{
  "abstract": "Blackwell and Cover both proposed the same method for guessing the larger of a pair of two numbers when one can only observe one and the other of the two numbers remains unobserved. As originally stated, the procedure ended with a computation showing that the probability of correctly guessing the larger number was greater than one-half. In this paper, we investigate what we can say when about the number in the pair that was not observed we employ the Blackwell/Cover procedure. Let α1 and α2 be two different numbers in (0,1]. Let G be the uniform distribution on [0, α1] and H be the uniform distribution on [0, α2]. We think of G and H as being represented by the heads probabilities of coins. We use a variant of the Blackwell-Cover strategy ro take pairs of coins chosen from distributions created from G and H such that one of the coins is flipped, and as a result of that flip the unobserved (unflipped) coin is placed in one of two sets A and B. We show that there are situations in which this can be done so that the mean of the heads probabilities of the unobserved coins in A is less than the mean of the heads probabilities of the unobserved coins in B. We show that there are situations in which recursive application of this process results in a set consisting almost completely of coins from one of the two distributions G and H, and another set consisting almost completely of coins from the other distribution.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23820",
  "author_total": 1,
  "authors": [
    {
      "name": "James Stein"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/563cvb2tyjvgy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23820",
  "fulltext_url": null,
  "id": "563cvb2tyjvgy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23820",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.23820",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/563cvb2tyjvgy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23820",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23820"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Using the Blackwell-Cover Guessing Strategy to Separate Unobserved Bernoulli Trials",
  "title_text": "Using the Blackwell-Cover Guessing Strategy to Separate Unobserved Bernoulli Trials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/563cvb2tyjvgy",
  "venue": "arXiv",
  "versions": []
}