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A variant first described by Claude Shannon provides an argument about the game-theoretic value of chess: he proposes allowing the move of “pass”. In this variant, it is provable with a strategy stealing argument that the first player has at least a draw thus: if the first player has a winning move in the initial position, let him play it, else pass.
A solved game is a game whose outcome (win, lose or draw) can be correctly predicted from any position, assuming that both players play perfectly.This concept is usually applied to abstract strategy games, and especially to games with full information and no element of chance; solving such a game may use combinatorial game theory or computer assistance.
Chess theory usually divides the game of chess into three phases with different sets of strategies: the opening, typically the first 10 to 20 moves, when players move their pieces to useful positions for the coming battle; the middlegame; and last the endgame, when most of the pieces are gone, kings typically take a more active part in the ...
In the game of chess, an endgame study, or just study, is a composed position—that is, one that has been made up rather than played in an actual game—presented as a sort of puzzle, in which the aim of the solver is to find the essentially unique way for one side (usually White) to win or draw, as stipulated, against any moves the other side plays.
Zermelo's theorem can be applied to all finite-stage two-player games with complete information and alternating moves. The game must satisfy the following criteria: there are two players in the game; the game is of perfect information; the board game is finite; the two players can take alternate turns; and there is no chance element present.
A proof game is a type of retrograde analysis chess problem. The solver must construct a game starting from the initial chess position, which ends with a given position (thus proving that that position is reachable) after a specified number of moves. A proof game is called a shortest proof game if no shorter solution exists. In this case the ...
Examples of games that are PSPACE-complete (when generalized so that they can be played on an board) are the games Hex and Reversi. Some other generalized games, such as chess, checkers (draughts), and Go are EXPTIME-complete because a game between two perfect players can be very long, so they are unlikely to be in PSPACE. But they will become ...
The following outline is provided as an overview of and topical guide to chess: Chess is a two-player board game played on a chessboard (a square-checkered board with 64 squares arranged in an eight-by-eight grid). In a chess game, each player begins with sixteen pieces: one king, one queen, two rooks, two knights, two bishops, and eight pawns.
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