The science

A shuffled deck of cards is almost certainly in an order no deck has ever been in. 52 cards can be lined up in 52! = 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000 ways, about 8.07 × 10⁶⁷. That is about 85 billion times the number of atoms in the Sun (about 9.4 × 10⁵⁶: 1.989 × 10³⁰ kg, about 73% hydrogen and 25% helium by mass). Even if all 8.2 billion people alive had shuffled once a second since the Big Bang, they would have made only about 3.6 × 10²⁷ decks, so the chance that a properly shuffled deck matches any of them is below 1 in 10⁴⁰.

'Properly' matters. A new deck comes in order, and a riffle shuffle only interleaves two packets, so each card keeps its order within its packet: one riffle leaves two rising sequences, and three usually leave eight, which is enough to reconstruct exactly how the deck was shuffled. Bayer and Diaconis worked out the exact chance of every order after any number of riffles (in the Gilbert–Shannon–Reeds model of a real riffle): the distance from random stays near its maximum of 1 through five shuffles (0.92 at five), then falls fast: 0.61 at six, 0.33 at seven, 0.17 at eight, halving with each further shuffle. Hence 'about seven'.

The deck on screen is a real seeded simulation of that model: the runs you see are counted from it, and the deck it ends on is the deck it opens on.