Reference for Combinatorial Game Theory

Question

I have become interested in the game of Go and have always loved mathematics. After some reading I have found the subject of combinatorial game theory. I'm looking for a book on the subject with a focus on two player sequential games. Thanks for any help.

See also Tutorials for Sprague-Grundy Theorem/Nimbers? – Mark S. Jan 25 '24 at 21:12 — Mark S., Jan 25 '24 at 21:12

score 3 · Answer 1 · answered Jan 25 '24 at 16:37

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Elwyn R. Berlekamp, John H. Conway, and Richard K. Guy, Winning Ways for Your Mathematical Plays.

answered Jan 25 '24 at 16:37

Ethan Bolker

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score 1 · Answer 2 · answered Jan 25 '24 at 17:19

Other suggestions besides Winning Ways:

For a "textbook" style introduction, see "Lessons in Play: An introduction to combinatorial game theory" by Wolfe, Albert, Nowakowski.

For a book specific to Go, see "Mathematical Go: Chilling gets the last point" by Berlekamp and Wolfe.

score 1 · Answer 3 · answered Jan 25 '24 at 18:31

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I personally like Siegel's Combinatorial game theory. It's less "fun" than Winning Ways, but by the same token the presentation in WW often feels (to me at least) pretty loose in a way that - especially where "large" infinitary constructions, and ill-founded objects (loopy games) are concerned - I'm not wild about. Siegel's book is a conventional textbook more-or-less, and that does have its advantages.

answered Jan 25 '24 at 18:31

Noah Schweber

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Just beware that not all the exercises are possible to solve – Mike Earnest Jan 25 '24 at 20:46
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@MikeEarnest I don't think that's unique to Siegel's book (to put it mildly). – Noah Schweber Jan 25 '24 at 20:49

Reference for Combinatorial Game Theory

3 Answers3