Lord Stanhope's papers on the ``Doctrine of Chances''
type: Item
instance of: scholarly article
title: Lord Stanhope's papers on the ``Doctrine of Chances''
zbMATH Open document ID: 1124.01006
author: David R. Bellhouse
published in: Historia Mathematica
publication date: 2007-07-23T00:00:00Z
review text: Drawing on archival sources, the author describes the stochastic work of Lord Philip Stanhope (1714--1786), an amateur mathematician who had not published anything. He was a sponsor for nominating Bayes to fellowship in the Royal Society (was he himself a fellow of that Society?) and corresponded with the leading English mathematicians of his time. Stanhope mostly enlarged on some of the problems from De Moivre's ``Doctrine of Chances'' and Montmort's ``Essay d'analyse\dots''. He derived a recurrence relation for the probability of runs in a series of Bernoulli trials; studied the duration of play when one of the gamblers possessed an infinite capital (providing a simpler and easier to calculate solution); and extended the solution of the Waldegrave problem. Among the studied sources Bellhouse also found some mistaken calculations made by Bayes, but then added that the pertinent problem remains unknown. His own mistake is that he credits Bayes only with one memoir of 1763 (actually, of 1764) [\textit{Th. Bayes}, Philos. Trans. R. Soc. Lond. 53, 370--418 (1763; Zbl 1250.60007)], but forgets about its supplement of 1765. He also states but regrettably does not prove that the Editor of the 1754 edition of the ``Doctrine of Chances'' was Patrick Murdoch (1710--1774) even the date of whose birth is not given by the ``Oxford Dictionary of National Biography''.
Mathematics Subject Classification ID: 01A50
Mathematics Subject Classification ID: 60-03
zbMATH DE Number: 5173600
zbMATH Keywords: doctrine of fluxions
zbMATH Keywords: duration of play
zbMATH Keywords: gambler's ruin
zbMATH Keywords: theory of runs
reviewed by: O. B. Sheĭnin
MaRDI profile type: Publication
full work available at URL: j.hm.2006.08.006
OpenAlex ID: W1975398285
cites work: LII. An essay towards solving a problem in the doctrine of chances. By the late Rev. Mr. Bayes, F. R. S. communicated by Mr. Price, in a letter to John Canton, A. M. F. R. S
cites work: Q5534179
cites work: Closed form summation for classical distributions: variations on a theme of de Moivre
cites work: Q5596192
cites work: Q3996908
cites work: Q3663249
cites work: Q3933679
cites work: Q3880793
cites work: Der Mathematiker Abraham de Moivre (1667--1754)
DOI: 10.1016/J.HM.2006.08.006
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description: scientific article; zbMATH DE number 5173600