Games of No Chance

A fascinating look at the mathematics behind games such as checkers, chess, Go, Nim, and Nine-Men Morris.

Richard J. Nowakowski (Edited by)

9780521646529, Cambridge University Press

Paperback, published 13 November 1998

552 pages, 199 b/w illus. 49 tables
23.4 x 15.6 x 2.8 cm, 0.78 kg

'A thoroughly edited volume, Combinatorial Game Theory at its best.' European Mathematical Society

Is Nine-Men Morris, in the hands of perfect players, a win for white or for black - or a draw? Can king, rook, and knight always defeat king and two knights in chess? What can Go players learn from economists? What are nimbers, tinies, switches and minies? This book deals with combinatorial games, that is, games not involving chance or hidden information. Their study is at once old and young: though some games, such as chess, have been analyzed for centuries, the first full analysis of a nontrivial combinatorial game (Nim) only appeared in 1902. The first part of this book will be accessible to anyone, regardless of background: it contains introductory expositions, reports of unusual tournaments, and a fascinating article by John H. Conway on the possibly everlasting contest between an angel and a devil. For those who want to delve more deeply, the book also contains combinatorial studies of chess and Go; reports on computer advances such as the solution of Nine-Men Morris and Pentominoes; and theoretical approaches to such problems as games with many players. If you have read and enjoyed Martin Gardner, or if you like to learn and analyze new games, this book is for you.

Part I. All Games Bright and Beautiful: 1. The angel problem John H. Conway
2. Scenic trails ascending from sea-level Nim to Alpine chess Aviezri Fraenkel
3. What is a game? Richard K. Guy
4. Impartial games Richard K. Guy
5. Championship-level play of dots-and-boxes Julian West
6. Championship-level play of domineering Julian West
7. The gamesman's toolkit David Wolfe
Part II. Strides on Classical Ground: 8. Solving Nine Men's Morris Ralph Gasser
9. Marion Tinsley: human perfection at checkers? Jonathan Schaeffer
10. Solving the game of checkers Jonathan Schaeffer and Robert Lake
11. On numbers and endgames: combinatorial game theory in chess endgames Noam D. Elkies
12. Multilinear algebra and chess endgames Lewis Stiller
13. Using similar positions to search game trees Yasuhito Kawano
14. Where is the 'Thousand-Dollar Ko'? Elwyn Berlekamp and Yonghoan Kim
15. Eyespace values in Go Howard A. Landman
16. Loopy games and Go David Moews
17. Experiments in computer Go endgames Martin Müller and Ralph Gasser
Part III. Taming the Menagerie: 18. Sowing games Jeff Erickson
19. New toads and frogs results Jeff Erickson
20. X-dom: a graphical, x-based front-end for domineering Dan Garcia
21. Infinitesimals and coin-sliding David Moews
22. Geography played on products of directed cycles Richard J. Nowakowski and David G. Poole
23. Pentominoes: a first player win Hilarie K. Orman
24. New values for top entails Julian West
25. Take-away games Michael Zieve
Part IV. New Theoretical Vistas: 26. The economist's view of combinatorial games Elwyn Berlekamp
27. Games with infinitely many moves and slightly imperfect information (extended abstract) David Blackwell
28. The reduced canonical form of a game Dan Calistrate
29. Error-correcting codes derived from combinatorial games Aviezri Fraenkel
30. Tutoring strategies in game-tree search (extended abstract) Hiroyuki Iida, Yoshiyuki Kotani and Jos W. H. M. Uiterwijk
31. About David Richman James G. Propp
32. Richman games Andrew J. Lazarus, Daniel E. Loeb, James G. Propp and Daniel Ullman
33. Stable winning coalitions Daniel E. Loeb
Part V. Coda: 34. Unsolved problems in combinatorial games Richard K. Guy
35. Combinatorial games: selected bibliography with a succinct gourmet introduction Aviezri Fraenkel.

Subject Areas: Game theory [PBUD]