{
  "abstract": "An ordered deck of $n$ cards is subjected to $k$ independent Gilbert--Shannon--Reeds riffle shuffles. A player then guesses each card without feedback, with repeated guesses allowed. For every fixed $k\\ge1$, we prove that, once $n$ is sufficiently large, an optimal guess at position $i$ in the top half of the deck is $\\lfloor i/2^k\\rfloor+1$; the bottom-half strategy is obtained by reflection. We also show that the optimal expected number of correct guesses is $2\\sqrt{n/((2^k-1)π)}+O_k(1)$. Our starting point is the result of our earlier work that the label at each position is distributed as an equally weighted mixture of $2^k$ components, each a shifted sum of two independent binomial random variables (a Poisson-binomial distribution). The proof of the optimal strategy combines three ingredients: a uniform concentration estimate that separates the mixture components, exact binomial inequalities that control the gaps between competing peaks, and a coefficient comparison that resolves modal ties. The expected-score asymptotic is proved independently of the strategy, using only the peak heights of the mixture components.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04339",
  "author_total": 2,
  "authors": [
    {
      "name": "Tipaluck Krityakierne"
    },
    {
      "name": "Thotsaporn Aek Thanatipanonda"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/639aj7qb54a3c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04339",
  "fulltext_url": null,
  "id": "639aj7qb54a3c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04339",
  "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.CO"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04339",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/639aj7qb54a3c.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04339",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04339"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Optimal no-feedback card guessing after a fixed number of riffle shuffles",
  "title_text": "Optimal no-feedback card guessing after a fixed number of riffle shuffles",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/639aj7qb54a3c",
  "venue": "arXiv",
  "versions": []
}