284 LIGHT SCIENCE FOR LEISURE HOURS. 



We find, however, that the odds taken are 180 to 80. 

 Hence, we learn that the offers against some or all of 

 the three horses are considerably short of what backers 

 require ; or else, that some person has been induced 

 to offer far heavier odds against Sir J. Hawley's lot 

 than are justified by the fair odds against his horses, 

 severally. 



We have heard it asked why a horse is said to be a 

 favourite, though the odds may be against him. This 

 is very easily explained. Let us take as an illustration 

 the case of a race in which four horses are engaged to 

 run. If all these horses had an equal chance of win- 

 ning, it is very clear that the case would correspond to 

 that of a bag containing four balls of different colours ; 

 since, in this case, we should have an equal chance of 

 drawing a ball of any assigned colour. Now, the odds 

 against drawing a particular ball would clearly be 3 to 

 1. This, then, should be the betting against each of 

 the three horses. If any one of the horses has less 

 odds offered against him, he is a favourite. There may 

 be more than one of the four horses thus distinguished ; 

 and in that case, the horse against which the least odds 

 are offered is the first favourite. Let us suppose there 

 are two favourites, and that the odds against the 

 leading favourite are 3 to 2, those against the other 

 2 to 1, and those against the best non-favourite 4 to 1 ; 

 and let us compare the chances of the four horses. We 

 have not named any odds against the fourth, because, 

 if the odds against all the horses but one are given, the 

 just odds against that one are de terminable, as we shall 



