# What is the probability of shuffling a deck of cards the same way twice?

## What is the probability 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.

### What are the odds of shuffling a deck of cards in the same order?

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.

How many outcomes of shuffling a 52 cards deck are possible?

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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 many ways can a 52 card deck be arranged?

In fact there are 52! distinct arrangements of the 52 cards in a standard deck,which = (8.06581751….)*( 10^67). Thus, 8 followed by 67 digits in random order are the number of distinct ways of shuffling it.

## How many shuffles are in a deck of cards?

In 1992, Bayer and Diaconis showed that after seven random riffle shuffles of a deck of 52 cards, every configuration is nearly equally likely. Shuffling more than this does not significantly increase the “randomness”; shuffle less than this and the deck is “far” from random.

### How many combinations of card shuffles are there?

The total number of different shuffles you can have is: 52! That’s 52 factorial, which is 52 x 51 x 50 x 49… all the way down to 1. So there isn’t enough space on earth to layout every possible shuffle.

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How many ways can cards be shuffled?

Now that we know there are 52! 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.

How many times we can divide 52 factorial by 2?

Answer: We can divide it 26 times.

## 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.

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How many possible combinations are there in a deck of cards?

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.

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.