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Heap game

From Wikipedia, the free encyclopedia

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 , where each is another heap game.

The nim-value of a game is represented as the nim-addition of each heap in a heap game.


Examples

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References

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  1. ^ Siegel, Aaron (20 November 2023). Combinatorial Game Theory. American Mathematical Society. ISBN 978-1-4704-7568-0.