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Games of No Chance [Hardcover]

Richard J. Nowakowski
4.7 out of 5 stars  See all reviews (3 customer reviews)
List Price: CDN$ 147.95
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Book Description

Nov. 13 1998 0521574110 978-0521574112
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

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
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Most helpful customer reviews
4.0 out of 5 stars Fascinating July 22 2002
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.
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5.0 out of 5 stars great book March 31 2000
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.
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5.0 out of 5 stars MAA Online review Sept. 11 1997
By A Customer
Format:Hardcover
See Ed Sandifer's MAA Online review at: [...]
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Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com: 4.8 out of 5 stars  4 reviews
8 of 8 people found the following review helpful
5.0 out of 5 stars great book March 31 2000
By skeezer - Published on Amazon.com
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.
1 of 1 people found the following review helpful
5.0 out of 5 stars If You Like Chess or GO, you'll LOVE this! June 28 2013
By Let's Compare Options - Published on Amazon.com
Format:Paperback|Verified Purchase
Combinatorial math is now part of discrete math, as well as graph theory and/or stats in some math departments, but is universally winked at as the "fun" part of "recreational" math. As I'm sure you know that does NOT mean it is simple! Applications of chess combinatorials include asteroid defense, and applications of go math include the immune system, so even fun can have practical value.

Example for GO players: "When neither black or white can make eyes, there are no kos, and all liberties are simple dame, with two competing groups where shared liberties are less than two, the black or white group MUST die." (p. 249). I've reviewed and read dozens of go books, and very few give this level of detail and subtlety, let alone the combinatorial details!

Will help gamers understand math better, and mathematicians understand gaming better. The "bible" of game theory today, Maschler's (Game Theory), though wonderful, doesn't even mention combinatorial games except briefly in the zero sum chapter, and doesn't cover GO at all! So, if you're into combinatorial math and gaming (non chance, two person, zero sum, full information to be exact), this book rocks!

You might already know this, but this is the first in a series of three volumes containing scholarly articles on the topics. Just in case you missed them, the other two are: More Games of No Chance (Mathematical Sciences Research Institute Publications) and Games of No Chance 3 (Mathematical Sciences Research Institute Publications).

Highly recommended, requires undergrad level math or self study. A little linear algebra and group theory will help, but analysis and calculus are optional. Boolean logic and computer science are plusses.

Speaking of, a GREAT audience for this book would be big O, complexity, computer science, programmers and other IT folks. Some of the fun anecdotes would be great for job interviews in these fields, and not seen very often by the interviewer-- distinguish yourself!

Library Picks reviews only for the benefit of Amazon shoppers and has nothing to do with Amazon, the authors, manufacturers or publishers of the items we review. We always buy the items we review for the sake of objectivity, and although we search for gems, are not shy about trashing an item if it's a waste of time or money for Amazon shoppers. If the reviewer identifies herself, her job or her field, it is only as a point of reference to help you gauge the background and any biases.
3 of 4 people found the following review helpful
4.0 out of 5 stars Fascinating July 22 2002
By Maurizio De Leo - Published on Amazon.com
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.
4 of 8 people found the following review helpful
5.0 out of 5 stars MAA Online review Sept. 11 1997
By A Customer - Published on Amazon.com
Format:Hardcover
See Ed Sandifer's MAA Online review at: [...]
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