How many ways can you arrange a deck of cards?

[Richard Forster]

Here is a problem ...

What is the number of random deck arrangements needed to reach a point were there is a 50% chance that one of the arrangements will be duplicated.

Sort of a variation of The Birthday Paradox.

Approximately 10574307231100289363611308602026251 arrangements.

[This comes from solving the bounding equation exp(-(n(n-1))/2.52!) < .5]

[Jonathan Townsend]

But if you go into a magic shop and everyone checks their packs of cards... maybe 10 people before you find a match (si stebbins etc)?

[brianarudolph]

Given the dozens of decks found in an actual magic shop, aren't the vast majority of them are already in the same order?

[Jonathan Townsend]

mmm that's why you're supposed to mix the cards until you feel comfortable before you start the reading... oh... right...

might be a story there about some packs at an actual magic shop which are always in the same order (sympathetic) which are read behind the scenes by a supervising reader and maybe some note taking that gets passed along ...

@Brad, what do you think?

@Rest 52! the same sort of large as 75! - according to most calculators they may as well be the same number ... big beyond utility, approximated by a number times ten to the power larger than the number of digits across the display (sixty seven digits for the fifty two factorial).