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f a. player A, who, having paid in his 31. to the pool of 10/. in all, should abstract a pound therefrom. If the layer of the odds wagered only 51. against 31., he would be in the position of a player B, who, having paid in his 71. to the pool of 10/. in all, should abstract 21. there from.
Or, if any difficulty should arise in the reader's mind from this way of presenting matters, let him put the case thus :--Suppose the sum of the stakes 10/.; then the odds being 7 to 3 against, the case is as though three tickets were marked for the prize and seven unmarked; and the two players ought therefore to contribute severally 31. and 71. to make up the 10/. If the 10/. is made up in any other way, there is unfairness; one player puts in too much, the other puts in too little. If one puts in 21. 10s. instead of 31., the other puts in 71. 10s. instead of 71., and manifestly the former has wronged the latter to the extent of 1l., having failed to put in 10s. which he ought to have put in, and having got the other to put in 10s. which ought not to have been put in. This seems clearer, I find, to some than the other way of presenting the matter. But as, in reality, bets are not made in this way, the other way, which in principle is the same, is more convenient. Bettors do not take a certain sum of money
for the total of 'their stakes, and agree how much each shall stake towards that sum; but they bet a certain sum against some other sum. It is easy to take either of these to find out how much ought to be staked against it, and thus to ascertain to what extent the proper total of the stakes has been affected either in excess or defect. And we can get rid of any difficulty arising from the fact that according to the side we begin from we get either an excess or a defect, by beginning always from the side of the one who wagers at least as much as he should do, at the proper odds, whatever they may be.
As a general rule, indeed, the matter is a good deal simplified by the circumstance that fraudulent bettors nearly always lay the odds. It is easy to see why. In fact, one of the illustrative cases above considered has already probably suggested the reason to the reader. I showed that when the odds are 9 to 1 and only 7 to ! is laid, in pounds, the fraud is the same as removing 21. from a pool of 10/.; whereas with the same odds, backing the horse by 18s. instead of 1/., corresponded to removing two shillings from such a pool Now, if a fraudulent gambler had a ready hand in abstracting coins from a pool, and were playing with some one who did not count the money handed over to him when he won, it would clearly be the same thing to him whether he contributed the larger or smaller sum to the pool, for he would abstract as many coins as he could, and it would be so much clear gain. But if he could not get at the pool, and therefore could only cheat by omitting to contribute his fair share, it would manifestly be far
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