Combinatorial Game Theory


Combinatorial Game Theory is my research topic. CGT is a branch of mathematics that studies sequential games (alternated decisions) with perfect information (no hidden information, no chance devices). Combinatorial games include well-known games like Amazons, Clobber, Domineering, Hackenbush, Konane, Nim, Octal Games, Wythoff’s Nim.


In 1982, Elwyn Berlekamp, John Conway and Richard Guy presented Winning Ways. In this book we can see a unified mathematical theory to analyze a large class of games. It is also important to mention the references Surreal Numbers (Donald Knuth, 1974) and On Numbers and Games (John Conway, 1976).


Nowadays, I highlight Aaron Siegel and Richard Nowakowski. The first one implemented the Combinatorial Game Suite, an open‑source program to aid research in CGT. Recently, Siegel published the book Combinatorial Game Theory with the most recent advances on the subject. Nowakowski is co-author of the book Lessons in Play, a formal introduction to the subject. He stands up an important CGT conference, every three years, in Banff International Research Station (Canada) and he is the games section editor of Integers.


See a list of open problems here and a list of combinatorial game links here. Also, a list of papers here (organized by Aviezri Fraenkel) and two historical works here and here.


In Portugal, I highlight Jorge Nuno Silva (Master’s Thesis Some Notes on Game Bounds; Elwyn Berlekamp as advisor) and myself (Phd Thesis Some Notes On Impartial Games and Nim Dimension, Richard Nowakowski as advisor and José Francisco Rodrigues as co-advisor). Moreover, I highlight the organization of the Combinatorial Game Theory Colloquia, every two years, in Lisbon.


Software for research on lattices of combinatorial games.

Software for research on guaranteed scoring combinatorial games.