THE STATE OF THE ODDS. 285 



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?. (because 84 contains 

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

 wagers 84?. to 561. against the leading favourite, 84?. to 

 42?. against the second horse, 84?. to 211. against the 

 third, and 84?. to 6?. against the fourth. Whichever 

 horse wins, the layer has to pay 84?. ; but if the 

 favourite wins, he receives only 42?. on one horse, 21?. 

 on another, and 6?. on the third that is 691. in all, so 

 that he loses 151. ; if the second horse wins, he has to 

 receive 56?., 21?., and 61. or 83?. in all, so that he loses 

 1?. ; if the third horse wins, he receives 56?., 42?., and 

 61. or 104?. in all, and thus gains 20?. ; and lastly, if 

 the fourth horse wins, he has to receive 56?., 42?., and 

 21?. or 119?. in all, so that he gains 35?. 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 



