Shuffling Playing Cards Produces Order Never Seen Before

December 22, 2012 at 6:00 pm Chad Upton

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 7×1022 stars 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

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