THE STATE OF THE ODDS. 283 



lay the same odds against Rosicrucian as would be the 

 true mathematical odds against drawing a white ball 

 out of a bag containing two white and seven black 

 balls ; but no one is willing to back the horse at this 

 rate. On the other hand, higher odds are not offered 

 against him. Hence it is presumable that his chance 

 is somewhat less than that above indicated. Again, 

 bettors are willing to lay the same odds against Pace 

 as might fairly be laid against drawing one white ball 

 out of a bag of seven, one only of which is white ; but 

 backers of the horse consider that they ought to get 

 the same odds as might be fairly laid against drawing 

 the white ball when an additional black ball had been 

 put into the bag. As respects Green Sleeve and Blue 

 Gown, bettors are willing to lay the odds which there 

 would be, respectively, against drawing a white ball 

 out of a bag containing (1) eleven balls, one only of 

 which is white, and (2) one hundred and seven balls, 

 seven only of which are white. Now, the three horses 

 Rosicrucian, Green Sleeve, and Blue Gown all belong 

 to Sir Joseph Hawley, so that the odds about the 

 three are referred to in the last statement of the list 

 just given. And since none of the offers against the 

 three horses have been taken, we may expect the odds 

 actually taken about ' Sir Joseph Hawley 's lot ' to be 

 more favourable than those obtained by summing up 

 the three former in the manner we have already 

 examined. It will be found that the resulting odds 

 (offered) against Sir J. Hawley 's lot estimated in 

 this way should be, as nearly as possible, 132 to 80. 



