What is the probability of shuffling cards into the same order?

Asked by: Chris Nicolson, Isle of Skye 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). That’s a huge number, roughly equal to the number of atoms in our galaxy.

What are the odds of shuffling a deck of cards the same way twice?

So the chances are 1/52! because, on the second shuffle, there’s exactly one order that’s exactly the same.

How many combinations of deck shuffling are there?

If you were to shuffle a deck of 52 cards and lay them out the possible order combinations are practically endless. The total number of combinations is a factorial of 52, or 52!, which translates to 8.06e+67, a number that means absolutely nothing to me.

How long would it take to shuffle every combination of cards?

You most likely meant to ask “… how long would it take to create a single iteration of every possible order, provided each shuffle creates a unique order?” And that is simply 52! (the amount of possible combinations) seconds, or 8.0658175e+67 seconds.

Has anyone shuffled a deck in order?

The chances that anyone has ever shuffled a pack of cards (fairly) in the same way twice in the history of the world, or ever will again, are infinitesimally small. The number of possible ways to order a pack of 52 cards is ’52! ‘ (“52 factorial”) which means multiplying 52 by 51 by 50… all the way down to 1.

How big is 52 factorial?

52! is approximately 8.0658e67. For an exact representation, view a factorial table or try a “new-school” calculator, one that understands long integers.

What does 52 factorial look like?

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.

How many possible arrangements are there for a deck of 52 playing cards?

How much is 8.06 e67?

ways, in which we can arrange a deck of cards. 52! is a damn high number which is equal to 8.06e+67. 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000 to be exact. It is a 68 digit number.

What is the probability that the cards have not been ordered?

The probability that any particular ordering of the cards has not occurred, given your initial assumptions, is ( 1 − 1 52!) ( 3 × 10 14), and the probability that it has occurred is 1 minus this value. But for small values of n ϵ, ( 1 + ϵ) n is nearly 1 + n ϵ.

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.

What are the odds of duplicating a deck of cards?

Dividing our estimate of the number of shuffles in history by the number of different ways a deck of cards can be ordered gives our odds that a thorough shuffle will duplicate an arrangement of cards that has already existed in history. Those odds are: That is, one in 28 sexdecillion.

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.