Games of No Chance
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.
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All Games Bright and Beautiful
The Angel Problem
Scenic Trails Ascending from SeaLevel Nim to Alpine Chess
What Is a Game?
ChampionshipLevel Play of DotsandBoxes
ChampionshipLevel Play of Domineering
The Gamesmans Toolkit
New Toads and Frogs Results
A Graphical XBased FrontEnd for Domineering
Infinitesimals and CoinSliding
Geography Played on Products of Directed Cycles
A First Player Win
New Values for Top Entails
Strides on Classical Ground
Solving Nine Mens Morris
Human Perfection at Checkers?
Solving the Game of Checkers
Combinatorial Game Theory in Chess Endgames
Multilinear Algebra and Chess Endgames
Using Similar Positions to Search Game Trees
Where Is the ThousandDollar Ko?
Eyespace Values in Go
Loopy Games and Go
Experiments in Computer Go Endgames
Taming the Menagerie
New Theoretical Vistas
The Economists View of Combinatorial Games
Games with Infinitely Many Moves and Slightly Imperfect Information
The Reduced Canonical Form of a Game
ErrorCorrecting Codes Derived from Combinatorial Games
Tutoring Strategies in GameTree Search
About David Richman
Stable Winning Coalitions
Unsolved Problems in Combinatorial Games
Selected Bibliography with a Succinct Gourmet Introduction
A. S. Fraenkel Algois algorithm Amelung analysis annihilation games atomic weight beans Berlekamp and Wolfe Berol Black canonical form capture checkers coalitions coins combinatorial game theory complete Computer Chess databases defined Diagram digraph Domineering Dots-and-Boxes E. R. Berlekamp Elwyn Berlekamp example eyes eyespace Figure finite function game G game tree heap impartial games infinitesimal integer J. H. Conway kothreats Left legal move Lemma line of play loopy games loses Mathematical Go Molien MSRI MSRI Publications Volume mutual Zugzwang nim-value Nine Men's Morris Numbers and Games opponent options P-positions partizan partizan games pawn pieces player wins position problem Proc PROOF Publications Volume 29 R. K. Guy retrograde analysis Right rules Section sequence solved square stones Table tax rate temperature Theodor Molien Theorem thermographs Tinsley Toads token vector vertex vertices White winning strategy Yesha zero Zugzwang