|
Winning Ways for your Mathematical Plays by Elwyn R. Berlekamp, John H. Conway, and Richard K. Guy is a compendium of information on mathematical games. It was first published in 1982 in two volumes.
The first volume introduces combinatorial game theory and its foundation in the surreal numbers; partizan and impartial games; Sprague–Grundy theory and misère games. The second volume applies the theorems of the first volume to many games, including nim, sprouts, dots and boxes, Sylver coinage, philosopher's football, fox and geese. A final section on puzzles analyzes the Soma cube, Rubik's Cube, peg solitaire, and Conway's game of life.
A republication of the work by A K Peters splits the content into four volumes.
Editions
* 1st edition, New York: Academic Press, 2 vols., 1982; vol. 1, hardback: ISBN 0-12-091150-7, paperback: ISBN 0-12-091101-9; vol. 2, hardback: ISBN 0-12-091152-3, paperback: ISBN 0-12-091102-7.
* 2nd edition, Wellesley, Massachusetts: A. K. Peters Ltd., 4 vols., 2001–2004; vol. 1: ISBN 1-56881-130-6; vol. 2: ISBN 1-56881-142-X; vol. 3: ISBN 1-56881-143-8; vol. 4: ISBN 1-56881-144-6.
==================================================
Winning Ways for Your Mathematical Plays, Vol. 1
http://www.amazon.com/Winning-Ways-Your-Mathematical-Plays/dp/1568811306
# Paperback: 296 pages
# Publisher: A K Peters/CRC Press; 2 edition (January 1, 2001)
# Language: English
# ISBN-10: 1568811306
# ISBN-13: 978-1568811307
This classic on games and how to play them intelligently is being re-issued in a new, four volume edition. This book has laid the foundation to a mathematical approach to playing games. The wise authors wield witty words, which wangle wonderfully winning ways. In Volume 1, the authors do the Spade Work, presenting theories and techniques to "dissect" games of varied structures and formats in order to develop winning strategies.
This is the most difficult collection of puns that I have ever read. Of course, that has something to do with the fact that they are surrounded by some of the most complex mathematical analyses of games that you will find. The types of games that are examined are processes that have the following general structure:
1) There are two players.
2) There are many different positions, with one singled out as the starting position.
3) Players move according to very specific rules.
4) The players move alternately.
5) Both players have complete information.
6) There is no chance element to the play. For example, dice are not involved.
7) The first player unable to move loses the game.
8) The game will always move to a state where a player cannot move, which is an ending condition.
The hardest part of the material is the notation, it is unusual and absolutely necessary to understand the treatment of nearly all the games. However, once you get over that, something that took me a couple of passes, the games become interesting. Some of them turn out to be trivial, although at first reading, that would not be your conclusion.
I also would caution you that this is not recreational mathematics in its base form. These games and problems are nontrivial and most require some serious thought, even when the result is simple. As I read through these games and the mathematical examination of the consequences of playing them, I was struck by two semi-profound thoughts.
1) The human mind can create a game out of just about anything. Some of these games are nothing more than colored marks on paper.
2) Even simple rules can generate complex results. However, mathematical analysis gives us powerful tools that inform us how to win, or as the case may be, how not to lose, or to lose as slowly as possible.
Berklekamp and company have created a classic work that is a must read if you want to understand game-like behavior. While not easy, it is some of the most worthwhile material that you will ever read. I read the first edition several years ago and found the going just as interesting the second time.
==================================================
Winning Ways for Your Mathematical Plays, Vol. 2
http://www.amazon.com/Winning-Ways-Your-Mathematical-Plays/dp/156881142X
# Paperback: 171 pages
# Publisher: A K Peters/CRC Press; 2 edition (January 1, 2003)
# Language: English
# ISBN-10: 156881142X
# ISBN-13: 978-1568811420
In the quarter of a century since three mathematicians and game theorists collaborated to create Winning Ways for Your Mathematical Plays, the book has become the definitive work on the subject of mathematical games. Now carefully revised and broken down into four volumes to accommodate new developments, the Second Edition retains the original's wealth of wit and wisdom. The authors' insightful strategies, blended with their witty and irreverent style, make reading a profitable pleasure. In Volume 2, the authors have a Change of Heart, bending the rules established in Volume 1 to apply them to games such as Cut-cake and Loopy Hackenbush. From the Table of Contents: - If You Can't Beat 'Em, Join 'Em! - Hot Bottles Followed by Cold Wars - Games Infinite and Indefinite - Games Eternal--Games Entailed - Survival in the Lost World
Starting with Hackenbush (thanks to Groucho Marx) this book describes and analyzes a great many interesting games. While the authors are mathematicians, and there is mathematics involved, much of the discussion can be followed by the lay reader.
