Optimal Betting Sizes for the Game of Blackjack

24 Pages Posted: 15 Sep 2013

Date Written: September 12, 2013


We develop the theory of Kelly and Thorp in analyzing the optimal bet sizes for blackjack by incorporating the practical considerations of players wherein only a finite number of plays shall occur as well as pursuing maximizing risk-adjusted returns. We show that the ratio of return to bet size is approximately proportional to the return / drawdown ratio and is a reasonable proxy for risk-adjusted returns. Thus, bet sizes that maximize this measure or its marginal increase are also reasonable choices. Both theoretical analysis and computer simulation show that these alternative choices of bet sizes are much more conservative compared to what the Kelly-Thorp theory suggests and makes sense in practice. In principle, the analysis and results here also apply to money management problems for investment as well as more generalized cumulative resource allocation considerations involving risk.

Keywords: Black Jack, betting size, risk management

Suggested Citation

Vince, Ralph and Zhu, Qiji Jim, Optimal Betting Sizes for the Game of Blackjack (September 12, 2013). Available at SSRN: https://ssrn.com/abstract=2324852 or http://dx.doi.org/10.2139/ssrn.2324852

Ralph Vince

None ( email )

Qiji Jim Zhu (Contact Author)

Western Michigan University ( email )

Kalamazoo, MI 49008
United States

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