- Impartial game
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, andchomp . Go andchess 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 likeZÈRTZ 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 .References
*cite book | author=E. Berlekamp, J. H. Conway, R. Guy | title=
Winning Ways for your Mathematical Plays | publisher=Academic Press | year=1982 | id=ISBN 0-12-091101-9, ISBN 0-12-091102-7
**cite book | author=--- | title=Winning Ways for your Mathematical Plays (2nd ed.) | publisher=A K Peters Ltd | year=2001--2004 | id=ISBN 1-56881-130-6, ISBN 1-56881-142-X, ISBN 1-56881-143-8, ISBN 1-56881-144-6
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