{
  "id": "2405.16660",
  "version": "v1",
  "published": "2024-05-26T18:49:40.000Z",
  "updated": "2024-05-26T18:49:40.000Z",
  "title": "A proof that HT is more likely to outnumber HH than vice versa in a sequence of n coin flips",
  "authors": [
    "Simon Segert"
  ],
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "Consider the following probability puzzle: A fair coin is flipped n times. For each HT in the resulting sequence, Bob gets a point, and for each HH Alice gets a point. Who is more likely to win? We provide a proof that Bob wins more often for every n>=3. As a byproduct, we derive the asymptotic form of the difference in win probabilities, and obtain an efficient algorithms for their calculation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-26T18:49:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "vice versa",
      "outnumber hh",
      "coin flips",
      "fair coin",
      "efficient algorithms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}