THE STATE OF THE ODDS. 303 



in all such cases. Tims, if tlie odds against a horse 

 are 7" to 1, we infer that the cognoscenti consider his 

 chance equal to that of drawing one particular ball 

 out of a bag of eight. 



A similar treatment applies when the odds are not 

 given as so many to one. Thus, if the odds against a 

 horse are as 5 to 2, we infer that the horse's chance is 

 equal to that of drawing a white ball out of a bag 

 containing five black and two white balls or seven 

 in all. 



We must notice also that the number of balls may 

 be increased to any extent, provided the proportion 

 between the total number and the number of a specified 

 color remains unchanged. Thus, if the odds are 5 to 

 1 against a horse, his chance is assumed to be equiva- 

 lent 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 (among others) en- 

 gaged 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 our readers of an amusing 

 sketch by Leech, called if we remember rightly 

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

 graduates are at a "wine," discussing matters equine. 



