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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. This article is on the theory of combinatorial games For the theory that includes games of chance and games of imperfect knowledge see Game theory This article is about using Mathematics to study the inner-workings of Multiplayer games which on the surface may not appear mathematical at all 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. In Combinatorial game theory, the Sprague&ndashGrundy theorem states that every Impartial game is equivalent to a Nimber.

Impartial games include nim, sprouts, kayles, quarto, cram, and chomp. Nim is a two-player mathematical Game of strategy in which players take turns removing objects from distinct heaps Sprouts is a Pencil-and-paper game with interesting mathematical properties Quarto is a Board game for two players invented by Blaise Müller Chomp is a 2-player game played on a rectangular "chocolate bar" made up of smaller square blocks (rectangular cells Go and chess are not impartial, as it is necessary to know whose turn it is in order to categorise the possible moves. Chess is a recreational and competitive Game played between two players. Games like Zertz and Chameleon are also not impartial, since although they are played with shared pieces, the payoffs are not necessarily symmetric for any given position. ZÈRTZ is the third Game in the ''GIPF'' Project of six abstract strategy games.

A game that is not impartial is called a partisan game. In Combinatorial game theory, a game is partisan or partizan if it is not impartial.

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