If I shuffle a deck of 52 cards and hold it out for you to pick one, I can do so with an astonishing guarantee: No other deck in history has ever existed in this exact configuration — and no other deck ever will.
That doesn’t seem right, does it? Playing cards have been around since the 9th century, the standard deck since 1516. A lot of shuffling has happened since then. Cowboys played cards. World War II soldiers played cards. Today, millions of people play poker, black jack, and bridge. How do configurations not repeat?
Well, as I learned from Tim Urban, the number of unique arrangements can be calculated with a simple formula: 52 factorial, or 52! in math terms.
A factorial is simply a multiplication of decreasing factors. 3! is 6. You take 3 * 2 * 1. 5! is 120. You take 5 * 4 * 3 * 2 * 1. Therefore, 52! is just 52 * 51 * 50…and so on. Here is the number this results in:
Yeah. There’s no decimal point in there. Let’s see if we can wrap our brains around this number.
If you were to reshuffle the deck every second while only getting new combinations as you continue, here’s how long it would take you to go through all possible options: First, you should stand close to the Pacific Ocean. San Diego, perhaps? Pick a spot near the water. Then, you start shuffling. Once a second. Shuffle. Shuffle. Shuffle.
You shuffle for a billion years. That’s right. A billion. Then, you take one step. One. Hold your horses and such. Then, you shuffle for another billion years. Great! Now, another step. You take one step every billion years of shuffling until you’ve circumvented the globe. That’s 40,000 kilometers by the way. 25,000 miles. A thousand marathons, if you will.
Eventually, you’ll be back in San Diego. Are you done? Haha — no. After you arrive from your slow trip around the world, you take a pipette and remove one drop from the Pacific Ocean. Then, you repeat. Not just the drop removal. The whole thing. Hey! Keep shuffling! One step every billion years, one trip around the world, one drop from the Ocean. At 700 million cubic kilometers of water, that too should take a while.