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Sprague–Grundy theorem

In combinatorial game theory, the Sprague–Grundy theorem states that every impartial game under the normal play convention is equivalent to a one-heap game of nim, or to an infinite generalization of nim. It can therefore be represented as a natural number, the size of the heap in its equivalent game of nim, as an ordinal number in the infinite…

Art, Development & Second Lemma

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Definitions

Second Lemma

Proof of the Sprague–Grundy theorem

Development

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Sprague–Grundy theorem

Nodes34
Edges33
Triples23
Avg. degree1.94
Density0.058824
Components1

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Sprague–Grundy theorem

Top relations

related to Definitions · 8
Sprague–Grundy theorem → Alice, As, At, Bob, For, Grundy, Referring, Sprague
related to Nimbers · 6
Sprague–Grundy theorem → Formally, Grundy, In, Sprague, The, While

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Important terminology

displaystyle position game mathcal player g' nim -position grundy bob approx moves sprague move two positions impartial one theorem equivalent

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
checkers is not impartial becauseinstance ofa game0.80text
supposing Alice were playing redinstance ofa game0.80text
Bob were playing blackinstance ofa game0.80text
for any given arrangement of pieces on the boardinstance ofa game0.80text
if it were Alice's turninstance ofa game0.80text
she would only be allowed to move the red piecesinstance ofa game0.80text
and if it were Bob's turninstance ofa game0.80text
he would only be allowed to move the black pieces.Note that any configuration of an impartial game can therefore be written as a single positioninstance ofa game0.80text
because the moves will be the same no matter whose turn it isinstance ofa game0.80text
Sprague–Grundy theoremrelated to DefinitionsFor0.60section
Sprague–Grundy theoremrelated to DefinitionsSprague0.60section
Sprague–Grundy theoremrelated to DefinitionsGrundy0.60section

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    Min side: 3
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