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

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

S. N. Ethier and D. A. Levin

Source: Adv. in Appl. Probab. Volume 37, Number 1 (2005), 90-107.

Abstract

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.

Primary Subjects: 60G09

Secondary Subjects: 60G35, 60C05

Keywords: Sampling without replacement; exchangeability; martingale; U-statistic; central limit theorem

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aap/1113402401
Digital Object Identifier: doi:10.1239/aap/1113402401
Mathematical Reviews number (MathSciNet): MR2135155
Zentralblatt MATH identifier: 02164619

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