Shuffle a deck of cards right now and you will do something no human being has ever done before. Not close to it, either.
Here’s the question that’s been stuck in my head: what are the odds of shuffling a 52-card deck into perfect order — Ace through King, in every suit? There are 52 factorial possible arrangements of a deck, which works out to 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000. That’s a 68-digit number. Don’t bother saying it out loud. The odds of landing on that one exact sequence come out to about 1 in 8.07 x 10^67, or 0.00000000000000000000000000000000000000000000000000000000000000000124% — 65 zeros marching by before you hit a real digit.
Numbers that size stop meaning anything to a human brain, so try this version instead. Shuffle a billion decks a second, nonstop, without ever sleeping, and you would expect to wait about 2.6 x 10^51 years before you saw that exact order once. The universe is 13.8 billion years old. That’s nothing.
Here’s the part that actually gets me. The boring-looking deck you get every single time you shuffle had exactly the same odds as the perfect one. Whatever’s sitting in your hand right now, some meaningless jumble like a 7 of clubs next to a jack of diamonds, beat the same one-in-8×10^67 shot that Ace-through-King would have beaten. Every shuffle you’ve ever done is that unlikely. You just don’t notice, because nothing about it looks special.
That’s the trick. “Looks random” and “looks like a perfect suited run” are mathematically identical in probability. One just happens to match a pattern your brain recognizes, so you call it a miracle when it lands there and shrug when it doesn’t. The cards don’t know the difference. Only you do.
This isn’t just a card trick, either. Play the lottery and pick 4, 17, 22, 35, 41, and 46 because it feels properly “random,” and you have the exact same odds as the guy who plays 1, 2, 3, 4, 5, and 6 and gets mocked for it at the gas station counter. The math doesn’t care that his ticket looks like a joke. Yours just looks like a ticket.
One more thing worth sitting with: 52 factorial is so much bigger than the number of shuffles that have ever happened in human history that it’s a safe bet no honestly shuffled deck has ever landed on the exact same order twice. Every hand of poker you’ve played and every card trick your uncle botched at Thanksgiving is a genuine one-of-one.
My two cents: the universe hands out this exact miracle every time somebody deals a hand of gin rummy, it just doesn’t bother telling you. The weird-looking shuffle and the ordinary one were always equally impossible. Deal accordingly.
Photo by Paul Huxley via Openverse, licensed CC BY 2.0.