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The minimax bookie

Part of: Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Daniel Barry  and
John A. Hartigan
Daniel Barry*
Affiliation:
University College, Cork
John A. Hartigan*
Affiliation:
Yale University
*
∗Postal address: Department of Statistics, University College, Cork, Eire.
∗∗Postal address: Department of Statistics, Yale University, PO Box 208290, New Haven, Connecticut 06520–8290, USA.
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Abstract

A bookmaker makes a book on a horse race: he offers odds against the various horses winning the race, and gamblers accept bets at those odds when they find the odds attractive. The book at a particular time consists of the bookmaker's winnings according to the different outcomes of the race if the race were run at that time. We consider strategies the bookmaker might adopt when deciding how to alter his quoted odds as bets accumulate. The bookmaker is assumed to behave conservatively in the sense that he tries to minimise his expected maximum loss over all possible outcomes of the race.

Keywords

DYNAMIC PROGRAMMINGMARKOV DECISION PROCESSBOOKMAKERHORSE RACE

MSC classification

Primary: 90B40: Search theory
Secondary: 90C39: Dynamic programming 90C40: Markov and semi-Markov decision processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 4 , December 1996 , pp. 1093 - 1107
Copyright
Copyright © Applied Probability Trust 1996 

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References

Aoki, M. (1967) Optimization of Stochastic Systems. Academic Press, New York.Google Scholar
Bellman, R. (1957) Dynamic Programming. Princeton University Press, Princeton, NJ.Google Scholar
Bellman, R. (1967) Introduction to the Mathematical Theory of Control Processes. Academic Press, New York.Google Scholar
Blackwell, D. (1976) The stochastic processes of Borel gambling and dynamic programming. Ann. Statist. 4, 370–374.Google Scholar
Dubins, L. E. and Savage, L. J. (1965) How to Gamble if you Must. McGraw-Hill, New York.Google Scholar
Henery, R. J. (1984) An extreme-value model for predicting the results of horse races. Appl. Statist. 33, 125–133.Google Scholar
Henery, R. J. (1985) On the average probability of losing bets on horses with given starting price odds. J. R. Statist. Soc. A 148, 342–349.Google Scholar
Hoerl, A. E. and Fallin, H. K. (1974) Reliability of subjective evaluations in a high incentive situation. J. R. Statist. Soc. A 137, 227–230.Google Scholar
Plackett, R. L. (1975) The analysis of permutations. Appl. Statist. 24, 193–202.CrossRefGoogle Scholar
Rieder, U. (1976) On optimal policies and martingales in dynamic programming. J. Appl. Prob. 13, 507–518.CrossRefGoogle Scholar
Whittle, P. (1982) Optimization Over Time: Dynamic Programming and Stochastic Control. Academic Press, New York.Google Scholar