{
  "abstract": "In this note we explore the following simple question: How does the classic \\emph{gambler's ruin} phenomenon change if we allow the gambler \\emph{financial leverage}? We show that, with a moderate amount of leverage, it is possible for an (idealized) gambler to sustain seemingly improbable profits over a remarkably long time horizon without ever going bankrupt, \\emph{even} if the gambler makes only fair bets. With a leverage ratio of $L = 10$ (less than what Lehman Brothers Holdings had from 1995--2008), the probability of multiplying one's money by $1000\\times$ without going bankrupt is roughly $50\\%$. More generally, given $L$-fold leverage, and given the goal of multiplying one's money by a factor of $r > 1$, the optimal gambling strategy has probability roughly $r^{-1/L}$ of success. The results in this note are designed as part of the course development for the CMU randomized algorithms course.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19239",
  "author_total": 1,
  "authors": [
    {
      "name": "William Kuszmaul"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1kgtsemjrmrgq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19239",
  "fulltext_url": null,
  "id": "1kgtsemjrmrgq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19239",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.DS"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2613|Probability and Statistical Research"
    ]
  ],
  "openalex": "W7222056333",
  "pdf_url": "https://arxiv.org/pdf/2610.19239",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1kgtsemjrmrgq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19239",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19239"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "With Leverage, the Gambler is Not the One Who Gets Ruined",
  "title_text": "With Leverage, the Gambler is Not the One Who Gets Ruined",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/1kgtsemjrmrgq",
  "venue": "arXiv",
  "versions": []
}