Estimating probability distributions by observing betting practices

Abstract

A bookmaker takes bets on a two-horse race, attempting to minimize expected loss over all possible outcomes of the race. Profits are controlled by manipulation of customer betting behavior; in order to do this, we need some information about the probability distribution which describes how the customers will bet. We examine what information initial customer betting behavior provides about this probability distribution, and consider how to use this to estimate the probability distribution for remaining customers.