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. Mathematicians playing Konane at a Combinatorial game theory workshop (for technical content, see external link) This article is on the theory of combinatorial games. ... Tug of war is an easily organized, impromptu game that requires little equipment. ...

Impartial games can be analyzed using the Sprague-Grundy theorem. In combinatorial game theory, the Sprague–Grundy theorem states that every impartial game is equivalent to a nimber. ...

Impartial games include sprouts and nim. Chess, however, is not impartial, since one player can move only white pieces, and the other only black. Go is also not impartial, although it is closer than chess, because of the "no suicides" rule Sprouts is a pencil-and-paper game with interesting mathematical properties. ... Nim is a two-player mathematical game of strategy in which players take turns removing objects from distinct heaps. ... Chess is a recreational and competitive game for two players. ... GO may mean: Glorioso Islands (FIPS country code) Gene Ontology, which describes gene and protein function General Officer, see General Greek Orthodox Church GO.com, Walt Disneys internet portal GO Corporation, a pen-based computing company GO Transit, a regional transit in Ontario, Canada Government-owned corporation Government Office...

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. ...

References

• E. Berlekamp, J. H. Conway, R. Guy (1982). Winning Ways for your Mathematical Plays. Academic Press. ISBN 0-12-091101-9, ISBN 0-12-091102-7. 
  • --- (2001--2004). Winning Ways for your Mathematical Plays (2nd ed.). A K Peters Ltd. ISBN 1-56881-130-6, ISBN 1-56881-142-X, ISBN 1-56881-143-8, ISBN 1-56881-144-6.