Shuffling Playing Cards Produces Order Never Seen Before

December 22, 2012 at 6:00 pm Chad Upton 4 comments

By Chad Upton | Editor

When you finish a game of cards, you must shuffle the deck (imperfectly) seven times before the card order is properly randomized again. Then, it’s also statistically impossible that order of cards has ever occurred before!

Because a deck of cards has 52 unique cards, the number of different orders of those cards is astronomical and I mean that rather literally. The combinations of cards is greater than the number of observable stars in the galaxy.

There are only 7×10²²stars in the galaxy, and the combinations of playing cards is too cumbersome to put into words, so here’s the number: 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000.

The BBC put it in perspective in the following video; you’d need over sextillion people, each with trillions of decks of cards, shuffling them all 1000 times per second for 4.5 billion years before you started to see repeat combinations.

Knowing that seven imperfect shuffles are needed for a properly randomized deck, casinos should do this too. But, they rarely do.

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Photo: Ivette D.L.G. (cc)

Sources: NYT, wikipedia (shuffling), nowiknow

Entry filed under: Demystified, Entertainment. Tags: 52!, 7 times, cards, deck, playing, poker, shuffle.

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4 Comments Add your own

1. Doug in Idaho | September 12, 2013 at 11:20 pm

I’ve actually came to this conclusion myself a long time ago and have thought about it many times. And to convince myself I consider all the number of decks of cards in which all of one color is on top and all the other is on bottom plus all the decks that alternate between the two colors (26 factorial times 4—a huge number). Think of how unusual it would be to shuffle a deck of cards and have them turn out in either of those ways.

But really those decks wouldn’t be any more “special” than any other deck of cards.

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2. Jone Arthur | October 11, 2022 at 12:05 am

I love to shuffle cards. it gives a nice feeling when i shuffle card while playing with my friends Good indoor game

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3. Laurie R. Whitten | March 7, 2023 at 10:46 pm

Nice Calculations. thank you for sharing. https://acaciawooddb.com/

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4. Wilbur K. Washington | March 7, 2023 at 10:52 pm

The vastness of the number of possible combinations of playing cards is truly mind-boggling.https://all-keyboard.com/

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