The Mathematics of Games

 
John D. Beasley (Autor)
 
Dover Publications (Verlag)
erschienen am 18. Januar 2013 | 176 Seiten
 
E-Book | ePUB mit Adobe DRM | Systemvoraussetzungen
978-0-486-15162-5 (ISBN)
 
"Mind-exercising and thought-provoking."-New ScientistIf playing games is natural for humans, analyzing games is equally natural for mathematicians. Even the simplest of games involves the fundamentals of mathematics, such as figuring out the best move or the odds of a certain chance event. This entertaining and wide-ranging guide demonstrates how simple mathematical analysis can throw unexpected light on games of every type-games of chance, games of skill, games of chance and skill, and automatic games.Just how random is a card shuffle or a throw of the dice? Is bluffing a valid poker strategy? How can you tell if a puzzle is unsolvable? How large a role does luck play in games like golf and soccer? This book examines each of these issues and many others, along with the general principles behind such classic puzzles as peg solitaire and Rubik's cube. Lucid, instructive, and full of surprises, it will fascinate mathematicians and gamesters alike.
Dover Publications
Englisch
New York
Höhe: 216 mm | Breite: 137 mm
10,12 MB
978-0-486-15162-5 (9780486151625)
048615162X (048615162X)
weitere Ausgaben werden ermittelt
John D. Beasley
  • Title Page
  • Copyright Page
  • PREFACE TO THE DOVER EDITION
  • ACKNOWLEDGEMENTS
  • Table of Contents
  • 1 - INTRODUCTION
  • 2 - THE LUCK OF THE DEAL
  • Counting made easy
  • 4-3-3-3 and all that
  • Shuffle the pack and deal again
  • 3 - THE LUCK OF THE DIE
  • Counting again made easy
  • The true law of averages
  • How random is a toss?
  • Cubic and other dice
  • The arithmetic of dice games
  • Simulation by computer
  • 4 - TO ERR IS HUMAN
  • Finding a hole in the ground
  • Finding a hole in the defence
  • A game of glorious uncertainty
  • 5 - IF A BEATS B, AND B BEATS C . . .
  • The assessment of a single player in isolation
  • The estimation of trends
  • Interactive games
  • Grades as measures of ability
  • The self-fulfilling nature of grading systems
  • The limitations of grading
  • Cyclic expectations
  • 6 - BLUFF AND DOUBLE BLUFF
  • I've got a picture
  • An optimal strategy for each player
  • Scissors, paper, stone
  • You cut, I'll choose
  • The nature of bluffing
  • Analysing a game
  • 7 - THE ANALYSIS OF PUZZLES
  • Black and white squares
  • Divisibility by three
  • Positions with limited potential
  • Systematic progress within a puzzle
  • Systematic progress between puzzles
  • 8 - SAUCE FOR THE GANDER
  • A winning strategy at nim
  • Nim in disguise
  • All cul-de-sacs lead to nim
  • Grundy analysis in practice
  • Some more balancing acts
  • Playing to lose
  • 9 - THE MEASURE OF A GAME
  • Nim with personal counters
  • Games of fractional measure
  • General piles
  • The nature of a numeric game
  • The measure of a feeble threat
  • Infinite games
  • 10 - WHEN THE COUNTING HAS TO STOP
  • The symptoms of a hard game
  • When you know who, but not how
  • The paradox underlying games of pure skill
  • 11 - ROUND AND ROUND IN CIRCLES
  • Driving the old woman to bed
  • Turing games
  • Turing's paradox
  • The hole at the heart of mathematics
  • FURTHER READING
  • INDEX
  • A CATALOG OF SELECTED DOVER BOOKS IN SCIENCE AND MATHEMATICS
  • DOVER BOOKS ON MATHEMATICS

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