SECT. 19.] Fallacies. 349 



18. In the second place, this example brings before us 

 what has had to be so often mentioned already, namely, that 

 the series of Probability are in strictness supposed to be 

 interminable. If therefore we allow either party to call 

 upon us to stop, especially at a point which just happens to 

 suit him, we may get results decidedly opposed to the 

 integrity of the theory. In the case before us it is a neces 

 sary stipulation for A that he may be allowed to leave off 

 when he wishes, that is at one of the points at which the 

 throw is in his favour. Without this stipulation he may be 

 left a loser to any amount. 



Introduce the supposition that one party may arbitrarily 

 call for a stoppage when it suits him and refuse to permit it 

 sooner, and almost any system of what would be otherwise fair 

 play may be converted into a very one-sided arrangement. 

 Indeed, in the case in question, A need not adopt this device 

 of doubling the stakes every time he loses. He may play 

 with a fixed stake, and nevertheless insure that one party 

 shall win any assigned sum, assuming that the game is even 

 and that he is permitted to play on credit. 



19. (V.) A common mistake is to assume that a very 

 unlikely thing will not happen at all. It is a mistake which, 

 when thus stated in words, is too obvious to be committed, 

 for the meaning of an unlikely thing is one that happens at 

 rare intervals; if it were not assumed that the event would 

 happen sometimes it would not be called unlikely, but im 

 possible. This is an error which could scarcely occur except 

 in vague popular misapprehension, and is so abundantly re 

 futed in works on Probability, that it need only be touched 

 upon briefly here. It follows of course, from our definition 

 of Probability, that to speak of a very rare combination of 

 events as one that is sure never to happen, is to use lan 

 guage incorrectly. Such a phrase may pass current as a 



