Links and Books



  • Surreal Numbers by Knuth. It is a rather accessible mathematical exploration that both teaches what the Surreal Numbers are, and teaches something about how mathematicians work, by getting a layman reader involved.
  • Foundations of Analysis over Surreal Number Fields by Alling. It is a text requiring a formidable background in mathematics (an advanced undergrad with significant background in algebra and real analysis might be ok) but which goes through the detailed theory of the Surreals very well.
  • On Numbers and Games by Conway. An introduction to number systems and some theory of partizan games with more proofs and fewer examples than Winning Ways.
  • Winning Ways by Berlekamp, Conway, and Guy. A fairly comprehensive introduction to CGT in four volumes with tons of examples, although it’s a bit light on the proofs and doesn’t have a great selection of exercises like a textbook would.
  • Mathematical Go: Chilling Gets the Last Point by Berlekamp and Wolfe. A decent introduction to CGT as applied to the Asian game of Go. It can get a little hard to follow if you don’t already have a bit of a background in Go and CGT, but is still a good book.
  • The Dots and Boxes Game: Sophisticated Child’s Play by Berlekamp. A collection of Dots and Boxes problems with some of the theory behind it. I hear it’s a bit difficult to read, though.
  • Lessons in Play: An Introduction to Combinatorial Game Theory by Albert, Nowakowski, and Wolfe. An excellent book covering some of the basics from Winning Ways vol. 1 in the style of a textbook suitable for a course or self-study.
  • Combinatorial Game Theory by Siegel. An amazing book covering essentially everything important. It’s a graduate textbook only because it doesn’t have the wealth of examples/games that Lessons in Play does. It’s written very well, though.

Above I have listed the stated authors for these books, but in some cases there may be controversy over who was responsible for which ideas, and who had permission from whom, etc.

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