case an agreement fails; or we use Japanese-style rules, swallow their complexity, but are able to humiliate our opponent with passes in case he stupidly keeps on going - it's as simple as that. Do I think the decision was wrong? It was absolutely wrong. Csaba should have swallowed his pride and "kicked" Robert's stones off the board (if he knew the rules). But Robert Jasiek shouldn't feel too well either: If he's a proponent of play-it-out rules, as e-mails and posts suggest, he ironically hasn't done them a big favor, and, even worse, he missed a chance to demonstrate kihin. It's true that under area scoring of Ing-type approaching "dead" stones doesn't waste time because you have to fill in for counting anyway, but under the AGA-type it would be extremely unpolite to disagree if things are clear - and neither is it good style to let clocks run longer than necessary, under whatever rules. Robert should ask himself why he passed as soon he had removed the "dead" stones. Why didn't he continue with filling his territory? Doesn't he has to do this anyway too under Ing rules? This wouldn't change the score? Come on, this argument backfires twice. First, should one start to drop a "dead" stone into each opposed territory just to let it technically ceases to be territory for the moment? Second, capturing clearly "dead" stones neither changes the score, at least not if we assume both players to behave well and to agree on them. But one gets the impression that he wants to play the game without agreement, that he wants to take "play it out" to its extreme. (For a tiring discussion about all this see [RGG250902].) A slight chance for his excuse might be that Article 1 (Pass Play) says nothing about agreement (the only hint is using "taken away" instead of "removed"). One has to spot it in the Preface (3): "After play pauses, if there are no disagreements when the dead stones are taken away, both players make one more pass play each to end the game." So maybe he honestly wasn't aware of this option. Another try for excuse would be to deny the concept of "dead" stones to exist under "play it out" (that's why it's put in quotes in this context). I could try to define it ("clearly dead" is dead in LJRG's sense even if each worst case is worsened by adding a double-ko seki satellite which must survive successful proofs), but it's simpler to say that if we could agree on some stones to be "dead" without changing the expected score, then it's polite to do so. However, Robert certainly had to become aware of Csaba's lack of rule knowledge as Csaba allowed him to end the game "too soon". To exploit this isn't good style. Better warn your opponent and add a stone to the board just to give him the chance to make up for his technical error - even if you now lose. What's kihin worth if it always were for free? But again, technically Robert had won. As ridiculous it is that the EGF forces European go players to play under area scoring or, worse, Ing rules each time they meet for two weeks annually, when in fact they play under Japanese-style rules in the remaining 50 weeks of the year - as ridiculous it is when the EGF pockets Ing's money and equipment (including those silly measuring bowls, worth being smashed against the wall), but doesn't apply his rules in exchange. It's not the RRC's business to judge kihin (and maybe it didn't). Its business is to make clear what the rules are and how they should be applied in the future, but it failed to do so. If you want to make fun about Ing rules or protest against them, how about exploiting following garbage, quote, Article 8 Penalties [...] Unpenalized mistakes: The following are not penalized. (1) Mistaken pass: If a player makes a pass play when a point could still be made by a board play, thus failing to make a possible board play, he loses his turn, but is not penalized. [...] If you're behind and don't want to lose, the only thing you need are some "dead" stones somewhere in your potential territory. Since only their removal will convert it into territory, clearly "a [...] point still [can] be made by a board play". Now, every time you pass this is no pass, but just a lost turn. Since the game only is over if "BOTH players pass again" after a stop, you've made it: Ing's odd fill-in procedure is waiting in vain. You may disagree and point to Article 8's continuation, quote, If both players overlook the final neutral point and it is discovered during the fill-in procedure, since the game has ended and play cannot resume, the point is left as a shared space. There is no penalty. This only can happen if passes stay passes, no matter what. Fine with me. In this case you must agree that the "mistaken pass" rule indeed is garbage (likewise not recording passes when no board play follows - Article 10). The last quote also is another blow to Christoph's opinion: If neutrals may be overlooked - why not "dead" stones too?
I still owe you the fact that, besides being unbeatable simple and logical, stone scoring also seems to be the origin. Here's an analysis of four old game results supporting this. I don't think that this in question at all, but anyway (if only to show that one scoring definition can lead to several counting methods). [GW71a] presents this four ancient games (sorry for omitting game records and final diagrams - I just was too lazy): Game 1 "Four Fairies" (Song Dynasty, 920 - 1279 A.D.) Game 2 "Ranka" (Jin Dynasty, 265 - 420 A.D.) Game 3 "Golden Flowerpot" (Tang Dynasty, 618 - 907 A.D.) Game 4 "Jia Xuan" (Song Dynasty, as above) But Ing Chang-Ki misses to expressively point out to the reader that those four games were played under stone-scoring rules! He seems to be misled by scores reporting of captured stones and lu's (empty locations) each side managed to count. But the numbers of lu's given only make sense after you also consider the eyes and "unpaired" stones - as you would if a game under stone scoring isn't played out to its full length. In this case you can't use the natural counting method of simply counting your stones on the board. One way out is to count your area and subtract the number of eyes you need: Score = Area - Eyes (area style 1) The other avoids counting your stones by only counting your empty area - after filling in dead and captured stones - and again subtracting your number of eyes. But this depends on both players having used the same number of stones. If not, the number of extra (unpaired) stones must be added to the score of the player who played them: Score = Terr. - Dead - Eyes + Unpaired (territory style) = Area - Paired - Eyes (area style 2) with Terr. = Number of locations you surrounded after dead stone removal Dead = Number of captured or dead stones of your color Eyes = Number of eyes you would need to keep open Unpaired = Number of stones you played more than your opponent Paired = Number of stones used by a player who didn't use more (just to make both styles comparable) Area = Size of your territory plus number of your stones on the board - after dead stone removal Here are the figures. Those in column "Dead" and "lu's" quote the article. The rest was deduced by me from the final diagrams. Game Color Terr. Dead Eyes Unpaired Paired Area Score lu's ---- 1 Black* 55 9 4 1 132 179 | 43 | 42 White 57 7 8 0 132 182 | 42 | 43 | | 2 Black 37 9 10 0 155 183 | 18 | 18 White* 45 22 6 0 155 178 | 17 | 17 | | 3 Black 52 6 6 0 135 181 | 40 | 40 White* 51 6 6 0 135 180 | 39 | 39 | | 4 Black* 76 21 4 1 127 183 | 52 | 51 White 58 9 6 0 127 176 | 43 | 43 Seki 2 ---- The * indicates who started the game. In all 4 games each color occupied 2 diagonal corner hoshis before the first free move was made - a custom in those days. For instance, game 1 lasted for 132 + 132 + 1 - 4 = 261 (free) moves. All games were played till all "neutral" locations - besides those in seki, of course - were occupied. Dead stones seemed to have been removed by agreement. Comparing my scores with the lu's given in the article seems to reveal two errors in the article: 1. It mixed up the lu's in game 1. 2. It dropped 1 black lu in game 4. Since game 2 and 3 had no unpaired stones, it could also be that the number of unpaired stones was subtracted from the score of the player having played less stones instead of added to the score of their owner. This would lead to a similar error in game 4 - a score of 51 to 42 in contrast to 51 to 43 lu's, as reported - but the error in game 1 wouldn't be that "nice" any more - a score of 42 to 41 in contrast to 42 to 43 lu's. However, it seems pretty likely that stone scoring was also used in those two games - and there's no doubt about this for game 2 and 3.
JRG89 IN DEPTH
This chapter takes a critical look at the 1989 rules and suggests interpretations and fixes. It's a complicated mess because JRG89 is very ambiguous and incomplete. I hope its last section about the erring rule masters makes up for it. I'll include the English translation of JRG89 below, but for the comments and examples that accompany them see [P-ARS90] or [W-FH1] (or the Go Players Almanac). Figures labeled C-nn are from JRG89's commentary section. Those labeled LD-nn are from its life and death example section (and correspond to beast nn). All outer stones in JRG89's examples are assumed to be alive and not in seki.
The Japanese Rules of Go April 10, 1989 (Effective May 15, 1989) Translated by James Davies The Nihon Kiin and Kansai Kiin hereby revise the Nihon Kiin's Rules of Go formulated in October 1949 and establish the Japanese Rules of Go. These rules must be applied in a spirit of good sense and mutual trust between the players. Article 1. The game of go Go is a game in which two players compete in skill on a board, from the beginning of the game until the game stops according to Article 9, to see which can take more territory. A "game" refers to the moves played until the "end of the game." Article 2. Play The players can alternately play one move at a time, one player playing the black stones, his opponent the white stones. Article 3. Point of play The board is a grid of 19 horizontal and 19 vertical lines forming 361 intersections. A stone can be played on any unoccupied intersection (called an "empty point") on which Article 4 permits it to exist. The point on which a stone is played is called its "point of play." Article 4. Stones that may exist on the board After a move is completed, a group of one or more stones belonging to one player exists on its points of play on the board as long as it has a horizontally or vertically adjacent empty point, called a "liberty." No group of stones without a liberty can exist on the board. Article 5. Capture If, due to a player's move, one or more of his opponent's stones cannot exist on the board according to the preceding article, the player must remove all these opposing stones, which are called "prisoners." In this case, the move is completed when the stones have been removed. Article 6. Ko A shape in which the players can alternately capture and recapture one opposing stone is called a "ko." A player whose stone has been captured in a ko cannot recapture in that ko on the next move. Article 7. Life and death 1. Stones are said to be "alive" if they cannot be captured by the opponent, or if capturing them would enable a new stone to be played that the opponent could not capture. Stones which are not alive are said to be "dead." 2. In the confirmation of life and death after the game stops in Article 9, recapturing in the same ko is prohibited. A player whose stone has been captured in a ko may, however, capture in that ko again after passing once for that particular ko capture. Article 8. Territory Empty points surrounded by the live stones of just one player are called "eye points." Other empty points are called "dame." Stones which are alive but possess dame are said to be in "seki." Eye points surrounded by stones that are alive but not in seki are called "territory," each eye point counting as one point of territory. Article 9. End of the game 1. When a player passes his move and his opponent passes in succession, the game stops. 2. After stopping, the game ends through confirmation and agreement by the two players about the life and death of stones and territory. This is called "the end of the game." 3. If a player requests resumption of a stopped game, his opponent must oblige and has the right to play first. Article 10. Determining the result 1. After agreement that the game has ended, each player removes any opposing dead stones from his territory as is, and adds them to his prisoners. 2. Prisoners are then filled into the opponent's territory, and the points of territory are counted and compared. The player with more territory wins. If both players have the same amount the game is a draw, which is called a "jigo." 3. If one player lodges an objection to the result, both players must reconfirm the result by, for example, replaying the game. 4. After both players have confirmed the result, the result cannot be changed under any circumstances. Article 11. Resignation During a game, a player may end the game by admitting defeat. This is called "resigning." The opponent is said to "win by resignation." Article 12. No result When the same whole-board position is repeated during a game, if the players agree, the game ends without result. Article 13. Both players lose 1. After the game stops according to Article 9, if the players find an effective move, which would affect the result of the game, and therefore cannot agree to end the game, both players lose. 2. If a stone on the board has been moved during the game and the game has proceeded, the game continues with the stone returned to its original point of play. If the players cannot agree, both players lose. Article 14. Forfeit Violation of the above rules causes immediate loss of the game, provided the result has not yet been confirmed by both players.
