Example III. Suppose the same three as before, and the common bets 7 to 4 A against B; 21 to 20 (or 'gold to silver') B against C; we must state it thus:--7 guineas to 4 A against B; and 4 guineas to L4, B against C; which being reduced into shillings, the scheme will stand as follows:-- 147 A's expectation. 81 B's expectation. 80 C's expectation.----311 By which it will be 164 to 147 the field against A, (something more than 39 to 35). Now, if we compare this with the last example, we may conclude it to be right; for if it had been 40 to 35, then it would have been 8 to 7, exactly as in the last example. But, as some persons may be at a loss to know why the numbers 39 and 35 are selected, it is requisite to show the same by means of the Sliding Rule. Set 164 upon the line A to 147 upon the slider B, and then look along till you see two whole numbers which stand exactly one against the other (or as near as you can come), which, in this case, you find to be 39 on A, standing against 35 on the slider B (very nearly). But as 164/311 and 147/311 are in the lowest terms, there are no less numbers, in the same proportion, as 164 to 147,--39 and 35 being the nearest, but not quite exact. Example IV. There are four horses to start for a sweepstake, namely, A, B, C, D, and they are supposed to be as equally matched as possible. Now, Mr Sly has laid 10 guineas A against C, and also 10 guineas A against D. Likewise Mr Rider has laid 10 guineas A against C, and also 10 guineas B against D. After which Mr Dice laid Mr Sly 10 guineas to 4 that he will not win both his bets. Secondly, he laid Mr Rider 10 guineas to 4 that he will not win both his bets. Now, we wish to know what Mr Dice's advantage or disadvantage is, in laying these two last-mentioned wagers. First, the probability of Mr Sly's winning both his bets is 1/3 of 14 guineas; and Mr Dice's expectation is 2/3 of 14 guineas, or L9 16s., which being deducted from his own stake (10 guineas), there remains 14s., which is his disadvantage in that bet. Secondly, Mr Rider's expectation of winning his two bets is 1/4, and, therefore, Mr Dice's expectation of the 14 guineas, is 3/4, or L11 0s. 6d., from which deduct 10 guineas (his own stake), and there remains 10s. 6d., his advantage in this bet,--which being deducted from 14s. (his disadvantage in the other), there remains 3s 6d., his disadvantage in paying both these bets. These examples may suffice to show the working of the system; regular tables exist adapted to all cases; and there can be no doubt that those who have realized large fortunes by horse-racing managed to do so by uniformly acting on some such principles, as well as by availing themselves of such 'valuable information' as may be secured, before events come off, by those who make horse-racing their business.