Modified Kelly criteria

Abstract

This paper considers an extension of the Kelly criterion used in sports wagering. By recognizing that the probability p of placing a correct wager is unknown, modified Kelly criteria are obtained that take the uncertainty into account. Estimators are proposed that are developed from a decision theoretic framework. We observe that the resultant betting fractions can differ markedly based on the choice of loss function. In the cases that we study, the modified Kelly fractions are smaller than original Kelly.