312 LIGHT SCIENCE FOR LEISURE HOURS. 



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 56 against the leading favorite, 84 

 to 42 against the second horse, 84 to 21 against the 

 third, and 84 to 6 against the fourth. Whichever 

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

 favorite wins, he receives only 42 on one horse, 21 

 on another, and 6 on the third that is 69 in all, so 

 that he loses 15 ; if the second horse wins, he has to 

 receive 56, 21, and 6 or 83 in all, so that he 

 loses 1 ; if the third horse wins, he receives 56, 42, 

 and 6 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 

 favorite should win. Accordingly, as professional 

 book-makers are nearly always layers of odds, one 

 often finds the success of a favorite spoken of in the 



