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On a variation of gambler’s ruin problem

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  • Chi, Zhiyi
  • Pozdnyakov, Vladimir

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.

Suggested Citation

  • Chi, Zhiyi & Pozdnyakov, Vladimir, 2026. "On a variation of gambler’s ruin problem," Statistics & Probability Letters, Elsevier, vol. 236(C).
    • Handle: RePEc:eee:stapro:v:236:y:2026:i:c:s0167715226001471
    DOI: 10.1016/j.spl.2026.110783
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