E201 -- Calcul de la probabilité dans le jeu de rencontre

(Calculation of the probability in the game of Rencontre)


The Game of Recontre (coincidence), also called the game of treize (thirteen), involves shuffling 13 numbered cards, then dealing them one at a time, counting aloud to 13. If the nth card is dealt when the player says the number 'n,' the dealer wins (this is known in combinatorics as a derangement of 13 objects.). Euler calculates the probability that the dealer will win.

It should be noted that this problem was solved earlier, by P.R. de Montmort, in 1713, though his work was unknown to Euler.

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