= Sprague-Grundy theory
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Sprague-Grundy theory studies finite acyclic <impartial games> under the <normal-play convention> by assigning each position a <Grundy number>. The assignment recursively takes the <minimum excludant> of the values of all legal followers. The <Sprague-Grundy theorem> then reduces a <disjunctive sum of games> to the <bitwise exclusive or> of its component values. This framework explains both why a zero value is losing and how independently understood games can be combined without exploring the entire product of their state spaces.
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