In defining dead and alive, JRG89 concentrates on stones. All rule sets that take this path have the disadvantage that seki has to be covered by extra rules. If you ask someone knowing the game to teach it to you, it's very likely that you're told something about stones that can be removed at the end because they could be captured or because they can't avoid capture. It's less likely being told the opposite - that stones may stay on the board because the can be defended. If you nevertheless investigate it systematically, you might come up with C1 = capturable if their opponent has first turn C2 = capturable even if their opponent has second turn D1 = defendable if their owner has first turn D2 = defendable even if their owner has second turn detect these four relations C2 implies C1 C1 = not D2 D2 implies D1 D1 = not C2 and draw following picture with the areas surrounding the three small squares (C2,X,D2) being empty (follows from the is-not relations above). It seems obvious to take C2 as dead and D2 as alive. But what about X, the intersection of C1 with D1? If you consider snap back, the only choice that makes sense is to treat shaky X as alive. So you finally reach C2 is dead D1 is alive (each implying the other) This is a very popular definition. Many books introducing the game (carelessly) use it, including [P-IK] and [P-JDRB]. To quote the latter At the end of the game, any stones that cannot avoid being captured are removed as prisoners without actually being captured. This translates to "C2 is dead" (the stones may act first - their opponent only second). Note that the almost similar "stones that can be captured are dead" would be closer to "C1 is dead", which was rejected. "C2 is dead" isn't that bad at all. For instance, it covers "bent four in the corner is dead". Ironically the authors of above books don't seem to trust their own definition. Both include an extra rule for bent four. But if you follow the definition strictly, it's obvious that ko threats can be ignored because the only thing that matters is the question if those stones can be captured or not. This isn't a continuation of the game - just a (hypothetical!) test. ([W-RJ3] seems to have problems with the plural in statements of the kind "dogs that bark are alive". Of course this doesn't try to define if a group of dogs is alive - it simply means the same as that "one dog that barks is alive".) On the other side, "C2 is dead" - doesn't cover the seki exception - ignores defects (e.g. 3x2 in the corner would be territory) - treats "one slips" (beast 4) unfair (both groups are called dead because they can't avoid capture, ignoring the fact that capturing one enables the other to live) Neither LJRG nor JRG89 takes this path. LJRG instead defines who controls an area - live and death just follows. JRG89 still sticks to categorizing stones, but X isn't treated as alive - it's dead. Since this alone makes no sense (snap back), JRG89 has to define the strange exception class "capturable alive". Let's see what this means.
C-7b JRG89: 1 dead white stone in black territory. According to JRG89's Article 7, the two black stones are alive - not because they couldn't be captured by White, but because this enables Black to play a new stone his opponent can't capture (on the corner location or above it). Recall Article 7: Article 7 (life and death) 1. Stones are said to be "alive" if they cannot be captured by the opponent or if capturing them would enable a new stone to be played that the opponent could not capture. Stones which are not alive are said to be "dead". 2. In the confirmation of life and death after the game stops in Article 9, recapturing in the same ko is prohibited. A player whose stones have been captured in a ko may, however, capture in that ko again after passing once for that particular ko capture. Article 7.2, to start with the pass-for-ko rule, seems to be understood in the following way: The normal ko rule is sharpened. It's now harder to recapture in a ko. It doesn't help to play elsewhere after a ko capture - you still can't recapture. First you have to pass once after the ko capture for this ko. And certainly you have to inform your opponent which ko your pass was intended for because now several "hot" kos could be around at the same time. Robert Jasiek asks the good question if a recapture would be possible "if after the last opponent's capture in a ko the ko temporarily ceases to be a ko and then occurs again" [W-RJ3]. For instance, suppose White just has taken the ko at the right in a hypothetical line of play. Black then takes the center ko, and White passes for it. It should be out of question that there's no need for Black to pass himself for the "ko" at the right because at this moment it is no ko - he could capture two stones. Ok, but what if he passes instead and lets White recapture in the center (coming back to above's configuration). Would Black now still be allowed to capture in the ko at the right (now being one again)? The question is what Article 7.2 means with "same ko". The empty location in the right ko and all its neighboring locations didn't change color during the capture and recapture in the center ko. But is it still the same ko? This is a typical question that comes up when rule texts are not formal. Instead of giving a direct answer, I'll translate my interpretation into the parlance of LJRG (without really getting formal) and let you figure out: 1. A location is "in ko" if it is empty (uncolored), all its neighbors are not, all its neighboring stones have the same color, and exactly one stone in atari contacts it. 2. If your capture in a hypothetical line of play produces a new location in ko, you have to put a "semi-permanent" mark on it. 3. You only may put a stone on a semi-permanently marked location if this stone has the same color as the stones neighboring this location. In this case you have to remove the mark. 4. If your turn adds no new stone to the board, you may remove exactly one semi-permanent mark ("pass for a ko"). 5. You must remove all semi-permanent marks sitting on locations no longer in ko at the end of your turn. Note that allowing to remove marks produced by oneself does no harm. Note further that it's impossible that a location in ko changes the location of its stone in atari without going through a state in which it's not in ko. Now to the heart of Article 7 - its definition of life and death. Article 7.1 seems to be interpreted as follows: I1. The capturing player has the first turn. JRG89 uses C-7b and other snapbacks as examples of, quote, stones that are alive because capturing them would enable a new stone to be played that the opponent could not capture. Since Black could certainly avoid capture in C-7b if he started, the capturing player - here White - must have the first turn. I2. The new stone doesn't has to be played immediately after the capture. The stone Black plays after White captures in C-7b sets up a second snapback - it can be captured again, it isn't yet the uncapturable new stone. This will be played by Black's second capture, regardless if White passes or captures again. [W-FH1] takes another point of view: it understands Article 7.1 as a recursive definition. But then you would have to change the rule text of 7.1 from ...enable a new stone to be played that the opponent could not capture... to ...enable a new stone to be played that is alive... and this sounds like a cyclic definition. We could avoid this with some notion of degree, reformulating Article 7 like this: 7.1. Stones are said to be "alive" if they're alive in degree N >= 0. 7.2. Stones are said to be "alive in degree 0" if they cannot be captured by the opponent (who takes the first turn). 7.3. Stones are said to be "alive in degree N+1" if capturing them would enable a new stone to be played that is alive in degree M, with M in 0..N. But I don't believe this was the intention of JRG89. I3. The new stone doesn't always has to be played on the same location. I don't have an example for this (C-7b is none: a new uncapturable stone can always be produced on the corner location), but I can't rule out the possibility that the capturing player could at least influence where the new uncapturable stone will sit at the end even if he can't avoid it, and Article 7 doesn't seem to care about this case. I4. The new stone doesn't has to be played on locations cleared by the capture. For instance: LD-2 JRG89: Both are alive in seki. Black clearly can't capture White, so the white stones are alive. But couldn't White capture the 2 black stones in the corner? Yes, but this would enable Black to capture 2 white stones by playing 2 new black stones at A and B which White couldn't capture any more. Notice that White, even taking the second turn, could prevent this 2 new black stones if he is released from the commitment to capture the 2 black stones in the corner: after Black plays A, White captures with B. This justifies the term "enabled" (for the moment). Therefore the 2 black stones in the corner are also alive. I5. The new stone doesn't has to be uncapturable in the very moment of its staging. See beast 12 for an example where it matters.
But even interpreted as above, there remains the problem of how to formalize "enable". Notice that if the new stone pops up underneath the captured stones (on one of their locations after they have been removed) there is no question that it indeed was enabled by the capture - simply because not capturing prevents a new stone there. But unfortunately this isn't the only case. Wrecking my brain, I came to following conclusion: I6. An uncapturable stone is enabled to a set of locations by a capture only if the capturing player 1. - taking the first turn - can't perform the capture without permitting an uncapturable new stone of his opponent taking place on one of the locations in that set, but 2. - taking the second turn and restricting himself to a fixed number of stones of his choice - could prevent all locations in that set of getting occupied by an uncapturable new stone of his opponent. The first part is more or less what Article 7 told us already. The phrase "set of locations" makes explicit that the new stone doesn't has to pop up on the same location in all variations. The second part misses in Article 7. Here's why we need it: The capturing player certainly must be able to prevent the enabled stone in some circumstances because otherwise it would make no sense to talk of "capturing them would enable". But this also can't be in all circumstances for the following reason. Imagine two dead-or-alive groups of your opponent in your believed territory. Each could be brought to life or to death depending on who starts. Both groups don't depend on each other. The game has ended - silly, but may happen. If you now declare both dead, your opponent could say no, arguing: if you capture one, I'll save the other - with the new stone. And indeed, the stone would be enabled by this capture because you could prevent it with your first move! Therefore both groups would be alive: not what JRG89 wants, I guess. So, this is the reason for the "second turn" restriction. Explaining the need for the "fixed number of stones" restriction will take a bit longer: LD-11 "false eye and double-ko seki" (or "moonshine life and...")
