If you properly shuffle a deck of cards…

playing-cardsIf you properly shuffle a deck of cards, in all likelihood, the resulting deck has never been seen before in the history of the world. Number of permutations possible = 52! = 8.0658175e+67 (i.e. 8 followed by 67 zeroes)

Playing cards were invented in China in the 9th Century.

So, humans have been playing cards for 1200 years i.e 1200365246060 = 37843200000 seconds.
Even with the blown-out-of-proportion assumption that there are 1 billion shuffles per second in the world, the total number of shuffles is 3.78432e+19 which is about 2*10^48 times lesser than the total permutations.

Hence, the probability of at least 2 decks being the same is infinitesimally small.

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