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On the fundamental theorem of card counting, with application to the game of trente et quarante

Part of: Combinatorial probability Stochastic processes

Published online by Cambridge University Press:  01 July 2016

S. N. Ethier  and
David A. Levin
S. N. Ethier*
Affiliation:
University of Utah
David A. Levin*
Affiliation:
University of Utah
*
∗ Postal address: Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, UT 84112, USA.
∗ Postal address: Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, UT 84112, USA.
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Abstract

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A simplified proof of Thorp and Walden's fundamental theorem of card counting is presented, and a corresponding central limit theorem is established. Results are applied to the casino game of trente et quarante, which was studied by Poisson and De Morgan.

Keywords

Sampling without replacementexchangeabilitymartingaleU-statisticcentral limit theorem

MSC classification

Primary: 60G09: Exchangeability
Secondary: 60G35: Signal detection and filtering 60C05: Combinatorial probability

Information

Type
General Applied Probability
Information
Advances in Applied Probability , Volume 37 , Issue 1 , March 2005 , pp. 90 - 107
Copyright
Copyright © Applied Probability Trust 2005 

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