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THE KELLY CRITERION IN BLACKJACK, SPORTS
BETTING, AND THE STOCK MARKET
BETTING, AND THE STOCK MARKET
by Edward O. Thorp
Edward O. Thorp and Associates
Newport Beach, CA 92660
©1997
Paper presented at: The 10th International Conference on
Gambling and Risk Taking
Montreal, June 1997*
ABSTRACT
The central problem for gamblers is to find positive expectation bets. But the gambler also needs to know how to manage his money, i.e. how much to bet. In the stock market (more inclusively, the securities markets) the problem is similar but more complex. The gambler, who is now an ``investor'', looks for ``excess risk adjusted return''. In both these settings, we explore the use of the Kelly criterion, which is to maximize the expected value of the logarithm of wealth (''maximize expected logarithmic utility'').
The criterion is known to economists and financial theorists by names such as the ''geometric mean maximizing portfolio strategy'', maximizing logarithmic utility, the growth-optimal strategy, the capital growth criterion, etc.
The author initiated the practical application of the Kelly criterion by using it for card counting in blackjack. We will present some useful formulas and methods to answer various natural questions about it that arise in blackjack and other gambling games. Then we illustrate its recent use in a successful casino sports betting system. Finally, we discuss its application to the securities markets where it has helped the author to make a thirty year total of 80 billion dollars worth of "bets".
*Revised May 29, 1998
The following links are to files in .pdf format
The criterion is known to economists and financial theorists by names such as the ''geometric mean maximizing portfolio strategy'', maximizing logarithmic utility, the growth-optimal strategy, the capital growth criterion, etc.
The author initiated the practical application of the Kelly criterion by using it for card counting in blackjack. We will present some useful formulas and methods to answer various natural questions about it that arise in blackjack and other gambling games. Then we illustrate its recent use in a successful casino sports betting system. Finally, we discuss its application to the securities markets where it has helped the author to make a thirty year total of 80 billion dollars worth of "bets".
*Revised May 29, 1998
The following links are to files in .pdf format
- Abstract (Archive copy)
- 1 Introduction (Archive copy)
- 2 Coin Tossing (Archive copy)
- 3 Optimal growth: Kelly criterion formulas for practitioners (Archive copy)
- 4 The Long Run: When Will The Kelly Strategy ``Dominate''? (Archive copy)
- 5 Blackjack (Archive copy)
- 6 Sports Betting (Archive copy)
- 7 Wall Street: the biggest game (Archive copy)
- 8 A Case Study (Archive copy)
- 9 My Experience with the Kelly Approach (Archive copy)
- 10 Conclusion (Archive copy)
- Figures (Archive copy)
- APPENDIX 1. Integrals for deriving moments (Archive copy)
- APPENDIX II. Derivation of formula (3.1) (Archive copy)
- APPENDIX III. Expected time to reach goal (Archive copy)
- References (Archive copy)