If you thoroughly shuffle a standard deck of 52 playing cards, it is highly probable that the ordering of the cards has never happened before in thehistory of card shuffling. There are more possible combinations in a deck of cards (52! [factorial]) than there are atoms that comprise the earth. To put it another way, here's a guy's answer to the question of whether two decks have ever been shuffled in the same order:
"...let's overestimate. Currently, there are between 6 and 7 billion people in the world. Also, the modern deck of 52 playing cards has been around since 1300 A.D. probably. If we assume that 7 billion people have been shuffling cards once a second for the past 700 years, that will be way more than the actual number of times cards have been shuffled. 700 years is 255675 days (plus or minus a couple for leap year centuries), which is
22090320000 seconds. Now, if
7000000000 people had been shuffling cards once a second for
22090320000 seconds, they would have come up with
7000000000 •
22090320000 different combinations, or orderings of cards. When you multiply those numbers together you get 154632240000000000000, or rounding off, 1.546X1020.
So, it's safe to say that in human history, playing cards have been shuffled in less than 1.546X1020 different orders.
Is this order unique in human history?
Probably so. When I shuffled the cards this afternoon, that is one of 8.0658X1067 possible orders the cards can be in. However, in the past 700 years since playing cards were invented, cards have been shuffled fewer than 1.546X1020 times. So the chances that one of those times they got shuffled into the same exact order you see here are less than 1 in 100000000000000000000000000000000000000000000000 (1 in 1047).
Link:
http://www.matthewweathers.com/year2006/shuffling_cards.htm