Chance and Luck

I gave in my 'How to Play Whist' (under the head 'Whist Whittlings') a case in which a certain man of title used to offer freely 1,000£ to 1£ against the occurrence of a whist hand containing no card above a nine -- a most unfair wager. Odds of a thousand pounds to one are very tempting to the inexperienced. 'I risk my pound,' such a one will say, 'but no more, and I may win a thousand.' That is the chance; and what is the certainty? The certainty is that in the long run such bets will involve a loss of 1,828£ for each thousand pounds gained, or a net loss of 828£. As certain to all intents as that two and two make four, a large number of wagers made on this plan would mean for the clever layer of the odds a very large gain. Yet Lord Yarborough would probably have been indignant to a degree if he had been told that in taking 1 for each hand on which he wagered which did not prove to be a 'Yarborough,' he was in truth defrauding the holder of the hand of 9s.0³/₄d., notwithstanding the preliminary agreement, simply because the preliminary agreement was an unfair one. As to his being told that even if he had wagered 1,828£ against 1£ the transaction would have been intrinsically immoral, doubtless he and his opponent would equally have scouted the idea.

A curious instance of the loss of all sense of honor, or even honesty, which betting begets, occurred to me when I was in New Zealand. A bookmaker ('by profession,' as he said), as genial and good-natured a man as one would care to meet, and with a strong sense of right and justice outside betting, had learned somehow that ten horses can come in (apart from dead heats) in 3,628,800 different ways. This curious piece of information seemed to him an admirable way of gaining money from the inexperienced. So he began to wager about it, endeavoring -- though, as will be seen, he failed -- to win money by wagering on a certainty. Unfortunately, he came early across a man as cute as himself and a shade cuter (a brigand brigand et demi), who worded the question on which the wager turns thus: -- 'In how many ways can ten horses be placed?' Of course, this is 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.'