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Gambler's Ruin? Some Aspects of Coin Tossing
- Source :
- The Mathematical Scientist, 35, No. 2 (2010)
- Publication Year :
- 2019
-
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.
- Subjects :
- Mathematics - Probability
Mathematics - History and Overview
60G40, 91A60, 91A80
Subjects
Details
- Database :
- arXiv
- Journal :
- The Mathematical Scientist, 35, No. 2 (2010)
- Publication Type :
- Report
- Accession number :
- edsarx.1908.09234
- Document Type :
- Working Paper