Combinatorial Game Theory

If you're new to combinatorial game theory and interested in learning more, here are some resources to get you started:

  • There is a very high-level overview on Wikipedia.
  • The classic book on combinatorial game theory is Winning Ways for Your Mathematical Plays by Berlekamp, Conway, and Guy. First published in 1982, it omits many of the more recent advances in the subject, but it's still a great introduction.
  • A more recent introduction is Lessons in Play: An Introduction to Combinatorial Game Theory by Albert, Nowakowski, and Wolfe. It's an undergraduate-level mathematics textbook, unlike Winning Ways (which is more expository in nature).
  • CGSuite is a (free!) computer algebra system for combinatorial game theory. It's a great platform for experimenting and gaining insight into the subject.

After you've learned a bit, you'll probably also want to check out:

  • Siegel's Combinatorial Game Theory is a recent (2013) graduate-level textbook; you'll want to be at least somewhat familiar with the subject matter before tackling it.
  • Conway's On Numbers and Games - the book that started it all!
  • Games of No Chance (ed. Nowakowski et al, now up to 4 volumes) is an occasional series of peer-reviewed research articles devoted to CGT. Several are available online: Volume 1, Volume 2, Volume 3