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The minimax bookie: the two-horse case

Part of: Operations research and management science

Published online by Cambridge University Press:  08 September 2016

Daniel Barry  and
Caroline Lynch
Daniel Barry*
Affiliation:
University of Limerick
Caroline Lynch*
Affiliation:
University of Limerick
*
∗ Postal address: Vice President Academic & Registrar, Plassey House, University of Limerick, Limerick, Ireland.
∗∗ Cloncool, O'Callaghan's Mills, County Clare, Ireland. Email address: clynch@canada.com
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Abstract

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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, which is assumed to be determined uniquely by the price quoted for each horse. We consider different strategies for choosing these prices as bets accumulate, and examine the penalty incurred by the use of a strategy other than the optimal one, in the general case where the distribution of the customers' betting probabilities is unknown.

Keywords

Dynamic programmingbookmakerhorse raceMarkov decision process

MSC classification

Primary: 90B40: Search theory
Secondary: 90C39: Dynamic programming 90C40: Markov and semi-Markov decision processes
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 38 , Issue 4 , December 2006 , pp. 899 - 915
Copyright
Copyright © Applied Probability Trust 2006 

References

Barry, D. and Hartigan, J. A. (1996). The minimax bookie. J. Appl. Prob. 33, 1093–1107.Google Scholar