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 Nim, Sprouts, Kayles, Quarto, Cram, Chomp, and poset games. Go and chess are not impartial, as it is necessary to know whose turn it is in order to categorise the possible moves (for example, in chess only player 1 can move the white pieces). Games like ZÈRTZ and Chameleon are also not impartial, since although they are played with shared pieces, the payoffs are not necessarily symmetric for any given position.
A game that is not impartial is called a partisan game.
Famous quotes containing the words impartial and/or game:
“The United States must be neutral in fact as well as in name.... We must be impartial in thought as well as in action ... a nation that neither sits in judgment upon others nor is disturbed in her own counsels and which keeps herself fit and free to do what is honest and disinterested and truly serviceable for the peace of the world.”
—Woodrow Wilson (1856–1924)
“Even an attorney of moderate talent can postpone doomsday year after year, for the system of appeals that pervades American jurisprudence amounts to a legalistic wheel of fortune, a game of chance, somewhat fixed in the favor of the criminal, that the participants play interminably.”
—Truman Capote (1924–1984)