## Abstract

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).

## Keywords

Diffusion Equation Fourier Representation Effective Yield True Count Drift Diffusion Equation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## References

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