Risk and Reward (eBook)

N. Richard Werthamer is retired from a successful career as a scientist and executive,mostly recently as the Executive Officer of The American Physical Society. He earneda B.A. summa cum laude from Harvard College, followed by a Ph.D. from the Universityof California, Berkeley. His original scientific research has been published in theworld's leading journals. In RISK AND REWARD, he applies that background to hisanalysis of blackjack.

Contents Preface Introduction Working with the Interactive Edition Part I 1                    The Game 1.1              History of Casino Blackjack and Its Analysis 1.2              Rules, Procedures and Terminology 2                    Playing the Hand 2.1              Basic Strategy 2.1.1        Expected Return with Variant Rules and Procedures 2.1.2        Expected Return vs. Return on Investment 2.2              Composition-Dependent Play 3                    Tracking the Cards 3.1              Linear Counts 3.2              Choosing a Counting Vector 3.3              Unbalanced Counting Vectors 3.4              Relating the True Count to the Expected Return 4                    Betting 4.1              Yield, Risk, and Optimal Bet Strategies 4.11                Bet size in relation to true count 4.12                Other criteria 4.2              Betting Proportional to Current Capital 4.3                Multiple Hands 4.4                Back-Counting and Table-Hopping 5                    Playing the Hand When the Count and Bet Vary 5.1              Play Strategies that Vary with the Count 5.1.1        Reconsidering the Counting Vector 5.1.2        Count Dependence of the Play Parameters 5.1.3        The Insurance Bet 5.2             Counter Basic Strategy for the Variable Bettor 6                    Synthesis and Observations 6.1              A Practical, Nearly Optimal Strategy 6.2              Blackjack as a Recreation vs. a Profession   Part II 7                    Play Strategies 7.1              Basic Strategy, Large Number of Decks 7.1.1        Analytical Framework 7.1.2        Expected Player Return 7.1.3        Frequency of Tied Hands 7.1.4        Multiple Simultaneous Hands: Return, Variance, and Covariance 7.1.5        Expected Number of Cards Used per Round 7.2              Basic Strategy, Small Number of Decks 7.2.1        Analytical Framework 7.2.2        Expected Return, and Optimal Basic Strategy, vs. Number of Decks 7.2.3        Surrender; Insurance 7.3              Play Parameters Dependent on Identities of Initial Cards 7.3.1        Comparison with Previous Authorities 8                    Card Counting 8.1              Analytical Framework 8.1.1        Asymptotic Distribution 8.1.2        Expected Return; Invariance Theorem 8.1.3        Hermite Series 8.2              Expected Return at Nonzero Depth 8.3              Optimizing the Counting Vectors 8.4              Optimizing the Counting Vectors: Many-Cards Limit 8.5              Computation of the Derivatives of the Expected Return 8.6              Unbalanced Counts Appendix 8.A Asymptotic Distribution of Card Likelihoods Appendix 8.B Eigenmodes 9                    Bet Strategies 9.1              Risk and Capitalization 9.1.1        Risk in a Game with Fixed Return 9.1.2        Optimal Betting When Return Fluctuates: Expected Capital and Risk 9.1.3        Connections with Finance 9.1.4        Distribution of Capital 9.1.5        Properties of the Risk and Expected Capital Expressions 9.1.6        Optimal Betting When Return Fluctuates: Bet Strategy 9.1.7        Yield When the Bet Size Is Discrete; Wong Benchmark Betting 9.2              Betting Proportional to Current Capital 9.2.1        Mixed Additive and Multiplicative Betting 9.3              Betting When Playing Multiple Simultaneous Hands 9.4                Back-Counting and Table-Hopping 9.4.1       Entry 9.4.2       Entry and Exit 9.4.3       Entry and Departure 9.4.4       Entry, Exit, and Departure Appendix 9.A   Distribution of Player’s Capital, Asymptotically for Large N Appendix 9.B   The Chain Rule Convolution 10                Play Strategies with Card Counting 10.1          Count-Dependent Playing Strategy 10.1.1    Counting Vector Optimal for Play Variation Alone 10.1.2    Single Counting Vector Optimal for Bet and Play Together 10.1.3    Two Distinct Counting Vectors 10.1.4    Insurance with Variable Betting 10.2          Counter Basic Strategy References Index of Terms