Now let's take a look at how the game ends under JRG89. C-19a JRG89 would have to rule 7 points territory for Black because the black stones are alive. They certainly can't be captured because the most White can get is seki (at 2-2). But this only holds if the players managed to end the game. If both players pass in a row and can't agree to end the game nor one of them requests resumption to avoid giving his opponent the first turn - both lose. Recall Article 9 and 13: Article 9 (end of the game) 1. When a player passes his move and his opponent passes in succession, the game stops. 2. After stopping, the game ends through confirmation and agreement by the two players about the life and death of stones and territory. This is called "the end of the game". 3. If a player requests resumption of a stopped game, his opponent must oblige and has the right to play first. Article 13 (both players lose) 1. After the game stops according to Article 9, if the players find an effective move, which would affect the result of the game, and therefore cannot agree to end the game, both players lose. 2. If a stone on the board has been moved during the game and the game has proceeded, the game continues with the stone returned to its original point of play. If the players cannot agree, both players lose. (13.2 is only of practical matter and should be shifted over to tournament rules. I'll therefore ignore it here.) Wait a moment. They have to "agree" to life and death? But didn't our painful discussion above just has shown us that life and death is defined objectively? A game can be "resumed"? And what if this happens endlessly? What exactly is an "effective move"? We saw an example above, ok, but wouldn't filling my second eye also be one? They also have to "agree" to the end? And if not? Oh yes, both lose - wow. Anyone another cup sake? If this was too cynical for you, sorry, but I really get mad when I read stuff like this. Let's go through the points I don't agree to one by one: First, game end seems to rest on agreement. "The game is over when both players agree to end it" is the more popular version, to quote [P-JIE]. I can't hear it any more. This may fit to Japanese or East Asian mentality, where consensus is of high value, but not to a strategic board game. The definition of game end shouldn't depend on the good will of any of the two players because the one behind has no interest in ending ("Agree having lost?" "NO!") - it must be defined objectively (which also will take care of an endless number of resumptions). Second, neither should life and death rest on agreement ("Agree being dead?" "NO!"), and, since life and death already are defined objectively by JRG89, there is no need anyway. Agreement would additionally open the door to attempts to trick one's opponent without any risk: 0 0 W 0 If both pass above, White should try for an agreement in which all neutrals are filled (to get rid of seki) AND his stones being alive. In this case he'd win by 1 point. Viewed objectively, of course, his stones would be called dead by JRG89's standards. But even if someone would inform Black before counting, Black would have to stick to the agreement - otherwise agreement would be meaningless. White risks nothing. If Black disagrees and tells him why, White will smile (or pretend being surprised), add a stone (he couldn't avoid being forced by Black anyway) and accept jigo. But couldn't "confirmation" mean that both players work out the objective life and death status of all stones before game end? It could, but I'm also against this. In the example above, if White wouldn't be aware of his defect, Black would have to inform him that his stones would be dead after neutrals are filled: silly. Third, permitting the game to be resumed isn't necessary at all. Even "the BGA [British Go Association] Council [, which adopts JRG89,] makes the comment that restarting the game has never been the custom in the UK" [W-BGA1], and, I guess, nowhere else as well. Unfortunately the BGA lacks the guts to go further and "stipulates that all requests to restart the game after both players have passed be made only through the Event Organizer or Referee". But actually JRG89 works fine without resumption. For instance, we could let the game be over after the first stop. Since life and death are defined objectively, the players could step aside and let a referee count it. Ok, they now had to fill neutrals (to avoid seki) and eliminate (some) defects before they "stop", but so what? Don't they have to do this anyway? If we want to stick to tradition and separate both phases, we could also let the game go on until the second stop is made - the first stop to be made when turn possession becomes meaningless. But I hesitate strongly to punish someone who misses this point. How about this instead: After (again) the first stop, both players step aside and let the referee compute the perfect result for each in case each had the second turn. If BSW means "Black's score if White starts" and BR means "Black's result" etc., this could be expressed as: BR = BSW - WSW WR = WSB - BSB This also would give us a definition for "effective move" (without needing it here, however). None is around if BR = - WR which is the normal case. In the example C-19a above, if White had a territory of, say, 5 points (and no komi), this would lead to BR = 0 - 5 = - 5 WR = 5 - 6 = - 1 and both would have lost - the same as if no one requested resumption. If White had a territory of 7 points BR = 0 - 7 = - 7 WR = 7 - 6 = + 1 Black would still have lost, but White would have won - the same as if White had requested resumption. The interesting case is when White's territory would amount to 6 points BR = 0 - 6 = - 6 WR = 6 - 6 = 0 Again Black would have lost, but White at least would have got jigo. Not so with the resumption scheme: either both would lose or both would get jigo (since Black won't call for resumption). The last case shows that the "two results" scheme is fairer than the "resumption" scheme because nobody gets more than his worst case, but at least he gets that. If no effective move is around, both schemes meet and produce what we're used to. But since JRG89 tells us a different story and I'm no longer eager to cure it (this whole chapter is now more or less to show how deuced things are), I'll let it keep its resumption. Another reason is that resumption enables (by accident?) passes to be (trivial) ko threats, which was missing in the schemes above for simplicity. Fourth, if we could do without having to define "effective move", we should. It can be questioned anyway if referring to it wasn't more an example than a rule. Fifth, nobody should have the feeling that he requested resumption too early, that he should have waited a bit longer. Sixth, rules shouldn't depend on the commentary. For instance, you have to read JRG89's commentary on Article 9 to be told that moves after the stop are "no moves as defined by the rules and need not be played according to the rules" "if the players agree" and that "if a game is resumed, any moves played not in accordance with the rules during the period when the game was stopped are invalid". In the extreme: "Go is a game - look up the rest in the commentary". So, after considering all this, I'd like to (re)interpret Article 9 and 13 in this way: After each stop (two passes in succession) players get a chance to agree to an arbitrary final configuration (includes prisoners). If they do, this configuration is counted in accordance with JRG89's objectively defined terms (life, death, seki, territory). If no agreement is reached, both privately fix their answer to the question if they would like to resume (e.g. write it down). If both refuse resumption, both lose. If just one refuses, he starts in the resumption. If nobody refuses, the one to start in the resumption is chosen randomly. Each resumption starts, of course, with the configuration after the last stop. To come to an end, there's only one further (final) resumption allowed in case they dare to annoy us with an "empty" resumption (one that consists just of passes). Should this final resumption stop, its configuration is counted as if agreed upon. First, this scheme will certainly come to an end if at least one of the players wants to and no (balanced) cycles are around. Why? Because if your opponent keeps on playing stones this will eventually lead to a configuration consisting just of (1-point) eyes and live stones of your color. Then: He has to pass. You pass too. Stop. No agreement. You call for resumption. He starts with a pass. You pass too. Empty resumption. No agreement. You call for a (final) resumption... An unbalanced cycle won't "help" your opponent either. After you have piled up enough prisoners, you stick to passing. Since we play without suicide, he again can't play stones forever and will be caught by the final resumption. The only way for him to go one forever is to use a balanced cycle. But then he already could have prevented the first stop and forced you to agree to no outcome - so this scheme is out of charge. Note that allowing a final resumption isn't really necessary, but it would be annoying if the player starting in a resumption would have to play a neutral just to make sure that his opponent doesn't end the game too soon. You only have to keep an eye on this in the final resumption. Second, this scheme allows passes as (trivial) ko threats. For instance, 0 0 B 0 wont be won by Black: Black captures. White passes. Black passes. Stop. White calls for resumption. Black fills false eye. White recaptures. Black passes. White fills ko. Black passes. White passes. Stop... But what if Black passes instead to fill his false eye? Would White be allowed to recapture after three passes? Very good question! This is exactly one of this little annoying questions rule texts are there to answer us. Back to the rule book: Article 6 (ko) A shape in which the players can alternately capture and recapture one opposing stone is called a "ko". A player whose stone has been captured in a ko cannot recapture in that ko on the next move. The question is if a pass is a "move". If not, the three passes wouldn't count as moves, the recapture would be the "next" move, and White wouldn't be allowed to do so. But JRG89 doesn't make this clear. If you read the comment, you get the impression that a pass isn't a (trivial) ko threat: [...] White cannot [...] recapture unless he first plays at least once elsewhere [... ,] called a "ko threat". If a player recaptures on the next move without making a ko threat, he forfeits the game [...]. This could even mean that White wouldn't be allowed to recapture in the case where Black has filled his false eye because White himself hasn't yet made a "ko threat". JRG89's text isn't of much help. By now you should appreciate formal rule texts - undisturbed by comments that don't address every case and thereby make things worse. But since I don't trust this comment and favor passes to be moves as well as (trivial) ko threats anyway, I'll feel free to reject this interpretation. This has consequences: The nice one of passes being (trivial) ko threats, but also that of a single double-ko seki leading to no outcome - what I think is logical, because it exploits a weakness one can't get rid of, but may not be Japanese tradition. In case you don't like this, you may be happier with "there's at most ONE resumption". (By the way, "no resumption may be empty" isn't a good idea. The one behind will disagree without calling for resumption, but the other neither wants to because he doesn't wants to be force to add a stone when his opponent passes: both lose. And fixing this with "neither calls for resumption is agreement" would produce garbage in case of a forgotten effective move.) Third, all complex questions that ask for an objective answer like those concerning life and death or those about the existence of an effective move aren't part of the ending scheme any more. This only makes things unnecessarily complicated. [W-RJ3] is of this sort, quote, Hypothetical play is to be applied after the game stop and before the game end for determination of allowed dame and necessary defensive moves inside territory [...]. This intentionally restricts what can be done after the stop. Now, after each post-stop move a re-evaluation of what is dame and what is territory would have to be made. Besides being a nightmare for all referees, this wouldn't work as expected. In the second example above, White couldn't defend his 3x2 "territory" after Black takes one neutral because it still is in seki via the other neutral - it's technically not yet territory. White would have to resort to resumption - silly. Of course, this could be corrected by replacing "territory" by "eye points", but why bother at all? Why not instead let players agree to whatever they want to? Each of them will certainly watch for himself (safeguarded by the no-agreement path). Unfortunately, above's re-interpretation still leaves a chance to silently avoid defect elimination without any risk: 0 0 B 0 If they stop, agree to fill the neutral, and then let the referee count, White will win by 1 point - despite having seki aji (Black enters at A). It's a shortcoming of JRG89 that it only focuses on the status of stones, not on that of area. Since the possible seki doesn't harm the white stones' status of being alive, they surround territory according to JRG89. But if Black is aware, calls for resumption, and after White's pass fills the neutral, he gives White (who may be unaware) a hint and destroys his last chance to win. So, there's a tension between, on one hand, always to fill all neutrals before stop to avoid hints and, on the other hand, to leave them empty as tradition calls for. (This tension also exists under LJRG, but to a lesser degree because all defects, including seki aji, spoil territory. In most cases spoiled territory is a good enough compensation for unexploited aji. In the case above it's even better: Black spares a throw-in.)
