Deck

shuffle a new deck until it forgets its order.

shuffle a deck of cards seven times, then count the orders 52 cards can be in

A riffle shuffle (split the deck, let the two halves fall together) can only interleave two halves, so a new deck keeps runs of its old order for four or five riffles; Bayer and Diaconis (1992) showed about seven bring 52 cards close to random, and the bars are their formula for the riffles you made. Then count: 52 choices for the first card, 51 for the next, and so on: 52! is about 8 x 10^67. Even if 8.2 billion people had shuffled once a second since the Big Bang, the chance any of them matched your deck is under 10^-36.

Concepts: probability, combinatorics.

An interactive you play with one thumb, on Wundr.