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s a very different thing. Only the first three horses can be placed, and the sets of three which can be made out of ten horses number only 10 times 9 times 8, or 720 (there are only 120 actual sets of three, but each set can be placed in six different ways). My genial, but (whatever he thought himself) not quite honest friend, submitted the matter to me. Not noticing, at first, the technical use of the word 'placed,' I told him there were 3,628,800 different arrangements: he rejoiced as though the money wagered were already in his pocket. When
this was corrected, and I told him his opponent had certainly won, as the question would be understood by betting men, he was at first depressed; but presently recovering, he said, ' Ah, well; I shall win more out of this little trick, now I see through it, than I lose this time.'
It is well to have some convenient standard of reference, not only as respects the fairness or unfairness of betting transactions, but as to the true nature of the chances involved or supposed to be involved. Many men bet on horse races without any clear idea of the chances they are really running. To see that this is so, it is only necessary to notice the preposterous way in which many bettors combine their bets. I do not say that many, even among the idiots who wager on horses they know nothing about, would lay heavier odds against the winning of a race by one of two horses than he would lay against the chance of either horse separately; but it is quite certain that not one bettor in a hundred knows either how to combine the odds against two, three, or more horses, so as to get the odds about the lot, or how to calculate the chance of double, triple, or multiple events. Yet these are the very first principles of betting; and a man who bets without knowing anything about such matters runs as good a chance of ultimate success as a man who, without knowing the country, should take a straight line in the hunting-field.
Now, apart from what may be called roguery in horse-racing, every bet in a race may be brought into direct comparison with the simple and easily understood
chance of success in a lottery where there is a single prize, and therefore only one prize ticket: and the chance of the winner of a race, where several horses run, being one particular horse, or one of any two, three, or more horses, can always be compared with the easily understood chance of drawing a ball of one color out of a vase containing so many balls of that color and so many of another. So also can the chance of a double or triple event be compared with a chance of the second kind.
Let us first, then, take the ease of a simple lottery, and distinguish between a fair lottery and an unfair one. Every actual lottery, I remark in passing, is an unfair one; at least, I have never yet heard of a fair one, and I can imagine no possible case in which it would be worth anyone's while to start a fair lottery.
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