The Mind Blowing Odds Inside A Deck Of Cards

Want a quick way to feel unique? Want to do something that has most likely never been done before in the history of the planet? Ok simple, go shuffle a deck of cards real quick. The order that those 52 cards will end up in will be one possibility of 8.0658 X 1067. Or to put it another way:

1 of 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000

That big long number has 68 digits in it. With odds like that there’s a pretty good chance that the order of those cards you just shuffled has never happened before – ever. To put this into perspective let’s say that you had a machine that could arrange a deck of cards 1 million times per second. That’s 86.4 billion times a day. If this machine were to run constantly for the next 6 billion years (by this time our sun is a red giant and all life on Earth has been burnt to a crisp) you would still only have 189,216,000,000,000,000,000,000 permutations. Just enough to scratch the surface a little bit.

A full deck of 52 playing cards.
deck_of_cards

To do the math on this is pretty straight forward. After shuffling a deck of cards, you lay them out and look at the order. There are 52 cards in a deck so card number 1 will have 52 possibilities. Now, with 51 cards remaining in the deck, card number 2 will only have 51 possibilities. Card number 3 has 50 possibilities and so on. With this in mind we simply take:
52x51x50x49x48…x1 (or more easily written as factorial – 52!)
Multiply all this together and the insane product comes out to be the ridiculously large aforementioned number 8.0658 X 1067.

Now nothing’s impossible, but with a number this big it’s pretty safe to say that no two randomly shuffled decks of cards have ever been the same. Even after shuffling for 6 billion years the odds are still pretty outrageous.

So the next time you want to feel special, simply go shuffle a deck of cards and raise them up high. Shout with a confident bellow “THIS HAS NEVER BEEN DONE BEFORE AND WILL NEVER BE DONE AGAIN!”

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