GAMES OF NO CHANCE by Richard J. NowakowskiGAMES OF NO CHANCE by Richard J. Nowakowski


EditorRichard J. Nowakowski

Paperback | November 13, 1998

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Is Nine-Men's 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, 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. 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 anlaysis 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 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's Morris and Pentominoes; and new 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.
Title:GAMES OF NO CHANCEFormat:PaperbackDimensions:552 pages, 8.98 × 5.98 × 1.1 inPublished:November 13, 1998Publisher:Cambridge University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0521646529

ISBN - 13:9780521646529


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.

From Our Editors

Chess anyone? The 35 articles in Games of No Chance provide a lively account of combinatorial games -- two-person, perfect-information matches like chess, checkers, go, domineering, dots-and-boxes, hackenbush and nim. In the latter games, the positions tend to decompose into sums of simpler positions. Mathematicians can now solve many such decompositions, thanks to the theory of partisan games that John Conway pioneered in the 1970s. The paradigm provided by this theory is combinatorial and algebraic.

Editorial Reviews

"Some books make mathematics look like so much fun! This collection of 35 articles and a comprehensive bibliography is a marvelous and alluring account of a 1994 MSRI two week workshop on combinatorial game theory. This could be a menace to the rest of mathematics; those folks seem to be having such a good time playing games that the rest of us might abandon 'serious' mathematics and join the party...Even the technical terms are laced with humor." Ed Sandifer, MAA Online