126 MONTMORT. 



216. One of the problems is the following. The skill of ^, 

 that is his chance of success in a single trial, is ^, the skill of B 

 is q. A and B are to play for victory in two games out of three, 

 each game being for two points. In the first game B is to have 

 a point given to him, in the second the players are to be on an 

 equality, and in the third also B is to have a point given to 

 him. Required the skill of each player so that on the whole 

 the chances may be equal, ^'s chance of success in the first 

 game or in the third game is p^, and i?'s chance is ^ + '^qp. 

 u4's chance of success in the second game is p^ + ^p^q, and ^'s 

 chance is <f + 3^^. Hence ^'s chance of success in two games 

 out of three is 



/ (/ + 3/2) +/ (2' + ^P) (p' + 3/2) +/ (q" + 32» ; 

 and this by supposition must equal ^ . 



This agrees with Montmort's result by putting , for ^ 



and 7 for g, allowinc^ for a mistake which was afterwards 



corrected ; see Montmort's pages 34^3, 350, 352. 



217. The letter closes with the following interesting piece of 

 literary history. 



Je ne sgai si vous slaves qu'on reimprime la Recherche de la verite. 

 Le R. P. Malbranche m'a dit que cet Ouvi-age paroitroit au commence- 

 ment d'Avril. II y aura un grand nonibre d'additions sur des sujets 

 tres importans. Yous y verres entr'autres nouveautes une Disserta- 

 tion sur la cause de la pesanteur, qui apparemment fixera les doutes 

 de tant de Sgavans hommes qui ne sgavent a quoi s'en tenir sur 

 cette matiere. II prouve d'une maniere invincible la necessite de ses 

 petits tourbillons pour rendre raison de la cause de la pesanteur, de la 

 durete et fluidite des corps et des principaux plienomenes toucliant la 

 lumiere et les couleursj sa theorie s'accorde le niieux du monde avec 

 les belles experiences que M. Newton a rapporte dans son beau Traite 

 Be Natura Lucis et Colorum. Je peux me glorifier auprcs du Pub- 

 lic que mes prieres ardentes et reiterees depuis j)lusieurs annces, ont 

 contribue a determiner cet incomparable Philosoplie a ecrire sur cette 



