[zxcvbn4038]

And then you consider a game like blackjack where you often have six decks in play, 312! combinations instead of 52!.

Interesting question just popped into my head, if the orientation of the card matters, how do people randomize that?

[thedufer]

312! is way too high - there are 6 indistinguishable copies of each of 52 cards, not 312 unique cards.

[Chinjut]

(6 * 52)! / (6! ^ 52)