SECT. 14.] Fallacies. 345 



could not ensure winning eventually to any extent, he can 

 do so if he adopt such a scheme as the one in question. And 

 this is the state of things which seems to call for explanation. 



14. What causes perplexity here is the supposed fact 

 that in some mysterious way certainty has been conjured out 

 of uncertainty ; that in a game where the detailed events are 

 utterly inscrutable, and where the average, by supposition, 

 shows no preference for either side, one party is nevertheless 

 succeeding somehow in steadily drawing the luck his own 

 way. It looks as if it were a parallel case with that of a 

 man who should succeed by some device in permanently 

 securing more than half of the tosses with a penny which 

 was nevertheless to be regarded as a perfectly fair one. 



This is quite a mistake. The real fact is that A does 

 not expose his gains to chance at all; all that he so exposes 

 is the number of times he has to wait until he gains. Put 

 such a case as this. I offer to give a man any sum of money 

 he chooses to mention provided he will at once give it back 

 again to me with one pound more. It does not need much 

 acuteness to see that it is a matter of indifference to me 

 whether he chooses to mention one pound, or ten, or a 

 hundred. Now suppose that instead of leaving it to his 

 choice which of these sums is to be selected each time, the 

 two parties agree to leave it to chance. Let them, for 

 instance, draw a number out of a bag each time, and let that 

 be the sum which A gives to B under the prescribed condi 

 tions. The case is not altered. A still gains his pound each 

 time, for the introduction of the element of chance has not 

 in any way touched this. All that it does is to make this 

 pound the result of an uncertain subtraction, sometimes 10 

 minus 9, sometimes 50 minus 49, and so on. It is these 

 numbers only, not their difference, which he submits to luck, 

 and this is of no consequence whatever. 



