Lord Stanhope's papers on the ``Doctrine of Chances'' (Q997153)

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''.