Go (game)

Connection: Keeping one's own stones connected means that fewer groups need to make living shape, and one has fewer groups to defend.

Cut: Keeping opposing stones disconnected means that the opponent needs to defend and make living shape for more groups.

Stay alive: The simplest way to stay alive is to establish a foothold in the corner or along one of the sides. At a minimum, a group must have two eyes (separate open points) to be alive. An opponent cannot fill in either eye, as any such move is suicidal and prohibited in the rules.

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Mutual life (seki) is better than dying: A situation in which neither player can play on a particular point without then allowing the other player to play at another point to capture. The most common example is that of adjacent groups that share their last few liberties—if either player plays in the shared liberties, they can reduce their own group to a single liberty (putting themselves in atari), allowing their opponent to capture it on the next move.

Death: A group that lacks living shape is eventually removed from the board as captured.

Invasion: Set up a new living group inside an area where the opponent has greater influence, means one reduces the opponent's score in proportion to the area one occupies.

Reduction: Placing a stone far enough into the opponent's area of influence to reduce the amount of territory they eventually get, but not so far that it can be cut off from friendly stones outside.

Sente: A play that forces one's opponent to respond (). A player who can regularly play sente has the initiative and can control the flow of the game.

gote

Sacrifice: Allowing a group to die in order to carry out a play, or plan, in a more important area.

Liberty rule states that every stone remaining on the board must have at least one open point (a liberty) directly orthogonally adjacent (up, down, left, or right), or must be part of a connected group that has at least one such open point (liberty) next to it. Stones or groups of stones which lose their last liberty are removed from the board.

Repetition Rule () states that a stone on the board must never immediately repeat a previous position of a captured stone, thus only a move elsewhere on the board is permitted that turn. Since without this rule such a pattern of the two players repeating their prior moves (capturing stones in same places) could continue indefinitely, this rule prevents a stalemate.

the ko rule

Model of a 19×19 Go board, from a tomb of the Sui dynasty (581–618 CE)

Painting of a woman playing Go, from the Astana Graves. Tang dynasty, c. 744 CE.

Li Jing playing Go with his brothers. Detail from a painting by Zhou Wenju (fl. 942–961 CE), Southern Tang dynasty.

compensation points, called komi, which compensate the second player for the first move advantage of their opponent; tournaments commonly use a compensation in the range of 5–8 points, generally including a half-point to prevent draws;

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handicap stones placed on the board before alternate play, allowing players of different strengths to play competitively (see for more information); and

Go handicap

superko: Although the basic ko rule described above covers more than 95% of all cycles occurring in games, there are some complex situations—triple ko, eternal life,^[f] etc.—that are not covered by it but would allow the game to cycle indefinitely. To prevent this, the ko rule is sometimes extended to forbid the repetition of any previous position. This extension is called superko.^[108]

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The number of spaces on the board is much larger (over five times the number of spaces on a chess board—361 vs. 64). On most turns there are many more possible moves in Go than in chess. Throughout most of the game, the number of legal moves stays at around 150–250 per turn, and rarely falls below 100 (in chess, the average number of moves is 37). Because an exhaustive computer program for Go must calculate and compare every possible legal move in each ply (player turn), its ability to calculate the best plays is sharply reduced when there are a large number of possible moves. Most computer game algorithms, such as those for chess, compute several moves in advance. Given an average of 200 available moves through most of the game, for a computer to calculate its next move by exhaustively anticipating the next four moves of each possible play (two of its own and two of its opponent's), it would have to consider more than 320 billion (3.2×10¹¹) possible combinations. To exhaustively calculate the next eight moves, would require computing 512 quintillion (5.12×10²⁰) possible combinations. As of March 2014, the most powerful supercomputer in the world, NUDT's "Tianhe-2", can sustain 33.86 petaflops.^[141] At this rate, even given an exceedingly low estimate of 10 operations required to assess the value of one play of a stone, Tianhe-2 would require four hours to assess all possible combinations of the next eight moves in order to make a single play.

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The placement of a single stone in the initial phase can affect the play of the game a hundred or more moves later. A computer would have to predict this influence, and it would be unworkable to attempt to exhaustively analyze the next hundred moves.

In capture-based games (such as chess), a position can often be evaluated relatively easily, such as by calculating who has a material advantage or more active pieces. In Go, there is often no easy way to evaluate a position.^[145] However a 6-kyu human can evaluate a position at a glance, to see which player has more territory, and even beginners can estimate the score within 10 points, given time to count it. The number of stones on the board (material advantage) is only a weak indicator of the strength of a position, and a territorial advantage (more empty points surrounded) for one player might be compensated by the opponent's strong positions and influence all over the board. Normally a 3-dan can easily judge most of these positions.

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Go is bounded by a finite number of moves and every game must end with a victor or a tie (although ties are very rare);

the strategy is associative because every strategy is a function of board position;

the format is non-cooperative (that is, it's not a team sport);

positions are extensible, and so can be represented by board position trees;

the game is because player choices do not increase resources available, the rewards in the game are fixed and if one player wins, the other loses, and the utility function is restricted (in the sense of win/lose);

zero-sum

however, ratings, monetary rewards, national and personal pride and other factors can extend utility functions, but generally not to the extent of removing the win/lose restriction, although can theoretically add non-zero and complex utility aspects even to two player games.^[182]

Affine transformations

Games played with Go equipment

List of books about Go

List of top title holders in Go

Sensei's Library