Inevitably, I already used the term "territory" above. Let's now take a look how it actually is defined by JRG89. LD-9 JRG89: All stones inside are dead, but not in territory. Each player starting can capture the other without enabling a new uncapturable stone, so all stones inside are dead. By the way, this example shows clearly that the confirmation about life and death, Article 7 is talking about, is meant hypothetical because under normal play, with or without the pass-for-ko rule, of course only one group would die, never both. But what about the second part "not in territory"? What if sly White claims that the corner is his territory? Didn't he surround all these dead stones? Here's how JRG89 defines territory: Article 8 (territory) Empty points surrounded by live stones of just one player are called "eye points". Other empty points are called "dame". Stones which are alive but which posses dame are said to be in "seki". Eye points surrounded by stones that are alive but not in seki are called "territory", each eye point counting as one point of territory. And later JRG89 explains: Article 10 (determining the result) 1. After agreement that the game has ended, each player removes any opposing dead stones from his territory as is, and adds them to his prisoners. [...] But weren't we just told that territorial points (or locations) are special eye points and that eye points are empty? There never would be anything to be removed from them. And what's the exact meaning of "surrounded"? Is, for instance, Tokyo surrounded by water? Japan is, and Tokyo is a part of it. On the other hand, not every step crossing Tokyo's border will be wet. To solve the last problem I'll interpret "X is surrounded by S" as "S is the set of all locations that X has contact to but that don't share X's color". If you recall the definition of "contact", this means the same as that S is the set of all locations that can be reached from X by repeatedly moving to neighbors that all share X's color (including the case of staying on X) before finally moving to one that does not (empty is a "color" in this sense). Furthermore, I'll interpret "X posses Y" as "X has contact to Y". But this only makes sense if we clear the paths, that's, remove dead stones - which also solves our first problem that territory can be underneath dead stones. But if we remove ALL dead stones above, the corner indeed would become white territory. It seems that this isn't JRG89's intention, quote, If the game ends like this [LD-9], Black and White are both dead [their stones, of course] but none of the stones can be removed. According to Article 8 there is no territory. Therefore I'll guess only dead OPPOSING stones are removed when we check for territory of one side. Article 8 would then have to be fixed like this (adding the [...] and trying to delete nothing of the English translation of the "sacred" original text): Article 8 (territory) Empty [or with dead stones occupied] points [that are and only are] surrounded by live stones of just one player [if but not necessary only if his opponent's dead stones would be removed] are called [this player's] "eye points". [...] The additions also try to fight three ambiguities: 1. One could believe that it's also fine if not one live stone is surrounding, enabling shared territory. 2. One could believe that all live stones that surround have to belong to the same player without excluding the possibility that other things that aren't live stones also may surround. 3. One could believe that the condition on the points should only hold if opposing dead stones are removed but not if they stay. All three beliefs are wrong. The single dead white stone in LD-9 would now spoil White's ambition for territory. Don't confuse the abnormal not-played-out situation above with a "normal" one like this: The white stones are dead. But couldn't White declare the single black stone to be dead too, spoiling Black's territory at the left? No. It can't avoid capture, that's right, but Black can produce a new uncapturable black stone (on the same spot) if White captures. The single black stone is of this odd "capturable alive" kind. It seems that JRG89 is now producing reasonable results also in, admittedly, silly cases - but look at this comparison:
Proving stones to be alive is a hairy job under JRG89. If they can not be captured, they're alive. This is the simple case. But if they can be captured, you're confronted with the problem to prove that one can't do so without enabling a new uncapturable stone. And if you think you found one, don't miss to check that it really is ENABLED by the capture. This last check is likely to be forgotten - as we'll see. Since "dead" is defined as not being alive, its proof is as hairy. You always have to prove not only that those stones can be captured, but also that one can do so without enabling a new uncapturable stone. In both cases the delicate part is to prove if the capture enables the new uncapturable stone or not. Here's an example where even the creators of JRG89 failed: LD-1 JRG89: Seki - no territory. [?] JRG89's original comment: Black and White are both alive because if either side plays A, a cut or snapback follows, resulting in new stones that cannot be captured by the opponent. Since A is a dame point, the position is a seki. But it's wrong. Certainly, new uncapturable stones will pop up after a capture, but they must be ENABLED by the capture to qualify the captured stones as being alive. If White captures the 4 black stones, Black will produce a new uncapturable stone at B. Since White could prevent this simply by doing nothing, this stone was enabled in the sense of the rules. So, the 4 black stones are indeed alive. But now, what if Black captures the single white stone? White can recapture and will also produce some new uncapturable stones - underneath the 3 black stones neighboring B. Couldn't Black argue that this isn't enabled by his capture because he - taking the second turn - and restricting himself to a fixed number of stones couldn't prevent any of those new uncapturable stones? Yes indeed, he can. Here's the simple sequence:
BESTIARY
This chapter shows how diverse positions would be counted after the game ended. The first 25 beasts are the 25 life and death examples of JRG89. It should be mentioned that we don't care how the players have gone through JRG89's odd ending procedure. We'll just judge what they show us as their final position on board - prior to any removal of dead stones. Therefore I completed the examples by adding outer stones and eyes, and erasing irrelevant locations. So don't mind if a grid is shaped like a L or U. I checked not to erase too much, triggering play "underneath" stones or enabling sekis, but if any flaws slipped through: please inform me. The comments only mention and count those locations that are not obviously part of 2-eyed groups. Please keep this in mind when reading something like "Black controls nothing". The official rules of 1989 are called "JRG89" (see [P-ARS90] or [W-FH1] for an English translation of the full rule set and all accompanying examples) and this new rules "LJRG". For the purpose of easing comparison, I'll use following terms of JRG89 also in the context of LJRG. Here's their translation: 1. Locations belong to a player's "territory" only if he controls them and they aren't colored with his color. 2. Stones are in "seki" only if they sit on locations controlled by nobody. 3. Stones are "dead" only if they sit on locations controlled by their opposite color. 4. Stones are "alive" only if they are not dead. Under JRG89 it's possible that dead stones sit in neither sides territory and don't count. This never is the case under LJRG. The beasts of JRG89 - in their corrected version - that LJRG doesn't agree with are 1, 6, 8, 14, 15, 16, 17, and 24. The beasts of JRG89 I've dared to correct JRG89's result are 1, 5 (marginally), and 23. 18 was corrected by Robert Jasiek.
Beast 1 "three points without capturing" or "torazu san-moku" JRG89: Seki in lower left corner. [wrong original version] JRG89: 1 dead white stone in black territory. [my corrected version] LJRG: Seki in lower left corner. We already went through this beast above. I agreed that under JRG89 the block of four black stones is capturable alive, but I disagreed on this for the single white stone - it is dead: It can be captured, and it can't claim a new uncapturable white stone to be ENABLED by this because all new white stones that would pop up (underneath the black block except 2-2) couldn't be prevented by Black anyway. LJRG won't give anyone control of the 6 locations in the corner because every claim that includes them can't lock them all, and only including some of them isn't possible because the claim wouldn't be bordered. White should have captured. He would gain two points and win by 1 instead to lose by 4 (JRG89) respectively 1 (LJRG) - provided Black isn't two ko threats ahead, letting him save a jigo.
Beast 2 JRG89: Seki - no territory. LJRG: Seki - no territory. LJRG: Neither side can lock anything taking the second turn.
Beast 3 "hane-seki" According to [W-Ing91], hane seki was discovered by Kaise Takaaki. JRG89: Seki - no territory. LJRG: Seki - no territory. Whoever captures three stones will lose everything in this fight after his opponent occupies the center of the cleared area. Neither does it make sense for White to capture the single black (hane) stone because Black gains too much liberties by snap-back. Under JRG89 all stones are therefore alive. The three big groups are uncapturable alive. The three short ones are capturable alive. Under LJRG Black controls nothing because he can't lock anything. White only controls the obvious nine locations at the left side. He can't lock the whole board, and, even if he can't be prevented from extending his 2-eye formation on the left side as far as to the center stone of his 3-stone group, he can't extend his claim this far because it wouldn't be bordered any more.
