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But the most adequate explanation of the Frederician legend is the circumstance that public opinion has been systematically mobilized in favour of Frederick the Great by the great French leaders of the eighteenth century, the dispensers of European fame. It was not for nothing that Frederick the Great for forty years courted the good graces of Voltaire d’Alembert.
The common and natural impression is in favor of D’Alembert: the regular series would be thought much more unlikely than an irregular.
According to Laplace’s sixth theorem, which we demonstrated in a former chapter, the difference of probability arising from the superior efficacy of the constant cause, unfairness in the dice, would after a very few throws far outweigh any antecedent probability which there could be against its existence. D’Alembert should have put the question in another manner.
Among these thinkers may be numbered D’Alembert; who, in an Essay on Probabilities to be found in the fifth volume of his Mélanges, contends that regular combinations, though equally probable according to the mathematical theory with any others, are physically less probable.
The example of a coincidence selected by D’Alembert, that of sixes thrown on a pair of dice ten times in succession, belongs to this sort of cases rather than to such as Laplace’s. The coincidence is here far more remarkable, because of far rarer occurrence, than the drawing of the white ball.
Enviable evenings, no doubt, were passed in them; and if we could be carried back to any of them at will, we should hardly know whether to choose the Wednesday dinner at Madame Geoffrin’s, with d’Alembert, Mademoiselle de l’Espinasse, Grimm, and the rest, or the graver society which, thirty years later, gathered round Condorcet and his lovely young wife.
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