On these simple principles all calculations of chances, to be worth anything, must be based. But they are not so simple as they sound. Pascal’s formula, like all formulas of the higher mathematics, expresses an abstract truth only, and one that can never be realized in fact. The longer the run, the more certain will it be that the two events never will occur equally; and the more frequent will be long series of the recurrence of one or the other. Turning aside from abstruse calculations, which can be readily found elsewhere by those who would like to see them, let us inquire as to the practical results of this Logic of Chance when applied to the fortunes of the individual. These observed and calculated results establish the following interesting rule:――In matters of pure luck, about two-thirds of any given number of persons will come out substantially even, in any large number of trials; of the remaining third, about one-half will be noticeably lucky, and the remaining one-half noticeably unlucky. Thus, of six who venture, four will have no special fortune, good or bad; one will be quite “in vein”; one quite “out of vein.” Suppose the players are thirty-six, and we select the lucky six, and pit them against each other, as in “progressive” games; the same law will hold good, one coming out noticeably better, one noticeably worse than the rest; and so on indefinitely, the number of the extremes diminishing at the rate of six to one at each new trial. This is the Law of Luck; but it is obvious that it leaves luck, good and bad, a real fact; and among a million men, or in a great city like New York or London, we must find extraordinary examples of “sequences,” both of the favors and the frowns of fortune; not in gambling only, but in those thousands of accidental events which make up the welfare or misery of personal experience. All the moralists I have read on the subject seem to blink and stagger at this obvious and necessary conclusion,――that the history of many individuals is and must be enormously controlled, in spite of any efforts of their own, by pure luck. In cutting the cards twenty times in succession, about twenty people in a million will cut red every time and another twenty will cut black every time; and so it will be with all other matters of pure chance in life. There is no use in trying to dodge this certain result of a sum in simple division. We must count it in, in all plans and calculations for success and happiness in our individual life. The important question is, what value must we assign to it? Here is where men make several frequent and disastrous errors.