Beast 4 "one slips" JRG89: Seki - no territory. LJRG: Seki - no territory. This may not look familiar. Normally "one slips" is set up on two joining sides of a bigger board, having the eye in the corner, but let me spare as much as possible. Black can't claim the whole board under LJRG because he can't capture both white groups: 3 at A 3 at A prevented 2 eyes on the left side, but after 4 Black can't again prevent 2 eyes on the right side - he has to hurry on the left. Therefore he can't claim the whole thing. But couldn't he just claim, say, the left one? No, because his worst case would then look like this: 0 0 W 0 Now Black has lost his precious liberty on the right side and won't be able to capture the five white stones at the left nor fill his (smaller) claim with a 2-eye formation: it was not independent from the context! Black should have continued to gain 5 points (both capture 6 stones, but Black ends up with a 7-point territory compared to only 2 points in White's territory).
Beast 5 JRG89: Seki. The enclosed black and [wrong original version] white stones are all alive JRG89: Seki. The single white stone [my corrected version] is dead, but in no territory. LJRG: Seki - no territory. In analogy to beast 1, I explained above that the single white stone is dead under JRG89 because it certainly can be captured, but it can't claim a new uncapturable white stone to be enabled by its own capture. But since the 5 black stones left of it posses dame, this stone is in no territory and won't be counted. If under LJRG Black doesn't claim the 6 corner locations, he won't have the liberties gained there to capture the 3 white stones. But if he extends his claim by those 6 locations, he won't be able to fulfill it totally: White will intrude permanently after the removal of the 4 black stones. White, on the other side, could also try to extend his claim by the 6 locations in the corner, but now Black will refute this claim by a play underneath the stones.
Beast 6 "long life" JRG89: Dead black stones in a white territory. LJRG: No territory. LJRG: White doesn't control the left side because Black will start and prevent 2 eyes with A again and again. Since White has to fulfill his claim without going beyond a repeated situation, he fails. Black can't lock anything either because White would use his right to move first to make "knife five" at A.
Beast 7 "bent four in the corner" JRG89: Dead white stones in black territory. LJRG: Dead white stones in black territory. LJRG: Black can't be prevented from locking the whole board because he'll win the ko due to White's lack of ko threats - not to speak of an internal one. (If you wonder, it's called "bent four" because this form has to be sacrificed by Black in a proof. See beast 31 for a variant.)
Beast 8 "stable triple ko" or "moonshine double-ko seki" JRG89: Dead black stones in white territory. LJRG: No territory. JRG89: If White starts, he can capture all black stones inside using the pass-for-ko rule. Therefore they are dead. Black can't capture the white stones at the right because White defends by cycling. Therefore they are alive. You may ask if the single white stone at the right isn't dead. This would spoil the territory. The answer is no: this stone is capturable alive because White will produce a new uncapturable stone underneath it - which Black could prevent by passing. LJRG: Black can't lock anything, but White neither. Black doesn't even has to take the first turn. If White takes the left ko, Black flips the double ko and recaptures, since in the hypothetical proof the normal ko rule is still in use under LJRG. White can't ignore the flip because this area also belongs to his claim and he has to fill up the whole claim with a 2-eye formation. By the way, a triple ko of exactly this type appeared between Leszek Soldan (6d, Poland) and Christoph Gerlach (6d, Germany) in round 6 of the EGC 1999 - with Christoph enjoying the eye. Since Ing 1991 rules were in use, an expert had to be consulted (guess who). Far from being impressed by his expertise, only the presence of a similar position in the rule booklet finally convinced them: Leszek's stones being "disturbing dead" (indeed, VERY disturbing), prohibiting him to repeat and losing him the game and the day. [RGG100899] [DGZ0799]
Beast 9 "resolving a direct ko" JRG89: All stones at the right are dead, but in no territory. LJRG: No territory. LJRG: Nobody can lock anything. In case White claims, Black captures and lives in White's claim. In case Black claims, White takes the ko and wins it.
Beast 10 "approach-move ko" JRG89: Dead white stone in black territory. LJRG: Dead white stone in black territory. JRG89: The difference to LD-9 is that, after White has captured the single black stone, Black will use the pass-for-ko rule to win the ko - the extra liberty gives him time for a ko-opening pass - and produce the new uncapturable stone: the single black stone is capturable alive, and the single white stone is dead. LJRG: White can't claim being able to lock anything since Black simply captures him. But Black can claim being able to lock the corner because the extra liberty gives him the time he needs to win the ko: he uses a pass as a (trivial) ko threat. After White ataris, Black recaptures and succeeds.
Beast 11 "false eye and double-ko seki" or "moonshine life and double-ko seki" JRG89: The white stones in the left position are dead in territory. LJRG: The white stones in the left position are dead in territory. LJRG: LJRG has no problems here at all. Since Black can't and doesn't claim anything in the double-ko seki, it is removed and filled up with permanent white stones when proving Black's claim for control at the left. And since no internal ko threats on the left side exist for White either, nothing can annoy Black. There was a centuries lasting debate in Japan on how to decide this situation, starting with monk Nyobutsu's decision in the 13th century that the false-eye group is not dead. This is the global view. The rivaling local view called it dead. The decision flipped back and forth over the time. The rules of 1949 as well as those of 1989 apply the local view and call it dead. LJRG agrees in this case, but not when the attacking group depends on the double ko (see beast 8). It has to be mentioned that the exact position Nyobutsu was confronted with is lost - it was only assumed to be of the independent type. [W-MSO1]
Beast 12 "ten thousand year ko" or "mannen ko" JRG89: Seki - no territory. All stones alive. LJRG: Seki - no territory. LJRG: Neither side can lock anything. If Black claims he could lock the board, White simply connects (to pass would also work). Should Black then sacrifice his stones, White will live. And if instead White claims he could lock the board, Black passes until White approached. Then he takes the ko, captures the remaining white stones after White's pass, and builds two eyes in White's claim. JRG89: Black can't capture White by taking the ko and approaching because White would have time to pass for the ko, but White can't capture Black either because after his approach Black takes the ko, and passing for it is now too slow. But what about the single white stone? Is it dead or alive? JRG89's official commentary states that all stones are alive. Since the single white stones is certainly not uncapturable, it must be capturable alive. Black could try to refute this: Black captures it, White passes for the ko, and now Black passes too (instead to approach as told in [W-RJ3]). Where will White now produce his new uncapturable stone? Of course, he recaptures the ko, but after Black passes again for this ko we have the same situation: the (new) single white stone is still capturable. The solution is that White connects the ko and thereby makes the former stone uncapturable. Note that the connecting stone itself doesn't qualify to be the new uncapturable stone because Black never could have prevented it anyway. Note that this example suggests that JRG89's new uncapturable stone doesn't has to be uncapturable in the very moment of its staging. It further suggests that passes for a ko don't take part in ending JRG89's hypothetical play. Note that if the ko is in a state as if Black captured last, White can't be prevented from gaining a point before the end by capturing and connecting (under either of the two rule sets). Now imagine that sly White is behind and refuses to do so, just for the purpose of not to let the game end. This is possible if passing is unrestricted and game end is defined in a complex way like "the game is over if neither player can gain anything more". This definition is quite popular in go introductions and at least is better than "the game is over if both players agree", but it leads to an impasse. Black could only overcome White's tactics if he can afford to let his group die by filling the ko. Very strange. If you now think this is just the mad fantasy of a rule addict like me, you'll be surprised to hear that exactly this once happened. In round 2 of the 1928 Autumn Oteai, Takahashi Shigeyuki pulled this trick against Segoe Kensaku. Segoe was clearly ahead, despite giving two handicap stones. After Takahashi made move 302, there were only 12 neutrals and one mannen ko left. Takahashi had the option in it: rest omitted Segoe went on and filled the first neutral, expecting Takahashi to take the ko and to connect it subsequently since neither side had reasonable ko threats, but Takahashi filled the second neutral instead. They continued in this manner until Takahashi eventually filled the last neutral. Segoe, having no more left to play, laughed and expressed his bewilderment. Referee Iwasa Kei told Takahashi that he should have made seki long before since the game already was over. But Kubomatsu came over and claimed it to be a void game because no game can be over with a ko still pending. Segoe expected the mannen ko to be treated as seki since there were no reasonable ko threats around, but Takahashi just didn't believe that it was a mere seki and wanted the game to be treated as finished - but without having achieved a result (which isn't far from saying that it hasn't ended). Wow, what a mess. All other games were suspended because the outcome of the whole East-West match was affected. The dispute raged for a month, without any agreement. The final ruling of the referees was We declare that in the position up to move 302 White [Segoe] is adjudged to have won. However, this decision is limited to this game. Additionally, Takahashi was said to haven't lost because the fundamental problem still was waiting to be solved. [W-MSO2] "Just" 21 years later, 1949, Japan created its first written go rules.
Beast 13 JRG89: Seki - no territory. All stones alive. LJRG: Seki - no territory. LJRG: Surely White can't claim to be able to lock anything because Black, getting the first turn, simply passes, letting it stay a seki and preventing White from building a 2-eye formation. If Black claims the whole board, White passes too. He can't prevent Black from sacrificing 3 stones and start a ko in the lower left corner, but since White captures first in this ko and there are no internal ko threats for Black, this is useless for Black.
Beast 14 JRG89: Dead white stones in black territory. LJRG: Seki - no territory. JRG89: Black can capture White if he has the first turn. White, on the other side, can "only" produce a seki with the first turn. White should have made seki by throw-in before the end and accept losing a point (if Black doesn't forget to capture before end). LJRG: Both sides can make a seki if they get the first turn. White throws in a stone. Black just passes. So nobody can lock anything because the claiming player has to do with the second turn. Notice that under LJRG White can avoid losing a point by throw-in if the ko threats favor him. A claiming player can never base his claim on (non-trivial) ko threats (regardless if internal or external), but, as this example shows, the refuting player CAN - provided getting first turn compensates for losing external ko threats (in the proof).
