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Optimal strategy in a dice game

  • John Haigh (a1) and Markus Roters (a2)


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.


Corresponding author

Postal address: Centre for Statistics and Stochastic Modelling, School of Mathematical Sciences, University of Sussex, Falmer, Brighton BN1 9QH, UK. Email address:
∗∗ Postal address: Universität Potsdam, Institut für Mathematik, Postfach 60 15 53, D-14415 Potsdam, Germany.


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Roters, M. (1998). Optimal stopping in a dice game. J. Appl. Prob. 35, 229235.
Schäl, M. (1990). Markoffsche Entscheidungsprozesse. Teubner, Stuttgart.


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