154 Measurement of Belief. [CHAP. vi. 



equal ; in other words, if they were often to play in this 

 manner each would lose as frequently as he would gain. That 

 is all that Probability can say ; what under the circumstances 

 may be the determination and opinions of the men in ques 

 tion, it is for them and them alone to decide. There are 

 many persons who cannot bear mediocrity of any kind, and 

 to whom the prospect of doubling their fortune would out 

 weigh a greater chance of losing it altogether. They alone 

 are the judges. 



If we will introduce such a balance of pleasure and pain 

 the individual must make the calculation for himself. The 

 supposition is that total ruin is very painful, partial loss 

 painful in a less proportion than that assigned by the ratio 

 of the losses themselves; the inference is therefore drawn 

 that on the average more pain is caused by occasional great 

 losses than by frequent small ones, though the money value 

 of the losses in the long run may be the same in each case. 

 But if we suppose a country where the desire of spending 

 largely is very strong, and where owing to abundant produc 

 tion loss is easily replaced, the calculation might incline the 

 other way. Under such circumstances it is quite possible 

 that more happiness might result from playing for high than 

 for low stakes. The fact is that all emotional considerations 

 of this kind are irrelevant ; they are, at most, mere applica 

 tions of the theory, and such as each individual is alone 

 competent to make for himself. Some more remarks will be 

 made upon this subject in the chapter upon Insurance and 

 Gambling. 



80. It is by the introduction of such considerations as 

 these that the Petersburg Problem has been so perplexed. 

 Having already given some description of this problem we 

 will refer to it very briefly here. It presents us with a 

 sequence of sets of throws for each of which sets I am to 



