A game in which the possible moves are the same for each player in any position. All positions in all impartial games form an additive Abelian group. For impartial games in which the last player wins (normal-form games), the nim-value of the sum of two games is the nim-sum of their nim-values. If the last player loses, the game is said to be in misère form and the analysis is much more difficult.

fair game | game | misère-form game | nim-value | normal-form game | partisan game