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An Analytic Derivation of Blackjack Win Rates

Author

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  • Gary Gottlieb

    (New York University, New York, New York)

Abstract

We study the win rate for the game of blackjack and derive a stochastic model for the advantage (i.e., expected win) process. Assuming proportional betting, we derive an explicit formula that estimates the win rate as a function of the number of decks used and the proportion of cards dealt before reshuffling. We derive a relationship between the “aggressiveness” of betting and risk. Risk is measured as the probability of wealth dropping below a specified level before it exceeds a higher, specified level.

Suggested Citation

  • Gary Gottlieb, 1985. "An Analytic Derivation of Blackjack Win Rates," Operations Research, INFORMS, vol. 33(5), pages 971-988, October.
    • Handle: RePEc:inm:oropre:v:33:y:1985:i:5:p:971-988
    DOI: 10.1287/opre.33.5.971
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    Cited by:

    1. van der Genugten, B.B., 1995. "Blackjack in Holland Casino's : Basic, optimal and winning strategies," Research Memorandum FEW 711, Tilburg University, School of Economics and Management.
    2. van der Genugten, B.B., 1995. "Blackjack in Holland Casino's : Basic, optimal and winning strategies," Other publications TiSEM 7deafece-aaf5-4de0-85e4-0, Tilburg University, School of Economics and Management.

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