Beast 15 JRG89: Dead white stones in black territory. LJRG: No territory. LJRG: Black can't lock anything because White starts a ko in the upper right corner and then ataris the single black stone with A. Black can't exclude this ko threat because he has to include this stone in his claim for the purpose of bordering - in this sense the ko threat is "internal" to the upper right corner. White neither controls anything because each of his claims will suffer from white stones in atari - Black starts, captures them, and intrudes. If Black wants to avoid above's disaster, he has to connect at A before the game ends. White can then gain another point by starting the ko - even if he lacks ko threats. After Black captured in it, White simply passes. Since a direct ko would prevent his lock, Black can't allow the game to end without filling it. By playing one stone more than White inside his territory he loses a second point. The same would happen under JRG89, except that Black could omit A: Black loses only one point.
Beast 16 JRG89: Dead white stones in black territory. LJRG: Seki - no territory. LJRG: Similar to LD-8. If Black wants to declare the white stones on the lower side dead, he has to include his 7-stone group at the right to close the border. But this group needs 2 liberties. So Black has to extend his claim over its eye and the lower ko. Bordering is ok, but one stone in the border again is in atari. Black is forced to add the rest of the right side to his claim, but then White will exploit the double ko for ko threats and refute the claim by cycling.
Beast 17 JRG89: Dead white stones in black territory. LJRG: Seki - no territory. LJRG: Again Black can't declare White's corner group to be dead because of the double ko he has to include in his claim. White will exploit it to defend the liberty in ko on the right side. If Black tries to bring White down to 1 liberty in the corner to make the ko threats worthless, a further ko in the corner will start. Black captures first in it, but since White still enjoys his outer liberty, he has time to flip the double ko, recapture, and win this ko.
Beast 18 "bent four i.t.c. with irremovable internal threat" JRG89: Dead black stones in white territory. [wrong original version] JRG89: Seki. [RJ's corrected version] Stones in the double ko are dead, but in no territory. LJRG: Seki - no territory. JRG89: For the longest time I took JRG89's example for granted. I had to stumbled over [RGG151199] to get it. Of course, Robert Jasiek is right. White has no chance to capture black stones under pass-for- ko, except those in ko. This is because he has to omit a pass in the double ko to make atari via bent four. His stones are caught and he has to throw a stone into the cleared area to prevent two eyes. Now Black doesn't setup the ko as usual (and maybe I did), but simply captures in the double ko since White isn't yet allowed to do alike. It's not a matter of ko threats, it's just a lack of liberties. (By the way, Robert Jasiek's suggestion to solve this problem by letting passes unlock ALL kos wouldn't work. Imagine two approach- move kos (beast 10) hanging around. You start one and approach when your opponent passes. He recaptures. You do the same in the second. Then you pass, unlocking both kos simultaneously. Either you save your stone, or you produce a new uncapturable one: not JRG89's intention.) LJRG: The bent four isn't dead here because White can't ignore the threats in the double ko. If he does, capturing the black stones on the right side, Black would capture in the second-step ko and build two eyes in White's claim. Of course, White can't exclude the double ko from his claim because the big white group needs these liberties. So under LJRG bent four isn't dead in every case any more - but it wasn't anyway (see beast 31). Notice that in this special situation White can't enhance his proof by removing the internal ko threats during the proof before starting the ko, because he needs the liberties. In most other cases he will be able to do so because he can hold back the ko. Therefore bent four in the corner still is dead in most cases under LJRG - except when INTERNAL ko threats are irremovable, like here. Whoever invented this example: THANK you - and I hope you're pleased by LJRG's ruling (even if this isn't such a big deal any more since I realized that JRG89 in fact rules in the same way). (Also included in [W-ST] - chapter VI, diag. 11.)
Beast 19 JRG89: Dead black stones in white territory. [unchecked by me] LJRG: Dead black stones in white territory. Under LJRG White will claim that he can lock the whole board. One path of the proof would go like this:
| 3 passed | |
Beast 20 JRG89: Both are alive. Seki. [unchecked by me] LJRG: Both are alive. Seki. Under LJRG White's claim of being able to lock the whole board will be refuted like this:
| 3 passed | |
| 1 passed | |
| 17 passed | |
Beast 21 JRG89: Dead white stones in black territory. [unchecked by me] LJRG: Dead white stones in black territory. Under LJRG Black claims that he can lock the whole board. If White starts with a pass, things could continue like this:
| 1 passed | |
| 1 passed | |
| 13 passed | |
| 24 passed | |
Beast 22 JRG89: Dead white stones in black territory. LJRG: Dead white stones in black territory. LJRG: Black claims the whole board. White starts but finds nothing better than to pass. Black captures 3 stones and conquers the right side, fueled by the liberties he has gained.
Beast 23 JRG89: Dead white stones in black territory. [wrong original version] JRG89: Seki. All stones alive, except 2 [my corrected version] dead white stones in the upper right corner and 3 dead white stones in the lower right corner - but all 5 not in territory. LJRG: Seki. No territory. White certainly can't capture the black stones. Could Black capture the white stones in the mid? No. The proof below holds for both rule sets. Under LJRG Black claims the whole board and White gets the first turn. But since White passes, we'll label black stones with odd numbers in this case too. Under LJRG we could use the internal ko threats in the seki at the left, but (again to unify) we'll do without them here:
| 9 passed (for ko under '89) |
| 0 3 W 0 | 0 6 W 0 |
| 1 8 W 0 (8 passed) | 1 9 W 0 |
Beast 24 "filling dame to obtain territory - two-stage ko" JRG89: Seki - provided game ended. White should fill A, B, C to get 2 points. Black should fill A to get 3 points. LJRG: 2 points for White and 3 for Black - without filling. JRG89's Article 8 punishes contacting dame with seki. In the confirmation phase both players must therefore fill up dame before they end the game. There's no doubt that A is dame. It has contact to live stones of both colors. What about B and C? (In the following I use my interpretation of Article 8 above.) The white stone below B is dead. The one left of B is alive. If we remove dead white stones, B wouldn't qualify as eye point. Neither would it if we remove dead black stones. In both cases not only live stones of just one player surround B - it's dame. The same test shows that C is a white eye point. Since B is dame, stones alive contacting it are in seki. This is the case for the white stone left of B. This prevents the white eye point C from becoming (white) territory: not all of its surrounding stones (after removal of dead black stones) are alive and not in seki. And since C is a non-territorial eye point or eye point in seki, the stones contacting it are in seki too. And this finally also prevents the 2 remaining white eye points to become territory. White has to get rid of dame and eye points in seki if he wants to convert these 2 eye points into territory - he has to fill B and C. LJRG doesn't care about dame. Sekis are where nobody controls something. White certainly controls the 2 empty locations and the stones bordering them on the upper side, as does Black control the 3 empty locations and the stones bordering them on the lower side. Nobody certainly controls A. And B and C aren't controlled by White, even if he bordered them, because, depending on how far White extends his claim, one of the single white stones will end up as a border stone. Proof setup will atari this stone by the permanent black stones on the outside, letting Black capture, connect, and refute Whites claim.
Beast 25 "double-ko seki" JRG89: Seki. The single stones are dead, but in no territory. LJRG: Seki - no territory. LJRG: Nobody can claim anything here because nobody will be able to fill the board with a 2-eye formation - even if he were allowed to start. Since not one location is controlled by anyone, there certainly are no dead stones around.
Beast 26 "rattlesnake - ends colored alike" JRG89: Dead white stones in black territory. LJRG: Everything except the ends is a seki. JRG89 would argue as follows: Black ataris the, let's say, left white group by approaching. A flip in the double ko follows, but after the flip the white group is still in atari and both kos are waiting for their pass each. Nothing else will open them. Therefore Black has time to defend whatever White tries on the rest of the board, preventing any uncapturable new stones if needed, and eventually captures all white stones at the left. This proved that they are dead. Similar on the right. LJRG is more sensible. If Black claims to be able to lock the whole board, White will refute this by starting an endless cyclic attack, flipping the double kos. Black must keep up in those kos because he may not lose anything of his claim. Technically the proof - or better each path in it - will stop at the first repeated situation. And if Black tries to claim only one white group? His own center stones will be ataried by the permanent white stones filling up the rest. White will capture some and extend into Black's claim. I invented this beast to bring down one of my former rules. The false eyes aren't essential any more, but at that time their purpose was to force the rules to treat the double kos separately. As we've seen: LJRG does not. Notice that the rattlesnake can grow: Both arguments above still hold: JRG89 piling up dead white stones, and LJRG only counting the ends for Black. Why kill'em? Let'em rattle.
Beast 27 "rattlesnake - ends colored opposite" JRG89: I guess the 5 white stones at the left and the 5 black ones at the right are dead in territory, and the 2 stones in the center double ko are dead in no territory - but don't nail me down. I didn't check for the uncapturable new stone. LJRG: Only the ends count - 2 points for each.
Beast 28 "bent four with large internal ko threat" [0 3 B 2] JRG89: Dead white stones at the right and lower side in territory - Black wins by 25 points. LJRG: Seki - Black wins by 1 point. This example is taken from [P-Ing86]. Under JRG89 Black will never touch the bent four till game end. After end, ko threats are worthless due to the pass-for-ko rule. Therefore Black can capture the bent four and the seki collapses, demonstrating that they are dead. Under LJRG Black won't start the ko either because he'll lose 16 - 14 = 2 points, and after the end Black can't separate the ko threat from the bent four because his stones surrounding it would only keep 1 liberty in the lower right corner - not enough to lock the right side. And if he includes the lower left corner in his claim, the ko threat will make locking the whole claim impossible. Since empty locations only count if they are controlled, Black - controlling nothing - can't count the 2 corners he has surrounded on the lower edge. If the threat were worth 3 points less, Black should start the ko before game end.
Beast 29 "bent four with small external ko threat" [0 0 B 2] JRG89: Dead white stones on the left side in territory - Black wins by 15 points. LJRG: Dead white stones on the left side - Black wins by 15 points. This example is taken from [P-Ing86]. Under JRG89 the ko threat is worthless after the end due to the pass-for-ko rule. Therefore Black can hypothetically capture the bent four without giving White compensation, proving that it's dead. Under LJRG Black can separate the ko threat from the bent four because his stones surrounding the bent four don't depend on it - are independent from outer liberties. He therefore controls the left side, agreeing with JRG89.
