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. Yet card players report it happening.

Has anyone ever shuffled a deck of cards in the same order?

No one has, and will likely never, hold the exact same arrangement of those 52 cards you did during that game. Just think about that...

How long would it take to shuffle the same deck of cards?

Longer than the universe is old: on average, 52! ≈ 8 * 10^67 shuffles, assuming all deck configurations are equally likely. (The universe has only been around for 4 * 10^17 seconds.)

How long does it take to shuffle every combination?

Try 300 quintillion years. To find out how many individual orders you can get using all 52 cards, we need to work out 52! – remember, that's 52 factorial, not 52 in an excited voice.

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

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 many ways can you arrange a deck of cards? - Yannay Khaikin

How big is 52 factorial story?

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 is considered a perfect shuffle?

A perfect shuffle is performed by splitting the deck into a top part and a bottom part and then (starting with the bottom part) repeatedly taking the bottom card from each part and placing them on top of a new deck. The process called an in-shuffle is shown for a deck of 8 cards below.

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.

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.

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.

Is every card shuffle unique?

Each thoroughly shuffled deck of cards is, in all likelihood, unique, meaning it has never existed before and will never exist again.

How many times do dealers shuffle cards?

And yet… dealers in Vegas would never shuffle 7 times, because that would take too much time and it would disrupt the flow of the game, lose momentum. The Vegas standard is 3: riffle, riffle, box, riffle, cut. “The 3 shuffle technique is the industry standard.” So Vegas is on team Marmie.

What is 52 factorial in words?

Similarly, Scott Czepiel has a great essay on imagine the immensity of 52!, or 80658175170943878571660636856403766975289505440883277824000000000000, which is the number of ways an ordinary deck of cards can be shuffled: This number is beyond astronomically large.

What is a fun fact about shuffling cards?

To find all arrangements of 52 cards in a deck, we compute 52!, which happens to be a really big number. Riffle seven times and you'll have a sufficiently random ordering of cards, an ordering that has likely never existed before. In other words, it's unlikely you'll ever shuffle two decks the same.

Can you count cards if the deck is shuffled every round?

Continuous Shuffle Machines (CSM's)

These machines continually shuffle together 3-5 decks, making it impossible to predict what types of cards are left in the shoe. Thus, it's impossible to count a CSM game.

Which is the donkey theorem?

The Donkey Theorem is also known as the triangle inequality theorem. It states that in a triangle ABC: AC < AB + BC. The name comes from the idea that if a donkey standing at point A, and a hay stack at point C, the donkey will always take the shorter path to go straight from A to C instead of from A to B to C.

What is the rule of Pick's theorem?

Pick's Theorem states that if a polygon has vertices with integer coordinates (lattice points) then the area of the polygon is i + {1\over 2}p - 1 where i is the number of lattice points inside the polygon and p is the number of lattice points on the perimeter of the polygon.

How many times do casinos shuffle?

“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.

Is shuffle good for you?

- It improves hand-eye coordination and reduces clumsiness. - It tones your legs, calves, and glutes. - It works your abdominal muscles with twists and turns. - It strengthens joints and ligaments in your legs.

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%.

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!)

What does e mean in maths?

In statistics, the symbol e is a mathematical constant approximately equal to 2.71828183. Prism switches to scientific notation when the values are very large or very small. For example: 2.3e-5, means 2.3 times ten to the minus five power, or 0.000023.