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:
“If God now wills the removal of a great wrong, and wills also that we of the North as well as you of the South, shall pay fairly for our complicity in that wrong, impartial history will find therein new cause to attest and revere the justice and goodness of God.”
—Abraham Lincoln (1809–1865)
“The notion that the public accepts or rejects anything in modern art ... is merely romantic fiction.... The game is completed and the trophies distributed long before the public knows what has happened.”
—Tom Wolfe (b. 1931)