{
  "abstract": "Let $X_1,\\ldots,X_n$ be independent random variables with arbitrary known distributions, where $n\\ge2$. The optimal probability $V_n(X_1,\\ldots,X_n)$ of choosing an overall maximum satisfies $V_n(X_1,\\ldots,X_n)\\ge(1-1/n)^{n-1}$, and this bound is attained. We obtain this known sharp bound by extending the reduction lemma of Allaart and Islas (2016) from continuous to arbitrary distributions. We construct a $V$-sequence whose optimal win probability does not exceed that of the original sequence, and then apply the bound for $V$-sequences. The construction first replaces atoms by uniform observations on strictly ordered intervals and applies the original continuous reduction lemma. The reduced distributions are determined by a common critical level and a common probability for splitting a possible atom at that level.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35600",
  "author_total": 1,
  "authors": [
    {
      "name": "José A. Islas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5ng2dats73t8j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35600",
  "fulltext_url": null,
  "id": "5ng2dats73t8j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35600",
  "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",
      "math.PR"
    ],
    [
      "openalex",
      "2613|Probability and Statistical Research"
    ]
  ],
  "openalex": "W7223900911",
  "pdf_url": "https://arxiv.org/pdf/2610.35600",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5ng2dats73t8j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.35600",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35600"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Extending the V-sequence reduction to arbitrary independent distributions",
  "title_text": "Extending the V-sequence reduction to arbitrary independent distributions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/5ng2dats73t8j",
  "venue": "arXiv",
  "versions": []
}