Improbable Probabilities

Want to do something that's probably never been done before--something that's not illegal, expensive, or kinky weird? Just get a standard deck of 52 playing cards and shuffle them well.

The chances are very good that the exact order of cards in your just-shuffled deck has never, ever occurred before, said Virginia Postret in a recent lecture titled "In Praise of Play" at the American Enterprise Institute.

That's because 'an ordinary deck of 52 cards offers 10⁶⁸ possible arrangements (that's 1 followed by 68 zeros--a really big number), which means that any order you happen to shuffle has probably never appeared before in the entire history of cards,' said Postrel, who is editor of Reason magazine.

Don't believe her? Here's one way to think about it. If 100 million card dealers each shuffled a deck of cards 1 million times a year for 1,000 years, they would exhaust no more than a quarter of the possibilities (10¹⁷) -- even if every shuffle produced a unique ordering, which is unlikely since all that shuffling would probably result in a few matches.

Still don't believe her? Start shuffling.

[Bylo's, ahem, observation: 10⁶⁸ is not merely four times larger than 10¹⁷. It's 10⁵¹ times larger -- that's one followed by 51 zeros.]