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Optimal Betting in Casino Blackjack

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  • N. Richard Werthamer

Abstract

In casino blackjack, the odds fluctuate from round to round as cards are dealt from a randomly shuffled pack. A player who 'counts cards' can estimate the odds on the next round and so can vary his bet size accordingly: better-than-average odds warrant a larger bet. The optimal relationship of bet to count is derived here under the criterion of maximum expected increase in capital per round subject to a specified risk of ruin. The optimisation analysis is complicated by the need to impose lower and possibly upper bounds on the bet size. A family of optimal betting schemes is found, depending on the risk selected and other parameters; among this family is the one found by Harris, Janecek and Yamashita using a different optimisation criterion. Representative computational results are displayed for a typical set of blackjack conditions. Some commentary is given on the choice of a bet scheme from the optimal family, depending on the player's style and objectives. Remarks are also made about Kelly betting, in the context of risk.

Suggested Citation

  • N. Richard Werthamer, 2005. "Optimal Betting in Casino Blackjack," International Gambling Studies, Taylor & Francis Journals, vol. 5(2), pages 253-270, November.
    • Handle: RePEc:taf:intgms:v:5:y:2005:i:2:p:253-270
    DOI: 10.1080/14459790500303485
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    Cited by:

    1. N. Richard Werthamer, 2008. "Optimal Betting in Casino Blackjack III: Table-Hopping," International Gambling Studies, Taylor & Francis Journals, vol. 8(1), pages 63-75, April.

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