DE MOIVRE. 137 



De Moivre says that Problems 16, 17, 18 in his memoir were 

 proposed to him by Robartes. In the Preface to the Doctrine of 

 Chances, which is said to have been written in 1717, the origin of 

 the memoir is explained in the following words : 



' Tis now about Seven Years, since I gave a Specimen in the Philo- 

 sojyJiical Transactions^ of what I now more largely treat of in this Book. 

 The occasion of my then undertaking this Subject was chiefly owing to 

 the Desire and Encouragement of the Honourable Francis Robartes Esq. 

 (now Earl of Kaclnor); who, upon occasion of a French Tract, called 

 L Analyse des Jeux de Hazard, which had lately been published, was 

 i)leased to propose to me some Problems of much greater difficulty than 

 any he had found in that Book ; which having solved to his Satisfaction, 

 he engaged me to methodize those Problems, and to lay down the Pules 

 which had led me to their Solution. After I had proceeded thus far, it 

 was enjoined me by the Poyal Society, to communicate to them what I 

 had discovered on this Subject : and thereupon it was ordered to be i)ub- 

 lished in the Transactions, not so much as a matter relating to Play, but 

 as containing some general Speculations not unworthy to be considered 

 by the Lovers of Truth. 



237. The memoir consists of twenty-six Problems, besides 

 a few introductory remarks which exj^laiu how probability is 

 measured. 



238. The first problem is to find the chance of throwing an 

 ace twice or oftener in eight throws with a single die ; see Doctrine 

 of Chances, page 13. 



239. The second problem is a case of the Problem of Points. 

 A is supposed to want 4 points, and B to want G points ; and ^-I's 

 chance of winning a single point is to ^'s as 3 is to 2 ; see Doctrine 

 of Chances, page 18. It is to be remembered that up to this date, 

 in all that had been published on tlie subject, the chances of the 

 players for winning a single point had always been assumed equal ; 

 see Art. 173. 



240. The third problem is to determine the chances of A and B 

 for Avinning a single game, supposing that A can give B two games 

 out of three ; the fourth problem is of a similar kind, supjDosing 



