THE STATE OF THE ODDS. 311 



ever horse wins the race. This is not strictly the case. 

 It is of course possible to make sure of winning if the 

 bettor can only get persons to lay or take the odds he 

 requires to the amount he requires. But this is pre- 

 cisely the problem which would remain insoluble if all 

 bettors were equally experienced. 



Suppose, for instance, that there are three horses 

 engaged in a race with equal chances of success. It is 

 readily shown that the odds are 2 to 1 against each. 

 But if a bettor can get a person to take even betting 

 against the first horse (A), a second person to do the 

 like about the second horse (B), and a third to do the 

 like about the third horse (C), and if all these bets 

 are made to the same amount say, 1,000 then, in- 

 asmuch as only one horse can win, the bettor loses 

 1,000 on that horse (say A), and gains the same sum 

 on each of the two horses B and C. Thus, on the 

 whole, he gains 1,000, the sum laid out against eacli 

 horse. 



If the layer of the odds had *aid the true odds to 

 the same amount on each horse, he would neither have 

 gained nor lost. Suppose, for instance, that he laid 

 1,000 to 500 against each horse, and A won ; then 

 he would have to pay 1,000 to the backer of A, and 

 to receive 500 from each of the backers of B and C. 

 In like manner, a person who had backed each horse 

 to the same extent would neither lose nor gain by the 

 event. Nor would a backer or layer who had wagered 



