More Games of No Chance
More Games of No Chance

Author: Richard Nowakowski

Publisher: Cambridge University Press

Published: 2002-11-25

Total Pages: 552

ISBN-13: 9780521808323

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This 2003 book provides an analysis of combinatorial games - games not involving chance or hidden information. It contains a fascinating collection of articles by some well-known names in the field, such as Elwyn Berlekamp and John Conway, plus other researchers in mathematics and computer science, together with some top game players. The articles run the gamut from theoretical approaches (infinite games, generalizations of game values, 2-player cellular automata, Alpha-Beta pruning under partial orders) to other games (Amazons, Chomp, Dot-and-Boxes, Go, Chess, Hex). Many of these advances reflect the interplay of the computer science and the mathematics. The book ends with a bibliography by A. Fraenkel and a list of combinatorial game theory problems by R. K. Guy. Like its predecessor, Games of No Chance, this should be on the shelf of all serious combinatorial games enthusiasts.

Games of No Chance 5
Games of No Chance 5

Author: Urban Larsson

Publisher: Cambridge University Press

Published: 2019-05-09

Total Pages: 499

ISBN-13: 1108485804

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Surveys the state-of-the-art in combinatorial game theory, that is games not involving chance or hidden information.

Games of No Chance 3
Games of No Chance 3

Author: Michael H. Albert

Publisher: Cambridge University Press

Published: 2009-05-29

Total Pages: 577

ISBN-13: 0521861349

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This fascinating look at combinatorial games, that is, games not involving chance or hidden information, offers updates on standard games such as Go and Hex, on impartial games such as Chomp and Wythoff's Nim, and on aspects of games with infinitesimal values, plus analyses of the complexity of some games and puzzles and surveys on algorithmic game theory, on playing to lose, and on coping with cycles. The volume is rounded out with an up-to-date bibliography by Fraenkel and, for readers eager to get their hands dirty, a list of unsolved problems by Guy and Nowakowski. Highlights include some of Siegel's groundbreaking work on loopy games, the unveiling by Friedman and Landsberg of the use of renormalization to give very intriguing results about Chomp, and Nakamura's "Counting Liberties in Capturing Races of Go." Like its predecessors, this book should be on the shelf of all serious games enthusiasts.

Games of No Chance 4
Games of No Chance 4

Author: Richard J. Nowakowski

Publisher: Cambridge University Press

Published: 2015-04-16

Total Pages: 351

ISBN-13: 1107011035

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Combinatorial games are the strategy games that people like to play, for example chess, Hex, and Go. They differ from economic games in that there are two players who play alternately with no hidden cards and no dice. These games have a mathematical structure that allows players to analyse them in the abstract. Games of No Chance 4 contains the first comprehensive explorations of misère (last player to move loses) games, extends the theory for some classes of normal-play (last player to move wins) games and extends the analysis for some specific games. It includes a tutorial for the very successful approach to analysing misère impartial games and the first attempt at using it for misère partisan games. Hex and Go are featured, as well as new games: Toppling Dominoes and Maze. Updated versions of Unsolved Problems in Combinatorial Game Theory and the Combinatorial Games Bibliography complete the volume.

Games of No Chance
Games of No Chance

Author: Richard J. Nowakowski

Publisher: Cambridge University Press

Published: 1998-11-13

Total Pages: 556

ISBN-13: 9780521646529

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Is Nine-Men 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 and 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. The first part of this book will be accessible to anyone, regardless of background: it contains introductory expositions, reports of unusual tournaments, and a fascinating article by John H. Conway on the possibly everlasting 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 Morris and Pentominoes; and 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.

The Book on Games of Chance
The Book on Games of Chance

Author: Gerolamo Cardano

Publisher: Courier Dover Publications

Published: 2015-11-04

Total Pages: 68

ISBN-13: 048680898X

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Mathematics was only one area of interest for Gerolamo Cardano ― the sixteenth-century astrologer, philosopher, and physician was also a prolific author and inveterate gambler. Gambling led Cardano to the study of probability, and he was the first writer to recognize that random events are governed by mathematical laws. Published posthumously in 1663, Cardano's Liber de ludo aleae (Book on Games of Chance) is often considered the major starting point of the study of mathematical probability. The Italian scholar formulated some of the field's basic ideas more than a century before the better-known correspondence of Pascal and Fermat. Although his book had no direct influence on other early thinkers about probability, it remains an important antecedent to later expressions of the science's tenets.

Combinatorial Game Theory
Combinatorial Game Theory

Author: Richard J. Nowakowski

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2022-08-22

Total Pages: 430

ISBN-13: 3110755416

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This volume is dedicated to the work of three leading mathematicians in combinatoric game theory, Elwyn Berlekamp, John Conway, and Richard Guy and includes 20 contributions from colleagues reflecting on their work.

Games, Puzzles, and Computation
Games, Puzzles, and Computation

Author: Robert A. Hearn

Publisher: CRC Press

Published: 2009-06-30

Total Pages: 250

ISBN-13: 1439865051

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The authors show that there are underlying mathematical reasons for why games and puzzles are challenging (and perhaps why they are so much fun). They also show that games and puzzles can serve as powerful models of computation-quite different from the usual models of automata and circuits-offering a new way of thinking about computation. The appen

Winning Ways for Your Mathematical Plays, Volume 3
Winning Ways for Your Mathematical Plays, Volume 3

Author: Elwyn R. Berlekamp

Publisher: CRC Press

Published: 2018-05-08

Total Pages: 364

ISBN-13: 0429945574

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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

Characteristics of Games
Characteristics of Games

Author: George Skaff Elias

Publisher: MIT Press

Published: 2012-08-24

Total Pages: 331

ISBN-13: 0262300443

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Understanding games—whether computer games, card games, board games, or sports—by analyzing certain common traits. Characteristics of Games offers a new way to understand games: by focusing on certain traits—including number of players, rules, degrees of luck and skill needed, and reward/effort ratio—and using these characteristics as basic points of comparison and analysis. These issues are often discussed by game players and designers but seldom written about in any formal way. This book fills that gap. By emphasizing these player-centric basic concepts, the book provides a framework for game analysis from the viewpoint of a game designer. The book shows what all genres of games—board games, card games, computer games, and sports—have to teach each other. Today's game designers may find solutions to design problems when they look at classic games that have evolved over years of playing. Characteristics of Games—written by three of the most prominent game designers working today—will serve as an essential reference for game designers and game players curious about the inner workings of games. It includes exercises (which can also serve as the basis for discussions) and examples chosen from a wide variety of games. There are occasional mathematical digressions, but these can be skipped with no loss of continuity. Appendixes offer supplementary material, including a brief survey of the two main branches of mathematical game theory and a descriptive listing of each game referred to in the text.