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sovereigns, it becomes more and more unlikely, the longer they toss, that the difference between them will fall short of any given sum. If they go on till
they have tossed twenty million times, the odds are heavily in favor of one or the other being a loser of at least a thousand pounds. But the proportion of the amount won by one altogether, to the amount won altogether by the other, is almost certain to be very nearly a proportion of equality. Suppose, for example, that at the end of twenty millions of tossings, one player is a winner of 1,000/., then he must have won in all 10,000,500/., the other having won in all 9,999,500/.; the ratio of these amounts is that of 100005 to 99995, or 20001 to 19999. This is very nearly the ratio of 10000 to 9999, or is scarcely distinguishable, practically, from actual equality. Now if these men had only tossed eight times for sovereigns, it might very well have happened that one would have won five or six times, while the other had only won thrice or twice. Yet with a ratio of 5 to 3, or 3 to 1, against the loser, he would actually be out of pocket only 21. in one case and 41. in the other; while in the other case, with a ratio of almost perfect equality, he would be the loser of a thousand pounds.
But now it might appear that, after all, this is proving too much, or, at any rate, proves as much on one side as on the other; for if one player loses the other must gain; if a certain set of players lose the rest gain: and it might seem as though, with the prevalent ideas of many respecting gambling games, the chance of winning were a sufficient compensation for the chance of losing.
Where a man is so foolish that the chance of having
more money than he wants is equivalent in his mind (or what serves him for a mind) to the risk of being deprived of the power of getting what is necessary for himself and for his family, such reasoning may be regarded as convincing. For those who weigh their wants and wishes rightly, it has no value whatever. On the contrary it may be shown that every wager or gambling transaction, by a man of moderate means, definitely reduces the actual value of his possessions, even if the wager or transaction be a fair one. If a man who has a hundred pounds available to meet his present wants wagers 50/. against 50/., or an equal chance, he is no longer worth 100%. He may, when the bet is decided, be worth 150/., or he may be worth only 50/. All he can estimate his property at is about 87/. Supposing the other man to be in the same position, they are both impoverished as soon as they have made the bet; and when the wager is decided, the average value of their possessions in ready money is less than it was; for the winner gains less by having his 100/. raised to 150%. (or increased as 2 to 3), than the loser suffers by having his ready money halved.
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