____ ____ _________ _________ / / / / / \ / / / / / / / ___ / / _____/ / / ____ / / / /__/ / / / _____ / / / / / / / ___/ / / /_ / / /_/__ /_/ / / /\ \ / /___/ / / / / / / \ \ / / /________/______/ /___/ \___\ \_________/ 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 - again taking 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 (normal action). Each action may (occasionally must) be omitted, but if both are performed, it must happen in the given order. 4. If a player neither adds nor removes stones in his turn, this is called a "pass" (and also is an action). 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 stone"), and - for each opposing stone that was removed (no matter by whom) during the game ("captive"). 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, - identify all opposing stones thereafter being without liberties, and, in case there are, - remove them from their locations ("capture"). 7. To "remove a cycle" means to remove all stones sitting on locations "used" by the cycle - which are those 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 would not 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 the new stone has none. 11. Putting a stone on an empty location makes "pseudo suicide" if after placement the new stone and all stones of opposite color still have liberties, but those of the new stone all are permanently prohibited. 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 the location it sits on contacts at least one empty location - each a "liberty" of the stone. A location "contacts" another if by starting from the former and repeatedly (including zero times) jumping to a neighboring location that, compared to the jump's origin, either also is empty or also occupied by a stone of same color, one can reach a location neighboring the other location. 14. A player "controls" a location if it is member of a set of locations he has bordered and he cannot be prevented from building a two-eye formation on this set even if - each location outside this set is cleared and 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 and actions are forgotten, 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 "two-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 at least has 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 at least has two liberties in this set. 17. In case the game started with no referee(s) designated to decide disputes about control, the game continues after its normal end as follows: Starting with the player who did not pass last, both players alternately either - point to an empty location that contacts opposing but no own stones, - point to an opposing stone, or - pass. Pointing to an empty location claims that it is neutral. Pointing to an opposing stone claims that it is dead, including all other opposing stones sitting in the claimant's smallest bordered set that includes the stone's location. In case of two passes in a row there is no disagreement and normal counting decides score and outcome. This solely depends on control, which is assigned as follows: Only for this purpose all claimed-as dead stones are treated as if gone. Then each location - that is empty, - that neither is nor contacts a claimed-as neutral location, - that contacts at least one occupied location, and - that only has one player to whom all stones on such locations belong is treated as if controlled by this player. To disagree, a player points to a location or stone claimed by his opponent. In this case a dispute is played out, which decides the game. In case of an empty location, the disagreeing player is the "prover", otherwise his opponent. The prover has to prove that he controls the empty location or the location occupied by the stone by building a two-eye formation on a set of locations. This set initially includes the prover's smallest bordered set that includes the disputed location, but may be extended by him repeatedly: each time he points to an empty location not yet in the set, his smallest bordered set including this location is added to the set. As soon he passes or doesn't extend, the initial situation for him trying to build a two-eye formation on this set is set up as defined in the definition of control. Starting with the "refuter", that's the prover's opponent, the game then continues until either - the refuter puts a stone on a location neighboring a location outside the set, - the refuter builds a two-eye formation that includes at least one location in the set, - a situation is similar to a former one, or - the prover has build a two-eye formation on the set (cases before the last two only to shorten disputes). In the last case the prover wins, otherwise the refuter. bulky rationale (from 2003)