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 the initiated, they offer them-and in general success—fully—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 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 1000l.—then, inasmuch as only one horse can win, the bettor loses 1000l. 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 1000l., 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 1000l. to 500l. against each horse, and A won; then he would have to pay 1000l. to the backer of A, and to receive 500l. 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.
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 3 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 84l. (because 84 contains the numbers 3, 2, 4, and 14). The layer of the odds wagers 84l. to 56l. against the leading favourite, 84l. to 42l. against the second horse, 84l. to 21l. against the third, and 84l. to 6l. against the fourth. Whichever horse wins, the layer has to pay 84l.; but if the favourite wins, he receives only 42l. on one horse, 21l. on another, and 6l. on the third—that is 69l. in all, so that he loses 15l.; if the second horse wins, he has to receive 56l., 21l., and 6l.—or 83l. in all, so that he loses 1l.; if the third horse wins, he receives 56l., 42l., and 6l.—or 104l. in all, and thus gains 20l.; and lastly, if the fourth horse wins, he has to receive 56l., 42l., and 2ll.—or 119l. in all, so that he gains 35l. 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 favourite should win. Accordingly, as professional book-makers are nearly always layers of odds, one often finds the success of a favourite spoken of in the papers as a ‘great blow for the book-makers,’ 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 favourite a blow to layers of the odds and vice versâ. In the case we have supposed, the money actually pending about the four horses (that is, the sum of the amount laid for and against them) was 140l. as respects the favourite, 126l. as respects the second, 105l. as respects the third, and 90l. as respects the fourth. But as a matter of fact the amounts pending about the favourites bear always a much greater proportion than the above to the amounts pending about outsiders. It is easy to see the effect of this. Suppose, for instance, that instead of the sums 84l. to 56l., 84l. to 42l., 84l. to 21l., and 84l. to 6l., a book-maker had laid 8400l. to 5600l., 840l. to 420l., 84l. to 21l., and 14l. to 1l., respectively—then it will easily be seen that he would lose 7958l. by the success of the favourite; whereas he would gain 4782l. by the success of the second horse, 5937l. by that of the third, and 6027l. by that of the fourth. I have taken this as an extreme case; as a general rule, there is not so great a disparity as has been here assumed between the sums pending on favourites and outsiders.
Finally, it may be asked whether, in the case of horses having unequal chances, it is possible that wagers can be so proportioned (just odds being given and taken), that, as in the former case, a person backing or laying against all the four shall neither gain nor lose. It is so. All that is necessary is, that the sum actually pending about each horse shall be the same. Thus, in the preceding case, if the wagers 9l. to 6l., 10l. to 5l., 12l. to 3l., and 14l. to 1l., are either laid or taken by the same person, he will neither gain nor lose by the event, whatever it may be. And therefore, if unfair odds are laid or taken about all the horses, in such a manner that the amounts pending on the several horses are equal (or nearly so), the unfair bettor must win by the result. Say, for instance, that instead of the above odds, he lays 8l. to 6l., 9l. to 5l., 11l. to 3l. and 13l. to 1l., against the four horses respectively; it will be found that he must win 1l. Or if he takes the odds 18l. to 11l., 20l. to 9l., 24l. to 5l., and 28l. to 1l. (the just odds being 18l. to 12l., 20l. to 10l., 24l. to 6l., and 28l. to 2l. respectively), he will win 1l. by the race. So that, by giving or taking such odds to a sufficiently great amount, a bettor would be certain of pocketing a large sum, whatever the event of a given race might be.
In every instance, a man who bets on a race must risk his money, unless he can succeed in taking unfair advantages over those with whom he bets. My readers will conceive how small must be the chance that an unpractised bettor will gain anything but dearly-bought experience by speculating on horse-races. I would recommend those who are tempted to hold another opinion to follow the plan suggested by Thackeray in a similar case—to take a good look at professional and practised betting-men, and to decide ‘which of those men they are most likely to get the better of’ in turf transactions.
(From Chambers’s Journal, July 1869.)