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a six because the previous throw of six lies absolutely in the past, yet you may safely bet something more than the usual odds against it. Then suppose the second throw turns up a six, that throw also now lies in the past, and cannot be proved to have an influence upon throw number three, which you are preparing to make. If any material influence is suspected you may change the box and die; and you may now bet twice the usual odds against the six. Why ? Because you know by experience that it is extremely difficult to throw six three times in succession, even if you do not know the precise odds against it. Granted certain odds against throwing six twice in succession, &c., yet at any given moment when the player shakes the box in which is a six-faced die, he has one chance in six of throwing
a six; and yet if he has just thrown sixes twice, you may bet twelve to one that he will not throw a six in that particular cast.' If I did not hold gambling to be near akin to swindling, and could find but a few hundred who held this doctrine, how much money might I not gain by accepting any number of wagers of this wise sort !
The fact is, the mistake here .is just the ridiculous mistake which Steinmetz called ' the maturity of the chances,' over again. It is a mistake which has misled to their ruin many thousands of gamblers, Who might have escaped the evil influence of that other equally foolish mistake about being lucky or unlucky, in the vein or out of it. Steinmetz puts the matter thus : 'In a game of chance, the oftener the same combination has occurred in succession, the nearer are we to the certainty that it will not recur at the next cast or turn up: this is the most elementary of the theories on probabilities; it is termed the maturity of the chances.' The real fact being that this is not a theory of probabilities at all, but disproved by the theory of probabilities-and disproved, whenever it has been put to the test, by facts. Take the case considered in 'The Complete Poker Player,' and note the evidence on the strength of which the author of that work rejects the theory in favor of a practical common-sense notion (as he thinks), which is, in reality, nonsense. You may expect 9 successful draws to a flush in 47 hands; therefore, in the 500 deals he experimented upon, he might have expected 95 or 96;
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