==================================================
Winning Ways for Your Mathematical Plays, Vol. 3
http://www.amazon.com/Winning-Ways-Your-Mathematical-Plays/dp/156881143
# Paperback: 275 pages
# Publisher: A K Peters/CRC Press; 2 edition (September 10, 2003)
# Language: English
# ISBN-10: 1568811438
# ISBN-13: 978-1568811437
In the quarter of a century since three mathematicians and game theorists collaborated to create Winning Ways for Your Mathematical Plays, the book has become the definitive work on the subject of mathematical games. Now carefully revised and broken down into four volumes to accommodate new developments, the Second Edition retains the original's wealth of wit and wisdom. The authors' insightful strategies, blended with their witty and irreverent style, make reading a profitable pleasure. In Volume 3, the authors examine Games played in Clubs, giving case studies for coin and paper-and-pencil games, such as Dots-and-Boxes and Nimstring. From the Table of Contents: - Turn and Turn About - Chips and Strips - Dots-and-Boxes - Spots and Sprouts - The Emperor and His Money - The King and the Consumer - Fox and Geese; Hare and Hounds - Lines and Squares
==================================================
Winning Ways for Your Mathematical Plays, Vol. 4
http://www.amazon.com/Winning-Ways-Your-Mathematical-Plays/dp/1568811446
# Paperback: 224 pages
# Publisher: A K Peters/CRC Press; 2nd edition (March 30, 2004)
# Language: English
# ISBN-10: 1568811446
# ISBN-13: 978-1568811444
In the quarter of a century since three mathematicians and game theorists collaborated to create Winning Ways for Your Mathematical Plays, the book has become the definitive work on the subject of mathematical games. Now carefully revised and broken down into four volumes to accommodate new developments, the Second Edition retains the original's wealth of wit and wisdom. The authors' insightful strategies, blended with their witty and irreverent style, make reading a profitable pleasure. In Volume 4, the authors present a Diamond of a find, covering one-player games such as Solitaire.
The new edition of these classic volumes has been completely reorganized, and this volume now contains mostly one person games or puzzles, such as peg solitaire, Soma, Rubik's Cube, mechanical wire and string puzzles, sliding block puzzles, magic squares, and life. The book is very readable and requires no mathematical background. However, this is no lightweight watered-down book and some sections of the books could take you months to understand completely (try the SOMA map or century puzzle map that appears in the Extras). Fortunately you can just skip over these parts if you don't want to dig down to this level of detail.
Conway's game of Life is the subject of the last chapter, perhaps the most interesting chapter in the book, and that which has probably been most changed since the last edition. Still, they could easily have expanded this chapter into a whole volume, and looking at the internet it is already out of date.
==================================================
About the Authors
Elwyn Berlekamp was born in Dover, Ohio, on September 6, 1940. After spending two years as Assistant Professor at the University of California, Berkeley, and five years at the Bell Telephone laboratories, in 1971 he became Professor of Mathematics and Electrical Engineering-Computer Science at Berkeley.His book Algebraic Coding Theory received the best research paper award of the IEEE Information Theory Group. Eta Kappa Nu named him the "Outstanding Young Electrical Engineer" of 1971 in the U.S., and he has been President of the IEEE Information Theory Society. In 1977 he was elected to membership of the US National Academy of Engineering.
John Conway is a Fellow of Gonville and Caius College and a former Fellow of Sidney Sussex College, Cambridge, and is Reader in Pure Mathematics at the University of Cambridge. He has held visiting professorships at several universities and has made original contributions to many branches of mathematics, notably transfinite arithmetic, the theory of knots, many-dimensional geometry and the theory of symmetry (group theory).
Richard Guy has taught mathematics at many levels and in many places-England, Singapore, India, Canada. Since 1965 he has been Professor of Mathematics at the University of Calgary and he is a member of the Board of Governors of the Mathematical Association of America.He edits the Unsolved Problems section of American Mathematical Monthly; he wrote the volume on Number Theory for the series:Unsolved Problems in Intuitive Mathematics and is preparing another on Combinators, Graph Theory, and Game Theory. He is a keen member of the Alpine Club of Canada.
|
