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Markov Chain Solution to the 3-Tower Problem

By Guido David

Abstract

Part 5: Applied Modeling and SimulationInternational audienceThe 3-tower problem is a 3-player gambler’s ruin model where two players are involved in a zero information, even-money bet during each round. The probabilities that each player accumulates all the money has a trivial solution. However, the probability of each player getting ruined first is an open problem. In this paper, the 3-tower problem recursions are modeled as a directed multigraph with loops, which is used to construct a Markov chain. The solution leads to exact values, and results show that, unlike in other models where the first ruin probabilities depend only on the proportion of chips of each player, the probabilities obtained by this model depend on the number of chips each player holds

Topics: Markov chains, Graph theory, Discrete mathematics, 3-dimensional gambler’s ruin, Applied probability, Tower of Hanoi, [INFO]Computer Science [cs], [SHS.INFO]Humanities and Social Sciences/Library and information sciences
Publisher: 'Springer Science and Business Media LLC'
Year: 2015
DOI identifier: 10.1007/978-3-319-24315-3_12
OAI identifier: oai:HAL:hal-01466211v1
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