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ossing of 'tail' four times running had not diminished the tendency towards 'tail' being tossed. Among the 68 cases which had thus given 'tail' five times running, 29 failed to give another 'tail,' while the remaining 39 gave another, that is, a sixth 'tail.' Of these 39, 25 failed to give another ' tail,' while 14 gave a seventh ' tail '; and here it might seem we have evidence of the effect of preceding tosses. The disproportion is considerable, and even to the mathematician the case is certainly curious; but in so many trials such curiosities may always be noticed. That it will not bear the interpretation put upon it is shown by the next steps. Of the 14 cases, 8 failed to give another 'tail,' while the remaining six gave another, that is, an eighth 'tail'; and these
numbers eight and six are more nearly equal than the preceding numbers 25 and 14; so that the tendency to change had certainly not increased at this step. However, the numbers are too small in this part of the experiment to give results which can be relied upon. The cases in which the numbers were large prove unmistakably, what reason ought to have made self-evident, that past events of pure chance cannot in the slightest degree affect the result of sequence trials.
To suppose otherwise is, indeed, utterly to ignore the relation between cause and effect. When anyone asserts that because such and such things have happened, therefore such and such other events will happen, he ought at least to be able to show that the past events have some direct influence on those which are thus said to be affected by them. But if I am going to toss a coin perfectly at random, in what possible way can the result of the experiment be affected by the circumstance that during ten or twelve minutes before, X tossed ' head' only or ' tail' only?
The system of which I now propose to speak is more plausible, less readily put to the full test, and consequently far more dangerous than the one just described. In it, as in the other, reliance is placed on a ' change' after a ' run' of any kind, but not in the same way.
Everyone is familiar with the method of renewing wagers on the terms ' double' or 'quits.' It is a very convenient way of getting rid of money which has been won on a wager by one who does not care for wagering, and, not being to the manner born, does not feel com-
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