The Theory of Gambling and Statistical Logic PDF
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The Theory of Gambling and Statistical Logic Thispageintentionallyleftblank The Theory of Gambling and Statistical Logic Second Edition Richard A. Epstein AMSTERDAM • BOSTON • HEIDELBERG • LONDON NEW YORK • OXFORD • PARIS • SAN DIEGO SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO Academic Press is an Imprint of Elsevier Academic Press is an imprint of Elsevier 225 Wyman Street, Waltham, MA 02451, USA The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, UK Copyright © 2013, 1977 Elsevier Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in Oxford, UK: phone: ((cid:2) 44) 1865 843830, fax: ((cid:2) 44) 1865 853333, E-mail: [email protected] . You may also complete your request online via the Elsevier homepage ( http://elsevier.com ), by selecting “ Support & Contact ” then “ Copyright and Permission ” and then “ Obtaining Permissions. ” Library of Congress Cataloging-in-Publication Data Epstein, Richard A., The theory of gambling and statistical logic / Richard A. Epstein. — 2nd ed. p. cm. Originally published: Burlington, MA: Academic Press, 2009. Includes index. ISBN 978-0-12-397857-8 1. Games of chance (Mathematics) 2. Statistical decision. I. Title. QA271.E67 2012 519.2(cid:3)7 — dc23 2012027637 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. For information on all Academic Press publications visit our Web site at www.store.elsevier.com Printed in the United States 09 10 11 12 13 10 9 8 7 6 5 4 3 2 1 It is remarkable that a science which began with the consideration of games of chance should have become the most important object of human knowledge. . . . The most important questions of life are, for the most part, really only problems of probability. Pierre Simon, Marquis de Laplace Théorie Analytique des Probabilitiés, 1812 Thispageintentionallyleftblank Contents Preface xi 1 . Kubeiagenesis 1 2 . Mathematical Preliminaries 11 The Meaning of Probability 11 The Calculus of Probability 12 Statistics 22 Game Theory 30 Random Walks 37 Quantum Games 40 3 . Fundamental Principles of a Theory of Gambling 43 Decision Making and Utility 43 Prospect Theory 48 Decision-Making Criteria 49 The Basic Theorems 51 4 . Parrondo’s Principle 74 The Basic Principle 74 Multiplayer Games 81 History -Dependent Parrondo Games 82 Quantum Parrondo Games 88 Cooperative Games 88 The Allison Mixture 91 5 . Coins, Wheels, and Oddments 95 Biased Coins 95 Statistical Properties of Coins 98 Coin Matching 108 Coin Games 111 Heads–Tails Interplay 115 The Two-armed Bandit 122 Nontransitive Sequences 123 Quantum Coin Tossing 124 Diverse Recreations 125 Casino Games 146 Public Games 156 Puzzlements 166 vii viii Contents 6 . Coups and Games with Dice 171 A Brief Chronicle 171 Detection of Bias 173 Divers Dice Probabilities 176 Structured Dice Games 184 Nontransitive Dice 198 Sicherman ’s Dice 202 Casino Games 202 Backgammon 216 Dice Divertissements 217 7 . The Play of the Cards 221 Origins and Species 221 Randomness and Shuffl ing 222 Card Probabilities 232 Matching Problems (Rencontres) 238 Selected Sidelights 244 Informal Card Games 245 Formal Card Games 251 Casino Games 262 Card Conundra 266 8 . Blackjack 271 Memorabilia 271 Rules and Format 272 Assumptions 273 Optimal Strategies 273 Card Counting 277 Shuffl e Tracking 284 Side Bets 285 Blackjack Variations 286 Pooled Resources 291 9 . Statistical Logic and Statistical Games 295 Strategic Selection 295 The Stock Market 296 Horse Racing 303 Duels and Truels 312 Tournaments 322 Random Tic-Tac-Toe 327 Inquizition 328 10 . Games of Pure Skill and Competitive Computers 335 Defi nitions 335 Tic-Tac-Toe 336 Contents ix Nim and Its Variations 342 Single-pile Countdown Games 351 The Grundy Function; Kayles 358 Seemingly Simple Board Games 365 More Complex Games 372 Games Computers Play 387 The Shadow of Things to Come 389 Board Baffl ers 389 11 . F allacies and Sophistries 397 Psychology and Philosophy 397 Fallacies 398 Paranormal Phenomena 400 Epilogue 413 Appendix 415 Index 441
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