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 84_l._ (because 84 contains the numbers 3, 2, 4, and 14). The layer of the odds wagers 84_l._ to 56_l._ against the leading favourite, 84_l._ to 42_l._ against the second horse, 84_l._ to 21_l._ against the third, and 84_l._ to 6_l._ against the fourth. Whichever horse wins, the layer has to pay 84_l._; but if the favourite wins, he receives only 42_l._ on one horse, 21_l._ on another, and 6_l._ on the third—that is 69_l._ in all, so that he loses 15_l._; if the second horse wins, he has to receive 56_l._, 21_l._, and 6_l._—or 83_l._ in all, so that he loses 1_l._; if the third horse wins, he receives 56_l._, 42_l._, and 6_l._—or 104_l._ in all, and thus gains 20_l._; and lastly, if the fourth horse wins, he has to receive 56_l._, 42_l._, and 2l_l._—or 119_l._ in all, so that he gains 35_l._ 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 140_l._ as respects the favourite, 126_l._ as respects the second, 105_l._ as respects the third, and 90_l._ 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 84_l._ to 56_l._, 84_l._ to 42_l._, 84_l._ to 21_l._, and 84_l._ to 6_l._, a book-maker had laid 8400_l._ to 5600_l._, 840_l._ to 420_l._, 84_l._ to 21_l._, and 14_l._ to 1_l._, respectively—then it will easily be seen that he would lose 7958_l._ by the success of the favourite; whereas he would gain 4782_l._ by the success of the second horse, 5937_l._ by that of the third, and 6027_l._ 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.