VOLUME 14 NUMBER 2 (July to December 2021)
SciEnggJ. 2021 14 (2) 249-256
available online: November 30, 2021
*Corresponding author
Email Address: rimarfil@math.upd.edu.ph
Date received: August 8, 2021
Date revised: October 31, 2021
Date accepted: November 14, 2021
ARTICLE
Solution to the Three-Player Gambler’s Ruin with Variable Bet Size Using Recursions Based on Multigraphs
Ramon Iñigo D. Marfil* and Guido David
1Institute of Mathematics, College of Science, University of the Philippines,
Diliman, Quezon City 1101 Philippines
Diliman, Quezon City 1101 Philippines
This paper studies the three-player gambler’s ruin with variable bet size, 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 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. Expected time until ruin is solved by modeling the game as a Markov process. A numerical algorithm is developed to solve the No Limit three-player gambler’s ruin problem for any positive integer chip total.
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