CCS Math 10: Combinatorial Game Theory


Click here to view the course syllabus in pdf format.

There is also a forum for this class. I hope to be able to set up TeX on this forum, but at the moment I have no idea how to do that.




  • The best book on combinatorial game theory is Winning Ways for your Mathematical Plays by Elwyn Berlekamp, John Conway, and Richard Guy. It comprises four volumes (in the second edition). We will only be covering the first volume in this course; however, the other volumes are worth looking at if you are interested in the topics they cover.
  • If you are interested in a more formal view of combinatorial game theory, On Numbers and Games by John Conway is a good place to start. I find it less “fun” than Winning Ways, but sometimes you may wonder why everything that is done is actually sensible. You’ll find justifications of all sorts of shady business in ONAG. There are also a number of interesting constructions in this book. For example, there is a simple of way of constructing the real numbers, the surreal numbers, the ordinal numbers, and many more fascinating objects. You can probably understand most of this book without much background in abstract algebra and real analysis, but if you have some familiarity with those subjects, you will be likely to understand this book on a deeper level.
  • There’s a new book on combinatorial game theory, Lessons in Play by Michael Albert, Richard Nowakowski, and David Wolfe, that just came out earlier in 2007. This book discusses many new games not mentioned in Winning Ways or ONAG, but the actual mathematical content is rather similar to Winning Ways, Volume 1. I prefer the structure of Winning Ways, but that’s really a matter of taste. There is also a website for this book.
  • There are two books, Games of No Chance and More Games of No Chance, edited by Richard Nowakowski, consisting of papers from conferences on combinatorial game theory. There are many topics not discussed in Winning Ways or ONAG that appear in these papers, including applications of combinatorial game theory to more interesting games (e.g. chess, go, mancala, amazons).


Papers and other resources


  • An introduction to Conway’s games and numbers” by Dierk Schleicher and Michael Stoll is a survey paper in the same spirit as ONAG, but I think it is an easier read.
  • All games bright and beautiful” by John Conway is a sort of summary of ONAG. (You need access to JSTOR for this link to work.)
  • Misère games and misère quotients” by Aaron Siegel is a good place to start if you are interested in misère games. More generally, this website has lots of information about misère games. Warning: the theory of misère games is much more complicated than that of normal-play games!
  • Combinatorial Game Suite is a Java program written by Aaron Siegel that helps you to find values of certain games.
  • Many of the papers from Games of No Chance are available online here. Similarly, the papers from More Games of No Chance are available here.


Please email me if you have any questions or suggestions.