Beast 30 "double bent four" [0 1 B 2] JRG89: Dead stones on the upper side, but not in territory - Black wins by 11 points. LJRG: Nobody controls the upper side - Black wins by 11 points. This example is taken from [P-Ing86]. If the game ended like this, JRG89 would declare all stones on the upper side to be dead but in no territory. The starting player can capture all - without allowing a new uncapturable stone. Note that both sides will avoid the ko in their proof because their opponent would capture first - a big advantage under the pass-for-ko rule. But all these dead stones aren't in territory because taking out dead stones of just one color won't produce eye points - always some surrounding dead stones remain to spoil it. Note that ignoring dead stones of BOTH colors would produce black territory. Since the advantage of having the first turn is lost after the end, Black would have done better if he had extended his 3 stones to form the bent four before game end. White will pass because he'll lose the semeai anyway. Black passes too, the game stops, and according to Article 7 all white stones are dead for the same reason as above. But the black stones now no more because, even if White starts, Black is still ahead in the capture race. The argument under LJRG is almost the same. If ended, nobody would control the upper side because the refuting player starts. Therefore Black continues the semeai by forming the bent four. White drops his hopes and passes. Black passes too. Since no ko capture preceded the 2 passes, the game has ended. Now Black claims to be able to lock the whole board. He's right because, even if White starts in his effort to refute Black's claim, Black still is ahead in the semeai. And a ko won't help White either because Black captures first and there's no internal ko threat. White, on the other side, can't claim anything because Black would then be ahead by 2 moves. The count then proceeds as under JRG89.
Beast 31 "bent four in the corner on 3x3" This is the smallest bent four in the corner on rectangular boards and - watch it - it is not of the common dead type. JRG89: Seki. LJRG: Seki. Since nobody can make 2 eyes, nobody controls anything under LJRG. Under JRG89 White proves that he is capturable alive as follows:
| 2 and 4 passed | |
| 12 at 10 |
Beast 32 "bent four in the corner on 4x3" Here's another minimization of bent four in the corner that's not of the common dead type (as Robert Jasiek falsely claims [W-RJ3]): JRG89: Seki. LJRG: Seki. If Black approaches (after the end), White won't capture (even if this would work too) but simply pass:
| 2 passed |
| 8,10 passed | 18,20 passed |
Beast 33 "Unsound pass-for-ko rule" JRG89: Black wins by 15 (jigo if resumed). LJRG: White wins by 1. This beast is essentially that from James Davies [RGG150696]. I just shrank it and swapped colors (to avoid White being a move ahead). JRG89 would not only call the black stones at the right dead, but also the white ones. Why? Because Black can capture them using the pass-for-ko rule: Black takes the upper ko and - after White defends his upper eye - also the lower ko. If White now wants to retake one of them, he first has to (identify it and) pass. But this lets Black take the third ko and White is lost. Since all those dead stones are in no territory, Black wins by 15. For this reason White will add a stone and a jigo will result. Note that White risks nothing by requesting resumption here because Black can't make any use of the first turn (without the pass-for-ko rule). LJRG will give White a 1-point win (16-15) because he controls the right side - as everyone would expect. There's no peculiar pass-for-ko rule that prevents him from retaking the older ko, saving his second eye, and eventually filling the whole right side with a 2-eye formation.
Beast 34 "Cyclops on 9x9" JRG89: Black wins by 1 (if not resumed). LJRG: Seki. JRG89 calls the black stones (capturable) alive because their capture enables new uncapturable black stones (on san-san, for instance). Therefore the eye in the center is territory. LJRG only laughs at this judgment and, of course, gives no one control of any location because neither side can lock the whole board (and Black neither can lock the whole board exclusive its center, of course). According to [W-RJ3] this is John Tromp's joke. Hope he likes how I named his baby. Here's how it may have looked right after birth: Area scoring: Black wins by 3. Stone scoring: Black wins by 2. JRG89: Black wins by 1. LJRG: Both score 0 - jigo.
CONCLUSION
This text presented precise rules to capture the essence of the Japanese Rules of Go, added some new ideas, and took a critical view on the official Japanese rules of 1989. The focus in this text was to give Japanese rules a solid base, not to prove that they're better than playing things out. Since I prefer diversity over global unification, I hope having done my best to save them from extinction. If, for instance, we would use pass stones as suggested above, we would effectively convert to area (or Chinese) scoring through the backdoor - be aware of this. One man's clinker is another man's nugget. Many of us got used to Japanese rules, many books explain the game in their terms, and, as was certainly shown here, they're not illogical at all - even if their opponents don't get tired telling us. Of course, the official rules of 1989 are no big help in this discussion - or do you want to defend that seki is an exception, that life and death is defined bizarrely, that the game may end with no outcome or even with both losing, that a game that seemed ended can be resumed, that unfilled neutrals enable the riskless avoidance of defect elimination, and, finally, that dependencies with internal ko threats are completely ignored (external ones have to be ignored if we don't want to play it out) ? Compare it with physics: if a theory explains things well, it stays in use, but if it fails to explain only a single phenomena, it has to be revised or be replaced by a new theory.
Could it be that LJRG are the logical,
loop-hole-free, unimpeachable,
and formal territory rules
most doubt could ever
be formulated, but
nevertheless
eagerly are
waiting
for
?
:
:
:
:
:
.:.
.:::::.
.:::::::::.
.:::::::::::::.
.:::::::::::::::::.
.:::::::::::::::::::::.
.:::::::::::::::::::::::::.
.:::::::::::::::::::::::::::::.
.:::::::::::::::::::::::::::::::::.
.:::::::::::::::::::::::::::::::::::::.
.:::::::::::::::::::::::::::::::::::::::::.
REF's
At this point many thanks to Georg Nassiokas for providing me with some of the material below. The references aren't sorted by author but by "channel": DGZxx Deutsche Go Zeitung (German Go Journal, 7+8'94=0794) GMRxx Go Monthly Review GR-xx Go Review (winter starts year) GWxx Go World P-xx paper, book, copy, or the kind RGGxx news://rec.games.go (sometimes meaning the whole thread) or groups.google.com/forum/#!forum/rec.games.go (formerly www.deja.com)(xx = ddmmyy = day month year) SL-xx http://senseis.xmp.net/?FrontPage W-xx WWW (http://...) [DGZ0669] "Gedanken zu einem seltsamen Unentschieden" Horst Hausa Deutsche Go Zeitung ("DGoZ"), 1969, No. 6, pp. 1.1.326-1.1.328, pp. 8.1.11-8.1.14 [DGZ0687a] "Der Meijin Titelkampf 1987 - 3. Runde - Der Alptraum" DGoZ, 1987, No. 6, pp. 46-47 [DGZ0687b] "Der Meijin Titelkampf 1987 - 4. Runde" DGoZ, 1987, No. 6, pp. 47-48 [DGZ0490] "Verbesserungvorschlaege zum Einstufungsystem von koreanischen Berufsspielern" Kang Chol-Min DGoZ, 1990, No. 4, pp. 38-40 [DGZ1093] "Honinbo-Partie: Ewiges Leben" James Davies (transl. Klaus Blumberg) DGoZ, 1993, No. 10, p. 16 [DGZ1293] "Kommentar zum 'Ewiges Leben'..." Werner Fabry DGoZ, 1993, No. 12, p. 13 [DGZ0794a] "Japans staerkster Amateur" Klaus Blumberg (transl.) DGoZ, 1994, No. 7+8, p. 8 [DGZ0794b] "Tong-Yang Secuirities Cup" Klaus Blumberg (transl.) DGoZ, 1994, No. 7+8, p. 8 [DGZ0994] "Hoefliche Eroeffnung" Christoph Gerlach DGoZ, 1994, No. 9+10, p. 14 [DGZ0395] "Rui - Feng (2)" DGoZ, 1995, No. 3+4, pp. 22-23 [DGZ0595] "Kato - Cho (1)" DGoZ, 1995, No. 5+6, p. 16 [DGZ0796] "Go auf dem runden Brett" Harald Schwarz DGoZ, 1996, No. 7+8, pp. 50-51 [DGZ0198a] "23. Tengen, Game 3" Klaus Blumberg (transl.) DGoZ, 1998, No. 1+2, p. 12 [DGZ0198b] "Go-Probleme" Andreas Fecke DGoZ, 1998, No. 1+2, p. 