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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Review
"This book must be read by every serious student of two-person full-information games, and it provides an excellent presentation for anyone seeking a proper introduction to the subject." Solomon W. Golomb, American Scientist
"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
"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
Book Description
This volume presents papers from the workshop on "Combinatorial Games" held at MSRI in July 1994. Combinatorial games are two-person perfect-information games such as chess, checkers, go, domineering, dots-and-boxes, hackenbush, nim, etc. The positions of the latter games in this list tend to decompose into sums of simpler positions. This book will be the newest addition to the literature on combinatorial games, covering many aspects of the current research and will be sought after as a state-of-the-art report in the field.
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The Angel and the Devil play their game on an infinite chessboard, with one square for each ordered pair of integers (x, y). Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Back Cover
The Angel and the Devil play their game on an infinite chessboard, with one square for each ordered pair of integers (x, y). Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Back Cover
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Customer Reviews
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Format:Paperback
I don't have read all the book, but I read most of the scientific papers it is composed by. I think they are very interesting and puzzling, on the border line between serious mathematics (game theory and all this stuff) and "recreational math" (like the angel problem). It would be a good read also for people interested in computer games.
By skeezer
Format:Paperback
This book is full of beatiful work. Every section is an investigation into some combinatorial game, or some idea in combinatorial game theory. Most of the material is clearly presented and all should be accessible to undergrads, but be warned: this is not simple stuff. But, as we all know, beautiful mathematics isn't always simple. The book also includes a section with 52 unsolved problems, which should be of considerable interest to the curious.
By A Customer
Format:Hardcover
See Ed Sandifer's MAA Online review at: http://www.maa.org/reviews/nochance.htm
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