{
  "abstract": "Let $X$ be a finite set and $\\mathcal{F} \\subseteq 2^X$ a non-trivial increasing property. We show that the bias-threshold $b(\\mathcal{F})$ for the Picker-Chooser $\\mathcal{F}$-game satisfies $b(\\mathcal{F}) \\ge α/ p_c(\\mathcal{F})$, where $p_c(\\mathcal{F})$ is the threshold for the property $\\mathcal{F}$ and $α> 0$ is an absolute constant. This proves that Picker-Chooser games satisfy one-sided ``probabilistic intuition''. The proof is based on the notion of influence from the theory of boolean functions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30730",
  "author_total": 1,
  "authors": [
    {
      "name": "Rajko Nenadov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1w4vz0v0cvmjq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30730",
  "fulltext_url": null,
  "id": "1w4vz0v0cvmjq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30730",
  "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.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7223294490",
  "pdf_url": "https://arxiv.org/pdf/2610.30730",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1w4vz0v0cvmjq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.30730",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30730"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Probabilistic and game thresholds",
  "title_text": "Probabilistic and game thresholds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/1w4vz0v0cvmjq",
  "venue": "arXiv",
  "versions": []
}