Fixed-point-free permutations: "Treize" (thirteen)

 

A betting game:
Someone shuffles 13 playing cards
and compares the shuffled sequence
with the original one.
Your are winning,
if all the cards have moved the position...
(de Montmori (1708), N. Bernoulli (1713))

Again a typical example of a permutation (the playing cards are permuted).
Remember:

The probability that at least one card lies on its old position is 63 %

nearly independent of the number of crads used ...

Analog: "Rencontre", using 52 playing cards: Leonhard Euler (1753),
also: The problem of the interchanged hats, coats, bags, letters ...
de Moivre (1718), Lambert (1771), Laplace (1812), ...