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A REAL-WORLD STOCHASTIC TWO-PERSON GAME

Published online by Cambridge University Press:  19 September 2006

Henk Tijms  and
Jan van der Wal
Henk Tijms
Affiliation:
Department of Econometrics and Operations Research, Vrije University, Amsterdam, The Netherlands, E-mail: tijms@feweb.vu.nl
Jan van der Wal
Affiliation:
Department of Quantitative Economics, Faculty of Economics and Econometrics, University of Amsterdam, Amsterdam, The Netherlands, and, Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands, E-mail: jan.v.d.wal@tue.nl
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Abstract

This article discusses a real-world application of a terminating two-person stochastic game. The problem comes from a Dutch television game show in which two finalists play a dice game. Each player chooses a number of dice to be rolled. The score of the roll is added to the player's total provided that none of the dice showed the outcome one. The first player reaching a prespecified number of points is the winner. This article discusses the computation and the structure of an optimal strategy.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 20 , Issue 4 , October 2006 , pp. 599 - 608
Copyright
© 2006 Cambridge University Press

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References

REFERENCES

Derman, C. (1970). Finite state Markovian decision problems. New York: Academic Press.
Maitra, A. & Sudderth, D. (1996). Discrete gambling and stochastic games. Berlin: Springer-Verlag.CrossRef
Van der Wal, J. & Wessels, J. (1977). Successive approximation methods for Markov games. In H.C. Tijms and J. Wessels (eds.), Markov decision theory, pp. 39–55. Amsterdam: CWI.