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about the second horse (B), and a third to do the like about the third horse (O), and if all these bets are made to the same amount--say 1,0001.--then, inasmuch as only one horse can win, the bettor loses 1,0001. on that horse (say A), and gains the same sum on each of the two horses B and O. Thus, on the whole, he gains 1,0001., 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 1,000l. to 500l. against each horse, and A won; then he would have to pay 1,000/. to the backer of A, and to receive 500l. from each of the backers of B and 0. 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; ho would gain or lose according to the event.
This will at once be seen, on trial.
Let us next take the case of horses with unequal prospects of success--for instance, take the case of the four horses considered above, against which the odds were respectively 8 to 2, 2 to 1, 4 to 1, and 14 to 1. Here, suppose the same sum laid against each, and for convenience let this sum be 84/. (because 84 contains the numbers 8, 2, 4, and 14). The layer of the odds
wagers 84l. to 56l. against the leading favorite, 841. to 421. against the second horse, 84l. to 21/. against the third, and 84/. to 61. against the fourth. Whichever horse wins, the layer has to pay 84l.; but if the favorite wins, he receives only 421. on one horse, 211: on another, and 61. on the third--that is 69/. in all, so that he loses 15/.; if the second horse wins, he has to receive 56/., 21/., and 6/.--or 83/. in all, so that he loses 11.; if the third horse wins, he receives 56/., 421., and 6/.--or 104/. in all, and thus gains 20/.; and lastly, if the fourth horse wins, he has to receive 56/., 42l., and 21/.--or 119/. in all, so that he gains 35/. He clearly risks much less than he has a chance (however small) of gaining. It is also clear that in all such cases the worst event for the layer of the odds is that the first favorite should win. Accordingly, as professional bookmakers are nearly always layers of odds, one often finds the success of a favorite spoken of in the papers as a ' great blow for the bookmakers,' while the success of a rank outsider will be described as a ' misfortune to backers.' But there is another circumstance which tends to make the success of a favorite a blow to layers of the odds and vice versa. In the case we have supposed, the money actually pending about the four horses (that is, the sum of the amounts laid for and against them) was 140/. as respects the favorite, 126/. as respects the second, 105/. as respects the third, and 90/. as respects the fourth. But, as a matter of fact,
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