THE STATE OF THE ODDS. 309 



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

 favorite, 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 colors ; 

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

 drawing a ball of any assigned color. 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 afcworite. 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 favorite. Let us suppose there 

 are two favorites, and that the odds against the lead- 

 ing favorite are 3 to 2, those against the other 2 to 1, 

 and those against the best non-favorite 4 to 1 ; and 

 let us compare the chance 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 determinable, as we shall 

 Bee immediately. The chance of the leading favorite 

 corresponds to the chance of drawing a ball out of a 

 bag in which are three black and two white balls, five 

 in all ; that of the next to the chance of drawing a ball 

 out of a bag in which are two black and one white ball, 



