Combinatorial Games

Based on lectures presented at an AMS Short Course on combinatorial games, the ten papers in this volume are intended to provide insight into the new field of combinatorial games.

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"The subject of combinatorics is only slowly acquiring respectability and combinatorial games will clearly take longer than the rest of combinatorics. Perhaps this partly stems from the puritanical view that anything amusing can't possibly involve any worthwhile mathematics." from the Preface. Based on lectures presented at the AMS Short Course on Combinatorial Games, held at the Joint Mathematics Meetings , the ten papers in this volume will provide readers with insight into this exciting new field. (BULLET) In the opening paper, Guy contrasts combinatorial games, which have complete information and no chance moves, with those of classical game theory. Conway introduces a new theory of numbers, which has emerged as a special case of the theory of games. Guy describes impartial games, with the same options for both players, and the Sprague-Grundy theory. Conway discusses a variety of ways in which games can be played simultaneously. Berlekamp uses the theory of "hot" games to make remarkable progress in the analysis of Go Endgames. Pless demostrates the close connection between several impartial games and error-correcting codes.
Fraenkel explains the way in which complexity theory is very well illustrated by combinatorial games, which supply a plethora of examples of harder problems than most of those which have been considered in the past. Nowakowski outlines the theory of three particular games - Welter's Game, Sylver Coinage, and Dots-and-Boxes. A list of three dozen open problems and bibliography of 400 items are appended.