A bookmaker takes bets on a two-horse race, attempting to minimise expected loss over all possible outcomes of the race. Profits are controlled by manipulation of customers' betting behaviour; 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 customers' betting behaviour provides about this probability distribution, and consider how to use this to estimate the probability distribution for remaining customers.
Keywords. EM Algorithm, bookmaker, horse race, Markov decision process
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Department of Mathematics
National University of Ireland, Galway
University of Limerick