Games of No Chance
Games of No Chance
£50.99
GBPIs 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.
- Presents the mathematics behind popular games such as checkers, chess, and Go in articles by top names in the field
- First two parts are written for a general audience, later chapters present research findings
- Contains an annotated list of unsolved problems and a comprehensive bibliography
Reviews & endorsements
'No one interested in two-person combinatorial games should hesitate before acquiring this splendid book. Leading experts report on the latest research involving such classic board games as checkers, chess, and go. Other familiar games are analyzed in depth, and many exciting new games are introduced. Did you know that go moku, nine-men morris, and Sol Golomb's pentomino game are now solved? Did you know that computers are getting close to solving checkers? Fifty-two tantalizing unsolved problems are posed by Richard Guy, and Aviezri Fraenkel's bibliography lists 666 references! Games of No Chance is a great collection of elegant, entertaining papers - a book to put on the shelf alongside the classic two-volume Winning Ways by Elwyn Berlekamp, John Conway, and Richard Guy.' Martin Gardner
'A thoroughly edited volume, Combinatorial Game Theory at its best.' European Mathematical Society
Product details
February 1999Paperback
9780521646529
552 pages
234 × 156 × 28 mm
0.78kg
199 b/w illus. 49 tables
Available
Table of Contents
- 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.
