Bet Strategies



Blackjack is a game in which the expected return on a given round differs from that of the previous round, because the pack composition has changed; as a result of the differing return, the bet should change correspondingly. A proper analysis of risk in such a game must account for these fluctuations. Nevertheless, analysis of a simplified game in which the return and bet stay fixed is a useful warm-up exercise, in terms of both the mathematical tools employed and some characteristics of the results. The reasoning here, as in much of this chapter, follows Werthamer (2005).


Diffusion Equation Fourier Representation Effective Yield True Count Drift Diffusion Equation 


  1. Carlson, Bryce, “Blackjack for Blood", CompuStar Press, 1992Google Scholar
  2. Cox, J.C., S.A. Ross, and M. Rubenstein, “Option Pricing: a Simplified Approach”, Journal of Financial Economics 7, 229–263, 1979MATHCrossRefGoogle Scholar
  3. Epstein, Richard A., “The Theory of Gambling and Statistical Logic", Academic Press, revised edition, 1995MATHGoogle Scholar
  4. Ethier, S.N., “The Kelly System Maximizes Median Fortune”, Journal of Applied Probability , 41, 230–6 (2004)MathSciNetCrossRefGoogle Scholar
  5. Griffin, Peter A., “The Theory of Blackjack", Huntington Press, 6th edition, 1999Google Scholar
  6. Harris, B., “The Theory of Optimal Betting Spreads; Janacek, K., “Theory of Optimal Betting”; Yamashita, W., “Optimal Betting Strategy”: all at (1997)
  7. Hull, J.C., “Options, Futures and Other Derivatives”, Prentice Hall, 2002Google Scholar
  8. Theory of Financial Decision Making”, Rowman & Littlefield, 1987Google Scholar
  9. Ito, C., “On Stochastic Differential Equations”, Memoirs of the American Mathematical Society 4, 1–51 (1951)Google Scholar
  10. Kelly, John L., Jr., “A New Interpretation of Information Rate", Bell System Technical Journal 35, 917–926 (1956)MathSciNetGoogle Scholar
  11. Merton, Robert C., “Theory of Rational Option Pricing”, Bell Journal of Economics & Management Science 4, 141 (1973)MathSciNetCrossRefGoogle Scholar
  12. Samuelson, Paul A., “Proof that Properly Anticipated Prices Fluctuate Randomly”, Industrial Management Review 6, 41 (1965)Google Scholar
  13. Schlesinger, Don, “Blackjack Attack: Playing the Pros' Way", RGE Publishing, 3rd edition, 2005Google Scholar
  14. Sileo, Patrick, “The Evaluation of Blackjack Games Using a Combined Expectation and Risk Measure”, in Eadington, W.R. and J.A. Cornelius (eds.), “Gambling and Commercial Gaming”, University of Nevada, Reno, 1992Google Scholar
  15. Vancura, Olaf, and Ken Fuchs, “Knock-Out Blackjack", Huntington Press, 1998Google Scholar
  16. Wong, Stanford, “Professional Blackjack" Pi Yee Press, 5th edition, 1994; “Blackjack Secrets”, Pi Yee Press, 1994Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.University of New YorkNew YorkUSA

Personalised recommendations