BUFFON. 345 



gambling in which an advantage is ensured to one of the parties. 

 Thus for example at a game like Pharaon, he says : 



... le banquier n'est qu'im fripon avoue, et le ponte une dupe, dont 

 on est convenu de ne se pas moquer. 



See his 12th section. He finishes the section thus : 



...je dis qu'en general le jeu est un pacte mal-entendu, un contrat 

 d^savantageux aux deux parties, dont I'effet est de rendre la perte tou- 

 jours plus grande que le gain; et d'oter au bien pour ajouter au mal. 

 La demonstration en est aussi aisee qu'evidente. 



64iQ. The demonstration then follows in the ISth section. 



Buffon supposes two players of equal fortune, and that each 

 stakes half of his fortune. He says that the player who wins 

 will increase his fortune by a third, and the .player who loses will 

 diminish his by a half ; and as a half is greater than a third 

 there is more to fear from loss than to hope from gain. Buffon 

 does not seem to do justice to his own argument such as it is. 

 Let a denote the fortune of each player, and h the sum staked. 



Then the 2:ain is estimated by Buffon by the fraction , and 



^ -^ -^ a+b 



the loss by - ; but it would seem more natural to estimate the 



loss by 7, which of course increases the excess of the loss 



to be feared over the gain to be hoped for. 



The demonstration may be said to rest on the principle that 

 the value of a sum of money to any person varies inversely as his 

 whole fortune. 



647. Buffon discusses at length the Petersburg Problem which 

 he says was proposed to him for the first time by Cramer at 

 Geneva in 1730. This discussion occupies sections 15 to 20 

 inclusive. See Art. 389. 



Buffon offers four considerations by which he reduces the ex- 

 pectation of A from an infinite number of crowns to about five 

 crowns only. These considerations are 



(1) The fact that no more than a finite sum of money exists 

 to pay A. Buffon finds that if head did not fall until after the 



