Trivia

If you take a regular deck of 52 cards and thoroughly shuffle them, you have very nearly a 100% chance of creating an exact order of cards that has never, ever, been created before!
Imagine all the times that a deck of cards has been shuffled in Vegas, Atlantic City, and elswhere. Think about every deck of cards ever shuffled in any card room, casino, or basement poker game. Then shuffle your own deck of cards and put a smile on your face because you can be fairly certain that you are creating something that has never existed before!
Want proof? Consider how many different ways you can arrange 52 cards. If you had only 3 cards you could arrange them a total of 6 different ways. 5 cards could be arranged 120 different ways.
What about 52 cards??? There are about 80,658,175,170,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 different ways to arrange the deck. If you added up the number of times a deck of cards has been shuffled throughout history, it would be just a small fraction of this number.

With regard to blackjack, we are not dealing with 52 unique cards. An ace is an ace, and it makes no difference if the ten value card in a blackjack is the ten of spades or the king of diamonds. If we exchange the position of each of the like value clubs and spades, for example, in a deck, we have made no changes at all as far as the game of blackjack is concerned (and of course, assuming no sidebets or bonus payoffs).

Actually, I never meant to imply anything regarding blackjack. It's just a piece of trivia about a deck of cards. The numbers represent exact ordering of cards. I.E. 2h, 4s, 6c is considered different than 2c, 4h, 6s.

Question, with respect to blackjack, how many unique decks are there.

We take the original 52!, and then realize that for the cards A-9, suit does not matter (divide by (4!)^10) and for the cards T,J,Q,K both suit and rank don't matter (divide by 16!). Thus, the final number of arrangements for blackjack is:

52!/(4!*4!*4!*4!*4!*4!*4!*4!*4!*4!*16!) = 4.886x10^40.

This is much less than 52!, maybe there's a chance if I get a nice long head's up single deck game, to see them all.

At the rate of 200 hands per hour, if every person on the planet played a different permutation with each hand, it would take about 4.63x10^24 years to see them all.

--Mayor

and then realize that for the cards A-9, suit does not matter (divide by (4!)^10)

There are only 9 ranks from A to 9, so you divide by (4!)^9.

The correct number is 1.46e32.

52!/(4!*4!*4!*4!*4!*4!*4!*4!*4!*4!*16!) = 4.886x10^40.

I get 6.08e40.