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d be the betting against each of the three horses. If any one of the horses has less odds offered against him, he is a favorite. There may be more than one of the four horses thus distinguished; and, in that case, the horse against which the least odds are offered is the first favorite. Let us suppose there are two favorites, and that the odds against the leading favorite are 3 to 2, those against the other 2 to 1, and those against the best non-favorite 4 to 1; and let us compare the chances of the four horses. I have not named any odds against the fourth, because, if the odds against all the horses but one are given, the just odds against that one are determinable, as we shall see immediately. The chance of the leading favorite corresponds to the chance of drawing a ball out of a bag in which are three black and two white balls, five 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 bails 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 practiced betting-men afford very little indication of the prices which would be forced (so to speak) upon an inexperienced bettor. Bookmakers 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 favorable terms than the known chances of the different horses engaged would suite to warrant. As they cannot offer such terms to the initiated, they offer them--and in general successfully --to the inexperienced.
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
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