%0 Conference Proceedings
%T Markov Chain Solution to the 3-Tower Problem
%+ University of the Philippines Cebu (UP Cebu)
%A David, Guido
%Z Part 5: Applied Modeling and Simulation
%< avec comité de lecture
%( Lecture Notes in Computer Science
%B 3rd International Conference on Information and Communication Technology-EurAsia (ICT-EURASIA) and 9th International Conference on Research and Practical Issues of Enterprise Information Systems (CONFENIS)
%C Daejon, South Korea
%Y Ismail Khalil
%Y Erich Neuhold
%Y A Min Tjoa
%Y Li Da Xu
%Y Ilsun You
%I Springer
%3 Information and Communication Technology
%V LNCS-9357
%P 121-128
%8 2015-10-04
%D 2015
%R 10.1007/978-3-319-24315-3_12
%K Markov chains
%K Graph theory
%K Discrete mathematics
%K 3-dimensional gambler’s ruin
%K Applied probability
%K Tower of Hanoi
%Z Computer Science [cs]
%Z Humanities and Social Sciences/Library and information sciencesConference papers
%X The 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.
%G English
%Z TC 5
%Z TC 8
%Z WG 8.9
%2 https://inria.hal.science/hal-01466211/document
%2 https://inria.hal.science/hal-01466211/file/978-3-319-24315-3_12_Chapter.pdf
%L hal-01466211
%U https://inria.hal.science/hal-01466211
%~ SHS
%~ IFIP-LNCS
%~ IFIP
%~ IFIP-TC
%~ IFIP-TC5
%~ IFIP-WG
%~ IFIP-TC8
%~ IFIP-ICT-EURASIA
%~ IFIP-WG8-9
%~ IFIP-LNCS-9357
%~ IFIP-CONFENIS