Impartial game

An impartial game is a game where the allowable moves depend only on the position of the game, not on which of the two players is currently moving, and where the payoffs are symmetric. In other words, the only difference between playing as Player 1 and playing as Player 2 is that, in some games, Player 1 goes first, while Player 2 does not. Examples of impartial games include the card game War and the game Nim. Chess, however, is not impartial, since one player can only move white pieces, and the other only black.

A game that is not impartial is called a partizan game.