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# IMath Webinar Series: Ramon Iñigo Marfil, Ph.D.

You are all invited to attend the first webinar of the IMath Webinar Series for this semester on Monday, September 27, 2021, 2:00pm.

Dr. Ramon Iñigo D. Marfil of the Mathematical Finance and Actuarial Science Group will present his work titled “On the Placing Probabilities and Expected Time Until Ruin for the N-Tower Problem Using Recursions Based on Multigraphs”.

Abstract: The $$N$$-Tower Problem is an $$N$$-player gambler’s ruin model where two players are involved in an even-money bet during each round. In this problem, the objective is to solve for each player’s final placing probabilities given their initial wealths. Weighted directed multigraphs were constructed to model the transitions between chip states. Linear systems 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. A numerical algorithm is developed to solve the $$N$$-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 the proportion, of chips each player holds.