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| In ], an '''impartial game''' is a ] 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. In other words, the only difference between player 1 and player 2 is that player 1 goes first. | In ], an '''impartial game''' is a ] 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. In other words, the only difference between player 1 and player 2 is that player 1 goes first. | ||
| Impartial games can be analyzed using ]. | Impartial games can be analyzed using the ]. | ||
| Impartial games include ] and ]. ], however, is not impartial, since one player can move only white pieces, and the other only black. | Impartial games include ] and ]. ], however, is not impartial, since one player can move only white pieces, and the other only black. | ||
Revision as of 22:14, 28 June 2006
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. In other words, the only difference between player 1 and player 2 is that player 1 goes first.
Impartial games can be analyzed using the Sprague-Grundy theorem.
Impartial games include sprouts and nim. Chess, however, is not impartial, since one player can move only white pieces, and the other only black.
A game that is not impartial is called a partisan game.
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