Risk and Reward

The Science of Casino Blackjack

  • Authors
  • N. Richard Werthamer

Table of contents

  1. Front Matter
    Pages i-xv
  2. Strategy

    1. Front Matter
      Pages 1-1
    2. N. Richard Werthamer
      Pages 3-8
    3. N. Richard Werthamer
      Pages 9-14
    4. N. Richard Werthamer
      Pages 15-20
    5. N. Richard Werthamer
      Pages 21-30
    6. N. Richard Werthamer
      Pages 31-36
    7. N. Richard Werthamer
      Pages 37-44
  3. Analysis

    1. Front Matter
      Pages 46-46
    2. N. Richard Werthamer
      Pages 47-66
    3. N. Richard Werthamer
      Pages 67-80
    4. N. Richard Werthamer
      Pages 81-114
    5. N. Richard Werthamer
      Pages 115-125
  4. Back Matter
    Pages 127-131

About this book


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 Berkley. 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.


Calc Counting Parameter Rack calculus computation derivation form graphs layers performance profession tracking university variable

Bibliographic information