Astounding Fact #1 - A shuffled deck of cards is unique

Properly shuffle a deck of 52 cards and you will be holding a combination that has never before been seen in history, and never will again… a fact an excellent magician like my friend Lee Warren would benefit from pointing out when dazzling audiences with his close up magic.

There are 52! ways to arrange 52 cards. That’s “52 factorial” for those who may have forgotten their probability class (52 x 51 x 50 etc.. all the way to 1). ¬†Factorials get large really quickly and this one turns out to be 8.1 x 10^67.

Sheldon, in an episode of the Big Bang Theory, writes this number down on his board when he can’t figure out Howard’s card trick using maths.

Big huh? But how big? We humans don’t have an intuitive grasp of big numbers, because we can write them down pretty easily. To give you an idea:

  • There are fewer stars than this in the entire visible universe. Way fewer.
  • If everyone on Earth shuffled a deck of cards properly randomly a billion times a year for a billion years, they wouldn’t stand a chance of shuffling the same arrangement twice.

(Incidentally, it’s combinatorics like this that allowed me to create the solution checker for The Looking Glass Club puzzles without fearing someone could use it to cheat to win the prize of up to a million pounds.)

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