THE STATE OF THE ODDS. 287 



to the same extent would neither lose nor gain by 

 the event. Nor would a backer or layer who had 

 wagered different sums necessarily gain or lose by the 

 race ; he would gain or lose according to the event. 

 This will at once be seen, on trial. 



Let us next take the case of horses with unequal 



prospects of success for instance, take the case of the 



four horses considered above, against which the odds 



were respectively 3 to 2, 2 to 1, 4 to 1, and 14 to 1. 



Here, suppose the same sum laid against each, and for 



convenience let this sum be 84 1. (because 84 contains 



the numbers 3, 2, 4, and 14). The layer of the odds 



wagers 847. to 567. against the leading favourite, 847. 



to 427. against the second horse, 847. to 217. against the 



third, and 847. to 67. against the fourth. Whichever 



horse wins, the layer has to pay 847.; but if the 



favourite wins, he receives only 427. on one horse, 217. 



on another, and 67. on the third that is 697. in all, so 



that he loses 157.; if the second horse wins, he has to 



receive 567., 217., and 67. or 837. in all, so that he loses 



17.; if the third horse wins, he receives 567., 427., and 



67. or 1047. in all, and thus gains 207. ; and lastly, if 



the fourth horse wins, he has to receive 567., 427., and 



217. or 1197. in all, so that he gains 357. He clearly 



risks much less than he has a chance (however small) 



of gaining. It is also clear that in all such cases the 



worst event for the layer of the odds is, that the 



favourite should win. Accordingly, as professional 



book-makers are nearly always layers of odds, one 



often finds the success of a favourite spoken of in the 



