SECT. 12.] Fallacies. 343 



tach that from the notion of chance at all, and then begin to 

 introduce this notion again for possible deflections from that 

 saving inch. 



12. (IV.) We will now notice a fallacy connected with 

 the subjects of betting and gambling. Many or most of the 

 popular misapprehensions on this subject imply such utter 

 ignorance and confusion as to the foundations of the science 

 that it would be needless to discuss them here. The follow 

 ing however is of a far more plausible kind, and has been a 

 source of perplexity to persons of considerable acuteness. 



The case, put into the simplest form, is as follows 1 . 

 Suppose that a person A is playing against B, B being 

 either another individual or a group of individuals, say a 

 gambling bank. They begin by tossing for a shilling, and 

 A maintains that he is in possession of a device which will 

 insure his winning. If he does win on the first occasion he 

 has clearly gained his point so far. If he loses, he stakes 

 next time two shillings instead of one. The result of course 

 is that if he wins on the second occasion he replaces his 

 former loss, and is left with one shilling profit as well. So 

 he goes on, doubling his stake after every loss, with the 

 obvious result that on the first occasion of success he makes 

 good all his previous losses, and is left with a shilling over. 

 But such an occasion must come sooner or later, by the 

 assumptions of chance on which the game is founded. Hence 

 it follows that he can insure, sooner or later, being left a 

 final winner. Moreover he may win to any amount; firstly 

 from the obvious consideration that he might make his 

 initial stake as large as he pleased, a hundred pounds, for 



1 It appears to have been long Edinburgh, for 1823) which discusses 



known to gamblers under the name certain points connected with it, but 



of the Martingale. There is a paper scarcely touches on the subject of the 



by Babbage (Trans, of Royal Soc. of sections which follow. 



