English

A symbolic computational approach to the generalized gambler's ruin problem in one and two dimensions

Combinatorics 2026-02-05 v1 Probability

Abstract

The power of symbolic computation, as opposed to mere numerical computation, is illustrated with efficient algorithms for studying the generalized gambler's ruin problem in one and two dimensions. We also consider a new generalization of the classical gambler's ruin where we add a third step which we call the mirror step. In this scenario, we provide closed formulas for the probability and expected duration.

Keywords

Cite

@article{arxiv.2412.07667,
  title  = {A symbolic computational approach to the generalized gambler's ruin problem in one and two dimensions},
  author = {Lucy Martinez},
  journal= {arXiv preprint arXiv:2412.07667},
  year   = {2026}
}

Comments

20 pages, 4 tables