THE STATE OF THE ODDS. 277 



between the total number and the number of a specified 

 colour remains unchanged. Thus, if the odds are 5 to 1 

 against a horse, his chance is assumed to be equivalent 

 to that of drawing one white ball out of a bag containing 

 six balls, only one of which is white ; or to that of 

 drawing a white ball out of a bag containing sixty balls, 

 of which ten are white and so on. This is a very 

 important principle, as we shall now see. 



Suppose there are two horses (amongst others) 

 engaged in a race, and that the odds are 2 to 1 against 

 one, and 4 to 1 against the other what are the odds 

 that one of the two horses will win the race ? This 

 case will doubtless remind my readers of an amusing 

 sketch by Leech, called if I remember rightly 

 ' Signs of the Commission.' Three or four under- 

 graduates are at a * wine,' discussing matters equine. 

 One propounds to his neighbour the following ques- 

 tion : 'I say, Charley, if the odds are 2 to 1 against 

 Rataplan, and 4 to 1 against Quick March, what's the 

 betting about the pair ? ' ' Don't know, I'm sure,' 

 replies Charley; 'but I'll give you 6 to 1 against 

 them.' The absurdity of the reply is, of course, very 

 obvious ; we see at once that the odds cannot be 

 heavier against a pair of horses than against either 

 singly. Still, there are many who would not find it 

 easy to give a correct reply to the question. What 

 has been said above, however, will enable us at once 

 to determine the just odds in this or any similar case. 

 Thus the odds against one horse being 2 to 1, his 

 chance of winning is equal to that of drawing one 



