390 Insurance and Gambling. [CHAP. xv. 



order to prove that gambling is necessarily disadvantageous, 

 and this to both parties. Take, for instance, Bernoulli s sup 

 position. It can be readily shown that if two persons each 

 with a sum of 50 to start with choose to risk, say, 10 upon 

 an even wager there will be a loss of happiness as a result : 

 for the pleasure gained by the possessor of 60 will not 

 be equal to that which is lost by the man who leaves off 

 with 40 . 



19. This is the form of argument commonly adopted ; 

 but, as it stands, it does not seem conclusive. It may surely 

 be replied that all which is thus proved is that inequality is 

 bad, on the ground that two fortunes of 50 are better than 

 one of 60 and one of 40. Conceive for instance that the 

 original fortunes had been 60 and 40 respectively, the 

 event may result in an increase of happiness ; for this will 

 certainly be the case if the richer man loses and the fortunes 

 are thus equaj^^Jpt This is quite true; and we are therefore 

 obliged to show, what can be very easily shown, that if 

 the other alternative had taken place and the two fortunes 

 had been made still more unequal (viz. 65 and 35 respec 

 tively) the happiness thus lost would more than balance 

 what would have been gained by the equalization. And 

 since these two suppositions are equally likely there will be a 

 loss in the long run. 



The consideration just adduced seems however to show 



1 The formula expressive of this bet. Then the balance, as regards 



, i . . x . happiness, must be drawn between 



moral happiness is c log - ; where x 



a . x 



. s , , ,,. - 



stands for the physical fortune pos- log a and ^ log ^T + * c log ~T 



sessed at the time, and a for that or logo; 2 and log (% + y)(x-y), 



small value of it at which happiness or x- and x 2 y 2 , 



is supposed to disappear : c being an the former of which is necessarily 



arbitrary constant. Let two persons, the greater. 



whose fortune is x, risk y on an even 



