ON THE BISKS OF LOSS OB GAIN. 107 



a = 30, b = 29, n = 50, g-\ gained h = l lost v = 50. 



1 gain x 50 = 50 probable total. 



Add 2. 



In this case the probability is absolutely given. The 

 square root is therefore the first one mentioned. 



8xwxox6 = 8x50x30x29 = 348,000 



348000 / - 51 



^ = 5898-3, V 5898-3 = 76-800, ^ = -664 = t. 



Table L, if t = '664, H = '652. 

 Consequently T 6 6 5 ^ is the chance that the bank shall not 



lose,, but shall gain something less than ^ 100; and 

 consequently the chance that the bank shall either lose, 

 or gain more than ,=100 is -jo 4 oV ^ n account of the 

 nearness of 30 and 29, the results last mentioned are 

 nearly equally probable, and it is near enough for our 

 present purpose, to say that -jftffo is the chance of the 

 bank gaining more than 100, the supposition being 

 against us ; for it is more likely that the bank should 

 gain more than 1 00 than that it should lose. Hence 

 it follows, that the chance of the bank gaining on 2950 

 games is more than -j^efo* or aDout fi ve t one ' K sucn ^ 

 be the case with a bank much less unfairly constituted 

 than is often the case, against a player who can not only 

 command 2^50, but who has the prudence to deter- 

 mine that he will only play 2950 games, at a stake of 

 , 1 for each game, what must be the chances against 

 those who risk a larger proportion of their means at 

 more unequal play, with a determination to win that is, 

 to go on till they are ruined ? 



The inequality of means is an important consider- 

 ation in calculating the chances of two antagonist game- 

 sters. If two persons, with equal means and equal 

 chances, play for equal stakes, it is an even chance 



