What are the odds of getting the same deck of cards?

So the chances are 1/52! because, on the second shuffle, there's exactly one order that's exactly the same. The number of ways that a deck of cards can be arranged is 52 x 51 x 50 x 49 x 48 3 x 2 x 1.

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Is a shuffled deck of cards unique?

While it's possible that two packs of cards may have been shuffled into the same order, the odds of that having happened are actually tiny and yes, it's hugely likely that each properly shuffled deck is indeed a unique variation of those 52 cards. But a full proper shuffle is almost certainly unique each time. Correspondingly, can you over shuffle cards? There's no such thing as "over-shuffling" the cards. Either you haven't shuffled enough for a fair game, or you have. Shuffling only two or three times produces less-than-random hands. To make sure that the cards are mixed-and that all players have the same chance-you should shuffle about seven times.

Thereof, what does 52 factorial look like?

52! is approximately 8.0658e67. For an exact representation, view a factorial table or try a "new-school" calculator, one that understands long integers. A billion years currently equals 3.155692608e16 seconds; however, the addition of leap seconds due to the deceleration of Earth's orbit introduces some variation. How do you shuffle cards back to order?

How many shuffles do you need to randomize 100 cards?

So if you're playing a 60-card Modern deck, riffle at least eight times (though you could probably get away with 7, still). If you're playing a 100-card EDH deck, riffle at least ten times. If you're playing a 500,000-card monster deck, riffle at least 28 times. How many shuffles is optimal? Jim Reeds at Bell Laboratories and showed that a deck is perfectly mixed if it is shuffled between 5 and 20 times. Next, Dr. Diaconis worked with Dr. Aldous and showed that it takes 5 to 12 shuffles to perfectly mix a deck.