Journal of Applied Probability

Card counting in continuous time

Patrik Andersson

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We consider the problem of finding an optimal betting strategy for a house-banked casino card game that is played for several coups before reshuffling. The sampling without replacement makes it possible to take advantage of the changes in the expected value as the deck is depleted, making large bets when the game is advantageous. Using such a strategy, which is easy to implement, is known as card counting. We consider the case of a large number of decks, making an approximation to continuous time possible. A limit law of the return process is found and the optimal card counting strategy is derived. This continuous-time strategy is shown to be a natural analog of the discrete-time strategy where the so-called effects of removal are replaced by the infinitesimal generator of the card process.

Article information

J. Appl. Probab., Volume 49, Number 1 (2012), 184-198.

First available in Project Euclid: 8 March 2012

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]
Secondary: 60F17: Functional limit theorems; invariance principles

Sampling without replacement invariance principle gambling theory optimal control


Andersson, Patrik. Card counting in continuous time. J. Appl. Probab. 49 (2012), no. 1, 184--198. doi:10.1239/jap/1331216841.

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