On optimal betting strategies with multiple mutually exclusive outcomes

Abstract

We examine the problem of how much risk‐averse agents would be willing to bet on events where there are multiple possible winners but only one will actually win. We describe how this problem can be solved for concave utility functions and illustrate the properties of the solution. The optimal betting strategy is more aggressive than strategies derived from considering each outcome separately such as the Kelly criterion. The strategy also recommends sometimes placing bets with negative expected returns because they act as hedges against losses on other bets. While this strategy maximizes the bettor's subjective expected utility, if betting odds incorporate a profit margin and reflect underlying probabilities correctly, then this more aggressive approach loses more money and results in lower realized utility.