This book surveys the state-of-the-art in the theory of combinatorial games, that is games not involving chance or hidden information. Enthusiasts will find a wide variety of exciting topics, from a trailblazing presentation of scoring to solutions of three piece ending positions of bidding chess. Theories and techniques in many subfields are covered, such as universality, Wythoff Nim variations, misère play, partizan bidding (a.k.a. Richman games), loopy games, and the algebra of placement games. Also included are an updated list of unsolved problems, extremely efficient algorithms for taking and breaking games, a historical exposition of binary numbers and games by David Singmaster, chromatic Nim variations, renormalization for combinatorial games, and a survey of temperature theory by Elwyn Berlekamp, one of the founders of the field. The volume was initiated at the Combinatorial Game Theory Workshop, January 2011, held at the Banff International Research Station.

'Overall this volume has several strengths. There is an excellent 'About this book' section introducing each article, providing minimal background, some results, and giving motivation for reading the paper … The figures and notation are nicely done and easy to read. All chapters include an abstract and list of references … the myriad source material accompanying the topics is extremely helpful in directing the reader to background and further study topics.'

Tricia Muldoon Brown Source: MAA Reviews

‘Those with a strong interest in combinatorial game theory may want to add this book to their library.’

David Bevan Source: The Mathematical Gazette