Heap games are a subclass of impartial games that involve the disjunctive sum of various single-heap games.
Single-heap positions, or Γ-heaps are games represented naturally by the ordinal amount of a heap of tokens, where players play according to a specific ruleset on that single heap.
[1] Every option of a heap game must be representable as
is another heap game.
The nim-value of a game is represented as the nim-addition of each heap in a heap game.