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Optimal strategy in a dice game

Part of: Stochastic processes Markov processes

Published online by Cambridge University Press:  14 July 2016

John Haigh  and
Markus Roters
John Haigh*
Affiliation:
University of Sussex
Markus Roters*
Affiliation:
Universität Potsdam
*
∗ Postal address: Centre for Statistics and Stochastic Modelling, School of Mathematical Sciences, University of Sussex, Falmer, Brighton BN1 9QH, UK. Email address: [email protected]
∗∗ Postal address: Universität Potsdam, Institut für Mathematik, Postfach 60 15 53, D-14415 Potsdam, Germany.
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Abstract

Computer simulations had suggested that the strategy that maximises the score on each turn in the dice game described by Roters (1998) may not be the optimal way to reach a given target in the shortest time. We give an analytical treatment, backed by numerical calculations, that finds the optimal strategy to reach such a target.

Keywords

Gamblingdice gamesMarkov decision theory

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 60J05: Discrete-time Markov processes on general state spaces
Type
Short Communications
Information
Journal of Applied Probability , Volume 37 , Issue 4 , December 2000 , pp. 1110 - 1116
Copyright
Copyright © by the Applied Probability Trust 2000 

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References

Roters, M. (1998). Optimal stopping in a dice game. J. Appl. Prob. 35, 229–235.Google Scholar
Schäl, M. (1990). Markoffsche Entscheidungsprozesse. Teubner, Stuttgart.Google Scholar