NICOLE. 201 



If the original heap contains n counters we should say that there 



are n ways of drawing one counter, -— ^ — ^-^ ways of drawing 



two counters, and so on. Mairan notices this view but con- 

 demns it. 



Laplace treated this problem in the Memoires . . . par divers 

 Savans...TomeYl., Paris, 1774, and he arrives at the ordinary result, 

 though not by the method of combinations ; he refers to Mairan s 

 result, and briefly records his dissent. The problem is solved by 

 the method of combinations in the Theori'e...des Proh. page 201. 



In the article Pair ou Non of the original French Encyclo- 

 pedie, which was published in 1765, Mairan's view is given ; this 

 article was repeated in the Encyclopedie Methodique, in 1785, 

 without any notice of Laplace's dissent. 



351. On page 68 of the volume of the Hist de VAcad.... 

 Paris, which contains Mairan's results, is the following paragraph : 



M. L'Abb6 Sauvenr, fils de feu M. Sauveur Academicien, a fait voir 

 une Metliode qu'il a trouvee pour determiner au Jeu de Quadrille quelle 

 est la probabilite de gagner sans prendre plusieurs Jeux differents, dont 

 il a calcule une Table. On a trouve que la matiere ej^ineuse et delicate 

 des Combinaisons etoit tres-bien entendlie dans cet ouvrage. 



352. We have next to notice a memoir by Nicole, entitled 

 Examen et Resolution de quelques questions sur les Jeux. 



This memoir is published in the volume for 1730 of the Hist, 

 de T Acad.... Paris; the date of publication is 1732 : the memoir 

 occupies pages 45 — oQ of the part devoted to memoirs. 



The problem discussed is really the Problem of Points ; the 

 method is very laborious, and the memoir seems quite superfluous 

 since the results had already been given in a simpler manner by 

 Montmort and De Moivre. 



One point may be noticed. Let a and h be proportional to 

 the respective chances of A and B to win a single game ; let them 

 play for an even number of games, say for example 8, and let 

 S be the sum which each stakes. Then ^'s advantage is 



^ ft8 + 8 a^6 + 'iMh'' + 56a^^^ - b^a'lf - 28a'h' - 8ah' - b' 



^ {a-^hy : • 



