CGT Resources

Winning Ways for Your Mathematical Plays (aka Winning Ways) by Berlekamp, Conway, and Guy: Originally published in 1982, this collection of books started the modern theory of CGT. The second edition, published in 2004, consists of 4 volumes. It is a bit more informal than some of the other books, but contains a very large variety of techniques.

On Numbers and Games (aka ONAG) by Conway: Written by Conway while work on Winning Ways was ongoing, this book studies surreal numbers, the connection between CGT and number theory, in detail. First edition in 1976, second edition in 2001.

Lessons in Play by Albert, Nowakowski, and Wolfe: This is a textbook at the upper undergraduate level. First edition in 2007, second edition in 2019.

Combinatorial Game Theory by Siegel: A very comprehensive textbook at the graduate level published in 2013.

The Games of No Chance (aka GONC) series of books are collections of papers across the entire spectrum of CGT. Volumes 1-4 contain a survey of literature by Aviezri Fraenkel (also a dynamic survey, last updated in 2012, in the Electronic Journal of Combinatorics and found here). Each volume also contains a list of interesting unsolved problems, started by Richard Guy and continued in recent volumes by Richard Nowakowski.

Playing with Discrete Math by Burke and Tennenhouse: A recent, free textbook for teaching discrete mathematics and proofs using CGT which can also be used as a low-level undergraduate CGT text. Available here.

Kyle Burke has several great resources: a blog on which he posts conference summaries, a list of upcoming and past conferences, and a list of rulesets with some of their properties. 

There is a group on Facebook posting updates on various related items. We also have a Discord server - email me to get an invite.

CGSuite by Aaron Siegel can be used for many computations and allows to program in new games. Many researchers also write their own code for impartial games - SageMath is very popular for this.

I am currently co-organizing a virtual seminar on CGT with both advanced tutorials and research talks. The website has more information.