Abstract
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.
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