The Amazing Truth About A Deck Of Cards

“Patience and shuffle the cards.” —Miguel Cervantes, Don Quixote

In A Nutshell

There are more possible arrangements in a deck of cards than there are stars in the known universe. The full number is 52 factorial, which is (very, very roughly) an eight followed by 67 zeroes.

The Whole Bushel

The standard 52-card deck has been around for 500 years or more. What is rather unbelievable is that there are so many possible arrangements of the cards, it is statistically unlikely that any two have ever repeated in all of history. There are in fact 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000 arrangements.

The above number, while impossible to get your head around in any conventional manner, is 52 factorial, the possible orders of a shuffled deck. While enormous, the number is rather simply arrived at, by multiplying 52 down to 1 (52 x 51 x 50 . . . ). There are more possible arrangements of cards than there are atoms on Earth.

With such an astonishing range, the science of “card counting,” or predicting the next cards to be dealt in a hand, seems more magic than math. There are, however, well-known formulas to tip the odds in a player’s favor. In American casinos, card counting is not illegal, though casinos frown upon it and employ various countermeasures to keep professional players from raking in huge pots.

Show Me The Proof

True Count Calculation: The Whole Story
Shuffling Into Hyperspace

  • gillybean

    Always amazed by card counters. For the effort they put in they deserve a little win now and again.

  • “it is statistically unlikely that any two have ever repeated in all of history” And yet, every time I open a brand new deck of cards, they’re always in the exact same order! Spooky. 🙂

    • Revo

      maybe, just MAYBE they were DESIGNED to be that way, because they are brand new. think about it, a machine will always do the same task.

      • PalestinianCitizen

        Maybe, just MAYBE you don’t understand sarcasm.

        • Revo

          No, I did not. Thank you for clarifying.

  • Timone

    One of the coolest knowledgenuts I’ve seen.

  • Wert????

    So something about cards…. then the rest is a blur…yawn

  • Eli Goldsmith

    I find the “more than atoms on the earth” statement “highly illogical”, as Mr. Spock would say.

    • Lacey W

      Actually quite logical, though it defies our personal sense of reason.
      There are 133,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 atoms that make up the earth.
      Or, to put it in a number to get you head around, 1.33*10(50). To simplify the number of card combinations (rounding to make it easy for me) there are 81*10(66) possible card combinations. (generally).

      To paraphrase the popular nasal spray ad, 66 > 50.
      There are a lot of atoms on Mother Earth, but there are more combinations of 52 different cards.