SECT. 16.] Fallacies. 347 



not affect him if the series ran to two hundred terms; it 

 would merely take him somewhat longer to win his stakes. 

 A man might safely, for instance, continue to lay an even 

 bet that he would get the single prize in a lottery of a thou 

 sand tickets, provided he thus doubled, or more than doubled, 

 his stake each time, and unlimited credit was given. 



16. So regarded, the problem is simple enough, but 

 there are two points in it to which attention may conveni 

 ently be directed. 



In the first place, it serves very pointedly to remind us of 

 the distinction between a series of events (in this case the 

 tosses of the penny) which really are subjects of chance, and 

 our conduct founded upon these events, which may or may 

 not be so subject 1 . It is quite possible that this latter may 

 be so contrived as to be in many respects a matter of abso 

 lute certainty, a consideration, I presume, familiar enough 

 to professional betting men. Why is the ordinary way of 

 betting on the throws of a penny fair to both parties? Be 

 cause a fair series is fairly treated. The heads and tails 

 occur at random, but on an average equally often, and the 

 stakes are either fixed or also arranged at random. If a man 

 backs heads every time for the same amount, he will of 

 course in the long run neither win nor lose. Neither will he 

 if he varies the stake every time, provided he does not vary 

 it in such a way as to make its amount dependent on the 

 fact of his having won or lost the time before. But he 

 may, if he pleases, and the other party consents, so arrange 

 his stakes (as in the case in question) that Chance, if one 

 might so express it, does not get a fair chance. Here the 

 human elements of choice and design have been so brought 

 to bear upon a series of events which, regarded by them- 



1 Attention will be further directed to this distinction in the chapter on 

 Insurance and Gambling. 



