Games of No Chance

Front Cover
Richard J. Nowakowski
Cambridge University Press, Nov 13, 1998 - Mathematics - 537 pages
0 Reviews
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.
  

What people are saying - Write a review

We haven't found any reviews in the usual places.

Selected pages

Contents

All Games Bright and Beautiful
1
The Angel Problem
3
Scenic Trails Ascending from SeaLevel Nim to Alpine Chess
13
What Is a Game?
43
Impartial Games
61
ChampionshipLevel Play of DotsandBoxes
79
ChampionshipLevel Play of Domineering
85
The Gamesmans Toolkit
93
Sowing Games
287
New Toads and Frogs Results
299
A Graphical XBased FrontEnd for Domineering
311
Infinitesimals and CoinSliding
315
Geography Played on Products of Directed Cycles
329
A First Player Win
339
New Values for Top Entails
345
TakeAway Games
351

Strides on Classical Ground
99
Solving Nine Mens Morris
101
Human Perfection at Checkers?
115
Solving the Game of Checkers
119
Combinatorial Game Theory in Chess Endgames
135
Multilinear Algebra and Chess Endgames
151
Using Similar Positions to Search Game Trees
193
Where Is the ThousandDollar Ko?
203
Eyespace Values in Go
227
Loopy Games and Go
259
Experiments in Computer Go Endgames
273
Taming the Menagerie
285
New Theoretical Vistas
363
The Economists View of Combinatorial Games
365
Games with Infinitely Many Moves and Slightly Imperfect Information
407
The Reduced Canonical Form of a Game
409
ErrorCorrecting Codes Derived from Combinatorial Games
417
Tutoring Strategies in GameTree Search
433
About David Richman
437
Richman Games
439
Stable Winning Coalitions
451
Unsolved Problems in Combinatorial Games
475
Selected Bibliography with a Succinct Gourmet Introduction
493
Copyright

Common terms and phrases

References to this book

All Book Search results »

Bibliographic information