  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.
