6 relations: Chess, Combinatorial game theory, Impartial game, Nimber, Sprague–Grundy theorem, Zugzwang.
Chess
Chess is a two-player strategy board game played on a chessboard, a checkered gameboard with 64 squares arranged in an 8×8 grid.
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Combinatorial game theory
Combinatorial game theory (CGT) is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information.
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Impartial game
In combinatorial game theory, an impartial game is a game in which the allowable moves depend only on the position and not on which of the two players is currently moving, and where the payoffs are symmetric.
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Nimber
In mathematics, the nimbers, also called Grundy numbers, are introduced in combinatorial game theory, where they are defined as the values of heaps in the game Nim.
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Sprague–Grundy theorem
In combinatorial game theory, the Sprague–Grundy theorem states that every impartial game under the normal play convention is equivalent to a nimber.
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Zugzwang
Zugzwang (German for "compulsion to move") is a situation found in chess and other games wherein one player is put at a disadvantage because they must make a move when they would prefer to pass and not move.
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