What are the chances of shuffling a deck in order twice?

You have 52 choices for first card, and then 51 choices for the second card, and so on, until there is only one card left and you have only one choice. We call this “52 factorial” and it’s written 52!. So the chances are 1/52! because, on the second shuffle, there’s exactly one order that’s exactly the same.

How many times would you have to shuffle a deck of cards to get them back in order?

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.

Is every shuffle of a 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.

How many possible orders are there for a deck of cards?

No one has or likely ever will hold the exact same arrangement of 52 cards as you did during that game. It seems unbelievable, but there are somewhere in the range of 8×1067 ways to sort a deck of cards. That’s an 8 followed by 67 zeros.

What does E mean in maths?

The number e, also known as Euler’s number, is a mathematical constant approximately equal to 2.71828, and can be characterized in many ways. It is the base of the natural logarithm. It is the limit of (1 + 1/n)n as n approaches infinity, an expression that arises in the study of compound interest.

What are the odds of shuffling a deck of cards perfectly?

It depends on how you shuffle them and the cards’ order when you start. If you truly randomise the deck, the chances of the cards ending up in perfect order – spades, then hearts, diamonds and clubs – are around 1 in 10 to the power 68 (or 1 followed by 68 zeros).

How many shuffles in a row can you randomize a deck?

It doesn’t really matter whether that ordering was previously achieved or not, other than to point out that if you are talking about two shuffles in a row, we will assume that your shuffles are adequate enough to actually randomize the deck. In order to calculate the answer, we need to know how many ways there are to shuffle a deck of cards.

What are the chances of a deck of 52 cards repeating?

If a unique order of a deck of 52 unique cards had been created every second since the big bang, the chances that any two of them were repeated is approximated by 1 − ( 1 − 1 / 52!) ( 10 17) = 1.2397999 × 10 − 51 .

What is the probability of getting the same order after shuffle?

That’s the answer if, by “shuffling” you mean some process of riffle, overhand, corgi, etc. continued long enough to fully randomize the deck. If you mean what’s the probability of getting the same order of cards after ONE riffle shuffle, the probability is exactly zero.