The Math · 01
52 factorial.
Every way to arrange a 52-card deck, in full
80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000
8.07 × 10⁶⁷
That's the shorthand for the number above: an 8, a 0, and a 7, followed by 67 more digits' worth of zeroes-and-then-some. It's the total count of distinct orders a standard 52-card deck can be arranged in, and it's the space every shuffle on this site lands somewhere inside.
What a factorial actually is
A factorial answers a simple counting question: if you're arranging a set of distinct items in a row, how many different orders are possible? The first slot can hold any of them. Once that one's placed, the second slot can hold any of the rest. And so on, down to the last slot, which only has one item left to go in it. Multiply all of those choices together and you get every arrangement.
For n items, that's written n! (“n factorial”) and means n × (n − 1) × (n − 2) × … × 2 × 1. It grows fast, because every extra item doesn't just add a few more possibilities. It multiplies all the existing ones. 5! is 120. 10! is already 3,628,800. By the time you reach 52 cards, the number of choices at each step is still shrinking by one at a time, but there are 52 of those multiplications stacked on top of each other, and the result is the 68-digit number at the top of this page.
A sense of scale
Earth is estimated to contain somewhere around 1.3 × 10⁵⁰ atoms. 52! is roughly 620 quadrillion times larger than that, meaning if every atom on the planet were itself a whole extra Earth's worth of atoms, repeated around 620 quadrillion times over, you'd be in the neighborhood of 52!.
Or, time: at one new arrangement every second, working through all of 52! would take roughly 2.6 × 10⁶⁰ years. The universe itself is about 13.8 billion (1.38 × 10¹⁰) years old, so that's on the order of 10⁵⁰ times the age of the universe so far, to exhaust the list once.
Where the archive sits inside it
The honest comparison: this archive holds 12,300,339 recorded shuffles against 8.07 × 10⁶⁷ possibilities, a fraction of roughly 1.5 × 10⁻⁶¹. That is not a meaningful bite out of the total space, and it was never going to be. No amount of ordinary shuffling (by this site, by every casino on Earth, by every person who has ever touched a deck of cards) comes close to covering a measurable share of 52!.
What the archive actually demonstrates isn't coverage: it's that across every shuffle recorded so far, checked against every other one, nothing has repeated. See the methodology page for how that check was actually run.