Conditional Gambler’s Ruin Problem with Arbitrary Winning and Losing Probabilities with Applications

• Published in: Methodology and computing in applied probability Vol. 27; no. 3; p. 54
• Main Authors: Lorek, Paweł, Markowski, Piotr
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.09.2025; Springer Nature B.V
• Subjects: Absorption; Business and Management; Economics; Eigenvalues; Electrical Engineering; Life Sciences; Mathematics and Statistics; Probability; Random variables; Random walk; Random walk theory; Statistics; 60J10; Strong stationary dual chain; Birth and death chain; Conditional absorption time; Random walk on a polygon; Möbius monotonicity; Random walk on a circle; 60G40; Gambler’s ruin problem; 60J80

In this paper we provide formulas for the expectation of a conditional game duration in a finite state-space one-dimensional gambler’s ruin problem with arbitrary winning p ( n ) and losing q ( n ) probabilities ( i.e.,  they depend on the current fortune). The formulas are stated in terms of the pa...