MIRACLES IN GAMES OF CHANCE.
[To THE EDITOR OF THE .` SPECTATOR." J SIB,—With reference to Professor Karl Pearson's calcula- tions on the mathematical possibilities of runs and deviations in games of chance, and his amazement at what he terms the -miraculous spins that actually occur at Monte Carlo and -elsewhere, the following account of a rubber of whisk played here on the 5th inst., in which hearts were trumps in nine deals out of thirteen, may possibly be of some interest. Two packs of cards were used, and were made after each round in the usual way. In the three games, which comprised thirteen rounds, clubs were trumps once, diamonds thrice, hearts nine times. Unfortunately no written record of the runs was kept; but it is almost certain they were as follows : Hearts— diamonds — clubs —hearts twice— diamonds — hearts three times—diamonds—hearts three times again. Some doubt was expressed whether diamonds did not occur in the fifth round instead of the sixth, thus making hearts to recur four times consecutively. But, however this may be, the remarkable fact remains that in thirteen deals, and out of 104 cards, repeatedly shuffled, hearts recurred nine times. To calcurate the mathematical chances against any particular snit turning up three times in seven is comparatively easy; but the odds, both theoretical and practical, against this deviation of nine in thirteen, seem to be millions to one. The absolute uncertainty as to when such a deviation may occur, does not in our opinion constitute its appearance as miraculous. Like the flower of the aloe, its cycle may be outside any attempted calculations ; and Professor Pearson hardly seems to be logical in speaking of the "exact science" of the laws of chance when the actualities of such chance exceed the possibilities known to empirical experience.—I am, Sir, &c.,