Risk and Reward (eBook)

The Science of Casino Blackjack
eBook Download: PDF
2009 | 2009
XVIII, 131 Seiten
Springer New York (Verlag)
978-1-4419-0253-5 (ISBN)

Lese- und Medienproben

Risk and Reward -  N. Richard Werthamer
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For decades, casino gaming has been steadily increasing in popularity worldwide. Blackjack is among the most popular of the casino table games, one where astute choices of playing strategy can create an advantage for the player.

RISK AND REWARD analyzes the game in depth, pinpointing not just its optimal strategies but also its financial performance, in terms of both expected cash flow and associated risk.

The book begins by describing the strategies and their performance in a clear, straightforward style. The presentation is self-contained, non-mathematical, and accessible to readers at all levels of playing skill, from the novice to the blackjack expert. Careful attention is also given to simplified, but still nearly optimal strategies that are easier to use in a casino. Unlike other books in the literature the author then derives each aspect of the strategy mathematically, to justify its claim to optimality. The derivations mostly use algebra and calculus, although some require more advanced analysis detailed in supporting appendices. For easy comprehension, formulae are translated into tables and graphs through extensive computation.

This book will appeal to everyone interested in blackjack: those with mathematical training intrigued by its application to this popular game as well as all players seeking to improve their performance.


For decades, casino gaming has been steadily increasing in popularity worldwide. Blackjack is among the most popular of the casino table games, one where astute choices of playing strategy can create an advantage for the player. Risk and Reward analyzes the game in depth, pinpointing not just its optimal strategies but also its financial performance, in terms of both expected cash flow and associated risk.The book begins by describing the strategies and their performance in a clear, straightforward style. The presentation is self-contained, nonmathematical, and accessible to readers at all levels of playing skill, from the novice to the blackjack expert. Careful attention is also given to simplified, but still nearly optimal strategies that are easier to use in a casino. Unlike other books in the literature the author then derives each aspect of the strategy mathematically, to justify its claim to optimality. The derivations mostly use algebra and calculus, although some require more advanced analysis detailed in supporting appendices. For easy comprehension, formulae are translated into tables and graphs through extensive computation.This book will appeal to everyone interested in blackjack: those with mathematical training intrigued by its application to this popular game as well as all players seeking to improve their performance.N. Richard Werthamer is retired from a successful career as a scientist and executive, most recently as the Executive Officer of the American Physical Society. He graduated summa cum laude from Harvard College before receiving his PhD in Theoretical Physics from the University of California at Berkeley. His original research has been published extensively in the world's leading journals. In this book, he applies his scientific background to the analysis of blackjack.

Preface 5
Introduction 7
Contents 10
List of Figures 13
List of Tables 15
Part I Strategy 17
Chapter 1 The Game 18
1.1 History of Casino Blackjack and Its Analysis 18
1.2 Rules, Procedures, and Terminology 20
Chapter 2 Playing the Hand 24
2.1 Basic Strategy 24
2.2 Composition-Dependent Play 29
Chapter 3 Tracking the Cards 30
3.1 Linear Counts 31
3.2 Choosing a Counting Vector 32
3.3 Unbalanced Counting Vectors 34
3.4 Relating the True Count to the Expected Return 35
Chapter 4 Betting 36
4.1 Yield, Risk, and Optimal Bet Strategies 36
4.2 Betting Proportional to Current Capital 42
4.3 Back-Counting and Table-Hopping 44
Chapter 5 Playing the Hand When the Count and Bet Vary 46
5.1 Play Strategies that Vary with the Count 46
5.2 Counter Basic Strategy for the Variable Bettor 50
Chapter 6 Synthesis and Observations 52
6.1 A Practical, Nearly Optimal Strategy 52
6.2 Blackjack as a Recreation vs. a Profession 58
Part II Analysis 60
Chapter 7 Play Strategies 61
7.1 Basic Strategy, Large Number of Decks 61
7.2 Basic Strategy, Small Number of Decks 72
7.3 Play Parameters Dependent on Identities of Initial Cards 77
Chapter 8 Card Counting 81
8.1 Analytical Framework 81
8.2 Expected Return at Nonzero Depth 87
8.3 Optimizing the Counting Vectors 89
8.4 Optimizing the Counting Vectors: Many-Cards Limit 90
8.5 Computation of the Derivatives of the Expected Return 92
8.6 Unbalanced Counts 92
Chapter 9 Bet Strategies 95
9.1 Risk and Capitalization 95
9.2 Betting Proportional to Current Capital 114
9.3 Back-Counting and Table-Hopping 119
Chapter 10 Play Strategies with Card Counting 129
10.1 Count-Dependent Playing Strategy 129
10.2 Counter Basic Strategy 138
References 140
Index 142
Index of Symbols 144

Erscheint lt. Verlag 7.7.2009
Zusatzinfo XVIII, 131 p.
Verlagsort New York
Sprache englisch
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Angewandte Mathematik
Mathematik / Informatik Mathematik Finanz- / Wirtschaftsmathematik
Mathematik / Informatik Mathematik Statistik
Mathematik / Informatik Mathematik Wahrscheinlichkeit / Kombinatorik
Technik
Wirtschaft Allgemeines / Lexika
Wirtschaft Volkswirtschaftslehre
Schlagworte Calc • Calculus • Computation • Counting • Derivation • Form • Graphs • Layers • Parameter • Performance • Profession • Rack • Tracking • University • Variable
ISBN-10 1-4419-0253-8 / 1441902538
ISBN-13 978-1-4419-0253-5 / 9781441902535
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