348 Fallacies. [CHAP. xiv. 



selves, exhibit nothing but the physical characteristics of 

 chance, that the latter elements disappear, and we get a 

 result which is arithmetically certain. Other analogous 

 instances might be suggested, but the one before us has the 

 merit of most ingeniously disguising the actual process. 



17. The meaning of the remark just made will be 

 better seen by a comparison with the following case. It has 

 been attempted 1 to explain the preponderance of male births 

 over female by assuming that the chances of the two are 

 equal, but that the general desire to have a male heir tends 

 to induce many unions to persist until the occurrence of this 

 event, and no longer. It is supposed that in this way there 

 would be a slight preponderance of families which consisted 

 of one son only, or of two sons and one daughter, and so forth. 



This is quite fallacious (as had been noticed by Laplace, 

 in his Essai)\ and there could not be a better instance 

 chosen than this to show just what we can do and what we 

 cannot do in the way of altering the luck in a real chance- 

 succession of events. To suppose that the number of actual 

 births could be influenced in the way in question is exactly 

 the same thing as to suppose that a number of gamblers 

 could increase the ratio of heads to tails, to something over 

 one-half, by each handing the coin to his neighbour as soon 

 as he had thrown a head : that they have only to leave off as 

 soon as head has appeared; an absurdity which we need not 

 pause to explain at this stage. The essential point about 

 the Martingale is that, whereas the occurrence of the 

 events on which the stakes are laid is unaffected, the stakes 

 themselves can be so adjusted as to make the luck swing one 

 way. 



1 As by Prevost in the Bibliothe- parently accepted, by Quetelet (Phy- 

 que Universelle de Geneve, Oct. 1829. sique Sociale i. 171). 

 The explanation is noted, and ap- 



