It is often said that a man may so lay his wagers about a race as to make sure of gaining money whichever 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 precisely 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 1000_l._—then, inasmuch as only one horse can win, the bettor loses 1000_l._ 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 1000_l._, the sum laid out against each horse. If the layer of the odds had laid the true odds to the same amount on each horse, he would neither have gained nor lost. Suppose, for instance, that he laid 1000_l._ to 500_l._ against each horse, and A won; then he would have to pay 1000_l._ to the backer of A, and to receive 500_l._ 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 _different_ sums _necessarily_ gain or lose by the race; he would gain or lose _according to the event_. This will at once be seen, on trial.