THE STATE OF THE ODDS. 281 



fore, the chance that one of the three will win is equal 

 to that of drawing a white ball out of a bag contain- 

 ing 180 balls, of which 103 (the sum of 45, 40, and 

 18) are white. Therefore, the odds are 103 to 77 on 

 the three. 



One does not hear in practice of such odds as 103 

 to 77. But betting-men (whether or not they apply 

 just principles of computation to such questions, is 

 unknown to us) manage to run very near the truth. 

 For instance, in such a case as the above, the odds on 

 the three would probably be given as 4 to 3 that is, 

 instead of 103 to 77, or, which is the same thing, 412 

 to 308, the published odds would be 412 to 309. 



And here a certain nicety in betting has to be men- 

 tioned. In running the eye down the list of odds, one 

 will often meet such expressions as 10 to 1 against 

 such a horse offered, or 10 to 1 wanted. Now, the 

 odds of 10 to 1 taken may be understood to imply that 

 the'horse's chance is equivalent to that of drawing a 

 certain ball out of a bag of eleven. But if the odds 

 are offered and not taken, we cannot infer this. The 

 offering of the odds implies that the horse's chance is 

 not better than that above mentioned, but the fact that 

 they are not taken implies that the horse's chance is 

 not so good. If no higher odds are offered against the 

 horse, we may infer that his chance is very little worse 

 than that mentioned above. Similarly, if the odds of 

 10 to 1 are asked for, we infer that the horse's chance 

 is not worse than that of drawing one ball out of 

 eleven ; if the odds are not obtained, we infer that his 



