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Runs and the generalised Fibonacci sequence

Published online by Cambridge University Press:  01 August 2016

Alan Tomkins  and
David Pitt
Alan Tomkins
Affiliation:
N. W. Surrey Health Authority, St Peters & Botleys Park Hospitals, Chertsey KT16 0QA
David Pitt
Affiliation:
University of Surrey, Guildford GU2 5XH
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Extract

The relationship in this article was discovered by Alan Tomkins and the proof supplied by David Pitt. The original inspiration was the statistical study of gambling systems—one method of attempting to win being to increase the amount staked each time you lose. The idea of this is that when you eventually win the amount won is sufficient to more than offset the losses on the preceding string of losers and put you back into the black. The snag is that this string of losers can leave you with insufficient funds to keep increasing the stake as necessary. The question which comes to mind is: in a given number of races, on how many occasions are we to expect a run of losers of a certain length?

Type
Research Article
Information
The Mathematical Gazette , Volume 69 , Issue 448 , June 1985 , pp. 109 - 113
Copyright
Copyright © Mathematical Association 1985

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