THE STATE OF THE ODDS. 283 



just odds against that one are determinate, as we shall 

 see immediately. The chance of the leading favourite 

 corresponds to the chance of drawing a ball out of a 

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

 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, 

 three in all ; that of the third, to the chance of drawing 

 a ball out of a bag in which are four black balls and 

 one white one, five in all. We take, then, the least 

 number containing both five and three that is, fifteen ; 

 and then the number of white balls, corresponding to 

 the chances of the three horses, are respectively six, 

 five, and three, or fourteen in all ; leaving only one to 

 represent the chance of the fourth horse (against which 

 the odds are therefore 14 to 1). Hence the chances of 

 the four horses are respectively as the numbers six, five, 

 three and one. 



I have spoken above of the published odds. The 

 statements made in the daily papers commonly refer to 

 wagers actually made, and therefore the uninitiated 

 might suppose that everyone who tried would be able 

 to obtain the same odds. This is not the case. The 

 wagers which are laid between practised betting-men 

 afford very little indication of the prices which would 

 be forced (so to speak) upon an inexperienced bettor. 

 Book-makers that is, men who make a series of bets 

 upon several or all of the horses engaged in a race 

 naturally seek to give less favourable terms than the 

 known chances of the different horses engaged would 

 suffice to warrant. As they cannot offer such terms to 



