Kelly betting on horse races with uncertainty in probability estimates

TL;DR

This paper develops stochastic optimization models for horse race betting under uncertain probability estimates, demonstrating improved returns by accounting for estimation errors in a simulated empirical study.

Contribution

It introduces models that incorporate probability uncertainty into betting strategies, especially focusing on two-outcome races and extending to multiple outcomes.

Findings

Accounting for probability estimation error improves betting returns.

Models outperform traditional methods in simulated scenarios.

Empirical results highlight the importance of uncertainty in probability estimates.

Abstract

We investigate the problem of gambling with uncertainty in outcome probabilities. Stochastic optimization models are proposed for optimal investing on events with mutually exclusive outcomes when probabilities are estimated using multinomial logistic regression. Special attention is given to the case of there being two outcomes, and the general case of many outcomes. An empirical study using simulated data was conducted where the loss of return from probability estimation error is observed, and superior returns are achieved taking it into consideration.