Optimal Betting in Casino Blackjack

N. Richard Werthamer

International Gambling Studies, 2005, vol. 5, issue 2, 253-270

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.

Date: 2005
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DOI: 10.1080/14459790500303485

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International Gambling Studies is currently edited by Katie Donnelly, David Marshall, Bronwyn Stuart, Alex Blaszczynski and Jan McMillen

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