Lucy Martinez, Rutgers University

Abstract

Consider a gambler who starts with x dollars. At each gamble, the gambler either wins a dollar with probability 1/2 or loses a dollar with probability 1/2. The gambler's goal is to reach N dollars without first running out of money (i.e., hitting 0 dollars). If the gambler reaches N dollars, we say that they are a winner. The gambler continues to play until they either run out of money or win. This scenario is known as the gambler's ruin problem, first posed by Pascal. We consider a new generalization of the gambler's ruin problem. A particle starts at some point x on a line of length N. At each step, the particle either moves from x to x-1 with probability q1, or moves from x to x+1 with probability q2, or moves from x to N-x with probability p where 0

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For further information see: https://sites.math.rutgers.edu/~zeilberg/expmath/