Adaptive strategy in Kelly's horse races model

We formulate an adaptive version of Kelly's horse model in which the gambler learns from past race results using Bayesian inference. A known asymptotic scaling for the difference between the growth rate of the gambler and the optimal growth rate, known as the gambler'sregret, is recovered. We show how this adaptive strategy is related to the universal portfolio strategy, and we build improved adaptive strategies in which the gambler exploits information contained in the bookmaker odds distribution to reduce his/her initial loss of the capital during the learning phase.