On a variation of gambler’s ruin problem
Abstract
Assume that letters (from a finite alphabet) in a text form a Markov chain. We track two distinct words, U and D . A gambler gains 1 point for each occurrence of U (including overlapping occurrences) and loses 1 point for each occurrence of D (also including overlapping occurrences). We determine the probability of gaining A points before losing B points, where A and B are integers. Additionally, we find the expected waiting time until one of the two events – gaining A points or losing B points – occurs.
Fields of Study & Subjects
Sports Analytics and Performance
Probability and Statistical Research
Publication details
- Journal / source
- Statistics & Probability Letters
- Volume
- 236
- Pages
- 110783–110783
- Publication date
- 12 April 2026
- Language
- EN