{
  "id": "1908.09234",
  "version": "v1",
  "published": "2019-08-24T23:54:56.000Z",
  "updated": "2019-08-24T23:54:56.000Z",
  "title": "Gambler's Ruin? Some Aspects of Coin Tossing",
  "authors": [
    "Porter W. Johnson",
    "David Atkinson"
  ],
  "journal": "The Mathematical Scientist, 35, No. 2 (2010)",
  "categories": [
    "math.PR"
  ],
  "abstract": "What is the average number of tosses needed before a particular sequence of heads and tails turns up? We solve the problem didactically, starting with doubles, finding that a tail, followed by a head, turns up on the average after only four tosses, while six tosses are needed for two successive heads. The method is extended to encompass the triples head-tail-tail and head-head-tail, but head-tail-head and head-head-head are surprisingly more recalcitrant. However, the general case is finally solved by a new algorithm that allows a simple computation that can be done by hand, even for relatively long strings. It is shown that the average number of tosses is always an even integer.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-24T23:54:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G40",
      "91A60",
      "91A80"
    ],
    "keywords": [
      "gamblers ruin",
      "coin tossing",
      "average number",
      "triples head-tail-tail",
      "general case"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}