Solution to the three-tower problem with variable bet size using recursions based on multigraphs - Marfil, Ramon Iñigo D.; David,Fredegusto Guido P. (Quezon City Institute of Mathematics, College of Science, University of the Philippines Diliman, 2015)
The three-tower problem is a 3-player gambler's ruin model where two players are involved in an even-money bet during each round.The Three-Tower Problem is extended to a No Limit scenario, that is, more than one chip may be transferred from one player to another. Weighted directed multigraphs were constructed to model the transitions between chip states. Linear system are constructed based on the connections between nodes in these graphs. Solutions for the placing probabilities of each player are obtained from these linear systems. Expected time until ruin is solved by modeling the game as a Markov process. numerical algorithm is developed to solve the No Limit 3-Tower Problem for any positive integer chip total. The solution leads to exact values, and results show that the equities in this model depend on the number, not just proportion, of chips each player holds.
Thesis (M.S. Applied Mathematics)--University of the Philippines Diliman
Keywords: Multigraph