Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-15T13:21:02.306Z Has data issue: false hasContentIssue false

Non-random shuffling for multiple decks

Published online by Cambridge University Press:  14 July 2016

Gary Gottlieb*
Affiliation:
New York University and Sanford C. Bernstein & Co., Inc.

Abstract

Non-randomness that arises in the shuffling of multiple numbers of decks of playing cards is modeled. An efficient way to exploit the non-randomness is derived, and its effect on the win rate for a simple game of chance is derived.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1987 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Anderson, T. W. (1958) An Introduction to Multivariate Statistical Analysis. Wiley, New York.Google Scholar
Breiman, L. (1961) Optimal gambling systems for favorable games. Proc. 4th Berkeley Symp. Math. Statist. Prob. 1, 6578.Google Scholar
Ethier, S. and Tavaré, S. (1983) The proportional bettor's return on investment. J. Appl. Prob. 20, 563573.Google Scholar
Finkelstein, M. and Whitley, R. (1981) Optimal strategies for repeated games. Adv. Appl. Prob. 13, 415428.CrossRefGoogle Scholar
Gottlieb, G. (1985a) An analytic derivation of blackjack win rates. Operat. Res. 33, 871988.CrossRefGoogle Scholar
Gottlieb, G. (1985b) An optimal betting strategy for repeated games. J. Appl. Prob. 22, 787795.CrossRefGoogle Scholar
Karlin, S. and Taylor, H. M. (1975) A First Course in Stochastic Processes, 2nd edn. Academic Press, New York.Google Scholar