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 had already been solved by P. R. de Montmort in 1713, though this work was unknown to Euler.
Original Source Citation
Mémoires de l'académie des sciences de Berlin, Volume 7, pp. 255-270.
Opera Omnia Citation
Series 1, Volume 7, pp.11-25.