Editing Impartial game (section)

==Heap game==
'''Heap games''' are a [[Subclass_(set_theory)|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_number|ordinal]] amount of a heap of tokens, where players play according to a specific [[Game rule|ruleset]] on that single heap.<ref>{{cite book |last1=Siegel |first1=Aaron |title=Combinatorial Game Theory |date=20 November 2023 |publisher=American Mathematical Society |isbn=978-1-4704-7568-0}}</ref>

Every option of a heap game must be representable as <math>H^{'}_{n} = H_{a_{1}} + H_{a_{2}} + H_{a_{3}} + ...</math>, where each <math>H^{a_{n}}</math> is another heap game.

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

Examples include:
* [[Octal games]]
* [[Nim]]
* [[Kayles]]