36, problem 1 [DGZ0598] "Die Benimmecke der DGoZ" DGoZ, 1998, No. 5+6, p. 41 [DGZ0799] "43. Go-Europameisterschaft in Podbanske/Slowakei" Christoph Gerlach DGoZ, 1999, No. 7+8, pp. 15-16 [DGZ1099] "24. Meijin" Klaus Blumberg (transl.) DGoZ, 1999, No. 9+10, p. 8 [DGZ0102] "Regeldisput am Ende der 5. Kisei-Partie" N.N. DGoZ, 2002, No. 1, pp. 24-27 [DGZ0202a] "26. Kisei" Thomas Rolle DGoZ, 2002, No. 2, pp. 32-33 [DGZ0202b] "Problemgo" Andreas Fecke DGoZ, 2002, No. 2, p. 44, problem 4 [DGZ0402] "46. Go-Europameisterschaft in Zagreb" Guido Tautorat DGoZ, 2002, No. 4, p. 14 [DGZ0502a] "Kiel" Juergen Beetz DGoZ, 2002, No. 5, p. 7 [DGZ0502b] "Bochum" Andreas Fecke DGoZ, 2002, No. 5, p. 9 + 32 [DGZ0502c] "6,5 Komi" Thomas Rolle DGoZ, 2002, No. 5, p. 23 [DGZ0602a] "40. Ama/Pro Honinbo" Thomas Rolle (transl.) DGoZ, 2002, No. 6, p. 21 [DGZ0602b] "50. Oza" Thomas Rolle (transl.) DGoZ, 2002, No. 6, p. 22 [DGZ0602c] "Karl-Ernst Paech zum 80. Geburtstag (3)" Karl Scheitler DGoZ, 2002, No. 6, pp. 35-38 (37) [DGZ0103a] "Abschaffung des Oteai" DGoZ, 2003, No. 1, p. 31 [DGZ0103b] "Ausschreibung der Vereins-DM" DGoZ, 2003, No. 1, p. 38 [GMR0469] "Famous Games [...] XII" Go Monthly Review, No. 4, 1969, p. 53 [GMR1069] "Takagawa beats Go Seigen by a rule" Go Monthly Review, No. 10, 1969, pp. 17-23 ["No komi" is wrong: it's 4.5] [GR-Au73] "The 1973 Honinbo Tournament" Go Review, Autumn 1973, 4th game, p. 17 [GR-Sp74] "From Iwamotos sensei's One Page Lesson" Iwamoto [Kaoru] Go Review, Spring 1974, p. 78 [GR-Su74] "Rin Kaiho's Fan" Seichi Ezaki Go Review, Summer 1974, pp. 31-36 [GR-Wi75] "Meijin Title Match: 5th Game" Go Review, Winter 1975, pp. 8-19 [GR-Au75] "Honinbo Title Match: 7th Game" Go Review, Autumn 1975, pp. 16-22 [GR-Sp76] "14th Meijin Title - 7th Game" Go Review, Spring 1976, pp. 29-37 [GW05] "The Chinese Rules of Go" James Davies Go World No. 5, Jan-Feb 1978, pp. 30-40 [GW45a] "When Is a Ko Not a Ko?" Bob Terry Go World No. 45, Autumn 1986, pp. 58-60 [GW45b] "Why Not Eliminate the Irrational in Go?" Kudo Norio, O Meien, Murakami Akira Go World No. 45, Autumn 1986, pp. 60-64 [GW50a] "Strange and Wonderful Shapes" Haruyama Isamu Go World No. 50, Winter 1987/88, pp. 16-22 [GW50b] "The Professional Rating Tournament" John Power Go World No. 50, Winter 1987/88, pp. 47-52 [GW50c] "The Suspicious Jigos" Nakayama Noriyuki Go World No. 50, Winter 1987/88, p. 53 [GW60] "Monster Go" John Fairbairn Go World No. 60, Summer 1990, pp. 46-48 [GW71a] "A Commemoration of Dr. Yang Liansheng's Contribution to Goe Rules, Part One" Ing Chang-Ki Go World No. 71 [no season], pp. 7-13 [GW71b] "Where Is the '$1,000 Ko'?" Elwyn Berlekamp & Yonghoan Kim Go World No. 71 [no season], pp. 65-80 [GW72] "History of Codification of Goe Rules" Ing Chang-Ki Go World No. 72, Spring 1995, pp. 12-13 [I've no idea why Ing calls it "Goe"] [P-ARS90] "The Japanese Rules of Go" Anton Steiniger (ed.) ARS electronica brochure, 1990, pp. 97-117 [P-BZHZ] "Spielklassenberechnung nach der Karlsruher Methode" Bodo Zinser & Hans Zschintzsch paper copy [P-DB] "Live in the Game of Go" David B. Benson Computer Games II, D.N.L. Levy (ed.), 1988, pp. 203-213 or webdocs.cs.ualberta.ca/~games/go/seminar/2002/020717/benson.pdf [P-IK] "Go - Das faszinierende Brettspiel aus China" Kaoru Iwamoto [family name given last] 1984, p. 150, dia. 4 [P-JDRB] "An Introduction to Go" James Davies & Richard Bozulich 1984, pp. 10-11 [P-JIE] "Go: Battle in Black and White" James Davies Japan - An Illustrated Encyclopedia, pp. 460-461 [P-MK] "Go - Die Mitte des Himmels" Michael Koulen 1994, p.31, p. 127 [P-Prag93] "Strange Dispute" Brian Timmings, George ? (ed.), Niek van Diepen Newsletters 3 and 5, European Go Congress, 1993, Prague [P-Ing86] "The SST Laws of Wei-Ch'i" (1986 version) Ing Chang-Ki [P-WD] "Das japanische Brettspiel Go" Winfried Doerholt 1978, Falken-Verlag, p. 12 [RGG150293] "Re: Sealed moves and morality" Wilfred Hansen [RGG011093] "Re: How strong is a professional?" Niek van Diepen [RGG090595] "A fun thing...the PHINWHEEL KO" Bill Taylor [RGG090895] "Lasker-Maas rules for the game of Go..." Robert Elton Maas or www-2.cs.cmu.edu/~wjh/go/tmp/rules/Lasker.html (By the way, it's Edward Lasker, not the famous Emanuel) [RGG300196] "Re: A question about territory" Eric Osman [RGG150696] "Problem in Japanese rules" James Davies [RGG010997] "Re: Simple Rules, was: ~20 kyu question" John Rickard [RGG110997] "Re: The worst practical case, was: In remembrance ..." Denis Feldmann [RGG120997] "Re: The worst practical case, was: In remembrance ..." Louise Bremner [RGG140998] "International Rules" Robert Jasiek [RGG090299] "Komi?" John Fairbairn [RGG100899] "EGC Triple Ko" Robert Jasiek [was consulted] [RGG151199] "Reinterpretation of official Pass for Ko Rule" Robert Jasiek [RGG170101] "Re: Japanese rules - Article 9.2" Bill Spight [RGG190202] "Re: Point to pass?" Hans F. Zschintzsch [played White] [RGG220202a] "Video Clarification of Kisei result" Louise Bremner [RGG220202b] "Re: Ryu's mistake" T. Mark Hall [RGG220202c] "Rules glitches" John Fairbairn [RGG100702] "Area vs Territory" "Planar" [RGG120902] "Decision about Robert's protest" Matti Siivola [RGG250902] "Game End Under Ing 1991 Rules" Robert Jasiek [RGG281102] "Re: Komi for non 19x19 games" Bill Taylor [RGG090303] "Why is play forced when the end [...] is disputed?" Tim Martin [RGG040403] "Rules incident" [well, not really] John Fairbairn [SL1] "Amateur Honinbo vs Pro Honinbo 2002" Dave Sigaty senseis.xmp.net/?AmateurHoninboVsProHoninbo2002 [SW0902] "Der Kampf um die Sechsecke" Ian Steward Spektrum der Wissenschaft, September 2002 [W-BGA1] "British Championship Rules" www.britgo.org/bchamp/chrules.html [W-BGA2] "BGA Rules of Go" www.britgo.org/rules/approved.html [W-Cho] "The Second Game of the 50th Oza Title Match" John Fairbairn www.xs4all.nl/~rongen17/Cho/Stories/story002.html [W-FH1] "The Japanese Rules of Go" Fred Hansen (ed.) www.cs.cmu.edu/~wjh/go/rules/Japanese.html [Where's the (darn) official nihonkiin.or.jp/... link ??] [W-FH2] "A Precise and Nearly Complete Description of the SST Ko Rules" Fred Hansen www.cs.cmu.edu/~wjh/go/rules/Precise.html [W-FH3] "The American Go Association Rules of Go" Fred Hansen www-2.cs.cmu.edu/~wjh/go/rules/AGA.html (former www.cs.cmu.edu/afs/cs /user/whj/public/go/Rules.AGA.html) [W-GB] "Meijin 12" gobase.org/games/japan/titles/meijin/12 [W-Ing91] "Ing's SST Laws of Wei-Chi 1991" Ing Chang-Ki (transl. James Davies) www-2.cs.cmu.edu/~wjh/go/rules/SST.html [W-IT] "Proposed Rules of Go" Ikeda Toshio gobase.org/studying/rules/ikeda/ [W-JCC] "Mathematical Rules of Go" Jean-Claude Chetrit brooklyngoclub.org/jc/rulesgo.html [W-MK] "The Milton Keynes Go Board" www.britgo.org/clubs/mk/mkboard.html [W-MSO1] "Nyobutsu's Judgement" John Fairbairn 14 March 2000 groups.google.com/forum/#!topic/rec.games.go/WgKwxzN61g4 [W-MSO2] "Early Oteai (2)" John Fairbairn 4 July 2000 www.msoworld.com/mindzine/news/orient/go/history/oteai2.html [W-NK0902] "First game played with new komi" 14 November 2002 www.nihonkiin.or.jp/topics2002/oldtopics2002-e/oldtopics2002-e.htm [W-PS] "The swapping rule" www.playsite.com/t/games/board/hex/rules.html [W-RJ1] "New Ko Rules" Robert Jasiek home.snafu.de/jasiek/newko.html (former www.inx.de/~jasiek/newko.html) [W-RJ2] "International Rules" Robert Jasiek (ed.?) home.snafu.de/jasiek/int.html [via home.snafu.de/jasiek/rules.html] [W-RJ3] "Commentary on the Nihon Kiin 1989 Rules" Robert Jasiek home.snafu.de/jasiek/j1989c.html [W-ST] "Igo no suri" Shimada Takuya I'm referring to translated parts that can be found here: harryfearnley.com/go/shimada/intro.html
If you find any errors or want to criticize - please inform me. I certainly didn't master grammar, spelling, and punctuation, but following "errors" are none: - favoring AE over BE ("color" = "colour", "center" = "centre", ...) - favoring contractions ("can't" = "cannot", ...) - favoring logic (my quotes don't swallow a trailing comma or period - ridiculous; my dashes don't glue words together - "...word--word..." hurts my eyes) Using "I" instead of "we" is just meant to be honest, and last but not least she may forgive me for preferring "his" over "his or her" etc. (and this "he is Black" and "she is White" doesn't attract me either - and should be the other way around anyway).