Combinatorial game theory

Combinatorial game theory (CGT) is a mathematical theory that studies a certain kind of game. These games are all two-player games which have a position, which the players

Related Topics:
Mathematical - Theory - Game

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take turns changing in certain well-defined ways or moves, trying to achieve a well-defined winning condition. CGT does not study games of chance (like poker), but restricts itself to games whose position is public to both players, and in which the set of available moves is also public. It can, in principle, be applied to games like Chess, checkers, Go, Hex, and similar board games, but these games are mostly too complicated to allow complete analysis (although the theory has had some recent successes in analyzing Go endgames).

Related Topics:
Chess - Checkers - Go - Hex

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In simple terms, by applying CGT to a position you are attempting to determine the optimum sequence of moves for both players until the game ends, and by doing so discovering the optimum move in the current position. In practice, this process is tortuously difficult unless the game is very simple.

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CGT should not be confused with another mathematical theory, traditionally called game theory, used in the theory of economic competition and cooperation: this other theory does involve chance and imperfect knowledge, and has the players deciding their moves simultaneously.

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