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A finite exact algorithm to solve a dice game

Published online by Cambridge University Press:  24 March 2016

Fabián Crocce  and
Ernesto Mordecki
Ernesto Mordecki
Affiliation:
Centro de Matemática, Facultad de Ciencias, Universidad de la República, Iguá 4225, CP 11400 Montevideo, Uruguay.
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Abstract

We provide an algorithm to find the value and an optimal strategy of the Ten Thousand dice game solitaire variant in the framework of Markov control processes. Once an optimal critical threshold is found, the set of nonstopping states of the game becomes finite and the solution is found by a backwards algorithm that gives the values for each one of these states of the game. The algorithm is finite and exact. The strategy to find the critical threshold comes from the continuous pasting condition used in optimal stopping problems for continuous-time processes with jumps.

Keywords

Markov control processdice gameoptimal controlfinite exact algorithm
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 1 , March 2016 , pp. 91 - 105
Copyright
Copyright © Applied Probability Trust 2016 

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