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:
“He is, in fact, the best tempered, and not the least impartial of reviewers. He goes out of his way to do justice to profligates and quacks.”
—Henry David Thoreau (1817–1862)
“Old age is far more than white hair, wrinkles, the feeling that it is too late and the game finished, that the stage belongs to the rising generations. The true evil is not the weakening of the body, but the indifference of the soul.”
—André Maurois (1885–1967)