{
  "abstract": "We present an analogue of the classical Gittins index for a one-armed decision problem with a continuous spectrum of payoffs. The model assumes that the decision-maker observes independent realizations of a random variable and, at each step, decides whether to accept the current opportunity or continue observing. We show that the optimal strategy takes the form of a threshold rule, while the corresponding reservation index is determined by a one-dimensional fixed-point equation with a direct decision-theoretic interpretation. The model is illustrated with an example of bookmaker betting related to horse racing and the Kelly criterion. This perspective allows the proposed index to be viewed as a threshold of informational advantage. This, in turn, points to potential applications in optimal stopping problems and decision-making under uncertainty.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Entropy. 2026; 28(8):875",
  "arxiv": "2610.30150",
  "author_total": 3,
  "authors": [
    {
      "name": "Marcin Makowski"
    },
    {
      "name": "Edward W. Piotrowski"
    },
    {
      "name": "Jan L. Cieśliński"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1309y379z2vfv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30150",
  "fulltext_url": null,
  "id": "1309y379z2vfv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30150",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.30150",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1309y379z2vfv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.30150",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30150"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "The Gittins Index for a Transparent One-Armed Bandit with a Continuous Payoff Spectrum in Equilibrium States",
  "title_text": "The Gittins Index for a Transparent One-Armed Bandit with a Continuous Payoff Spectrum in Equilibrium States",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/1309y379z2vfv",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.3390/e28080875",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}