How rare is it to shuffle a deck of cards?

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!

What are the odds of shuffling a deck of cards?

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.

Is shuffling a deck of cards random?

Mathematicians have figured out that seven proper riffle shuffles will result in a randomly distributed deck of cards. The overhand shuffle is when clumps of cards are pulled from the deck and thrown back in randomly.

Has anyone ever shuffled a deck of cards in order?

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 8x10⁶⁷ ways to sort a deck of cards. That's an 8 followed by 67 zeros.

How large 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. 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.

Combinations of 52 cards (52 factorial)

How big is 1000000 factorial?

(Note that one million factorial is an extremely large number. It has 5,565,709 digits. And yet we can easily say something about this number, namely how many digits it has!)

How many digits is 100000 factorial?

Factorial of 100000 is a number with 456569 digits (so I can't print it here), and my solution takes 3.5 seconds, more or less. If that's not assumible for you, you must design a multi-thread based solution. For instance, one thread multiply first half of n and another thread does the same but for the second half.

What is the perfect shuffle 8 times?

The Faro Shuffle is a perfect shuffle. When cut evenly at 26 cards and shuffled correctly eight times, the deck will return to its original order. Many aspiring magicians attempt to learn this shuffle by using a standard deck of Bicycle playing cards.

How unique is a random shuffle?

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. The number you get at the end is 8×10^67 (8 with 67 '0's after it), essentially meaning that a randomly shuffled deck has never been seen before and will never be seen again.

How many shuffles is enough?

For most games, four to seven riffle shuffles are sufficient: for unsuited games such as blackjack, four riffle shuffles are sufficient, while for suited games, seven riffle shuffles are necessary. There are some games, however, for which even seven riffle shuffles are insufficient.

Do card shufflers hurt cards?

As most gamers will tell you, automatic shufflers are dangerous for your cards and more often than not jam if your cards are sleeved (which could lead to serious damage to your cards.) Hand cranked models are thus much safer.

Why do you shuffle 7 times?

By saying that the deck is completely mixed after seven shuffles, Dr. Diaconis and Dr. Bayer mean that every arrangement of the 52 cards is equally likely or that any card is as likely to be in one place as in another.

What is the fastest time to shuffle a deck of cards?

The fastest time to arrange a deck of playing cards is 35.20 seconds, and was achieved by Lim Kai Yi (Malaysia) in Cheras, Malaysia, on 30 September 2022. Lim is an avid speed solver and has won many speed solving competitions. His first win came in a state-level 3x3 competition.

What are the odds of guessing a 52 card deck?

Picking cards

If you choose a card at random, there are 52 possibilities for what you might get. So, if a magician were to simply guess what card you have picked, there would be a chance of only 1/52 they guess it correctly, or a little less than 2%.

Is every shuffled deck 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.

What is a perfect shuffle called?

The Faro Shuffle

Before I begin going into the math, let's look at what it means to do a “perfect” /faro shuffle. To do a faro shuffle, you first split the deck into 2 equal parts and subsequently interweave them one card at a time, combining them.

Can you shuffle cards too much?

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.

How many times do casinos shuffle cards?

“Most people shuffle cards three or four times. Five times is considered excessive”. But five is still lower than the number required for an effective shuffle. Even dealers in casinos rarely shuffle the required seven times.

How do you play shuffle to 100?

Players make two 3-digit numbers and discard the extra card. Players record their numbers and sums on the Shuffle to 1,000 Record Sheet (Math Masters, page G11). Then players find and record the difference between their sums and 1,000. The player with the LOWEST total score after 4 rounds wins.

What is the 7 shuffle theorem?

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 zeros are there in 25?

Explanatory Answer

25 is the square of 5 and hence it has two 5s in it. In toto, it is equivalent of having six 5s. There are at least 6 even numbers in 25! Hence, the number 25! will have 6 trailing zeroes in it.

Is it possible for n to end in exactly five zeros?

There are no natural numbers whose factorials end with 5 zeroes.

What is factorial 9999?

For example, even though the function could handle arguments greater than 9999, the factorial of 9999 equates to a 35656-digit number.