OT (For Fun): What Is the Probability That Two Decks Of Cards Were Sequenced Identically...

RutgersRaRa

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...in the history of card shuffling, after having been properly shuffled, assuming that every deck ever used was a standard 52-card deck?

The answer is below so you won't automatically see it in case you want to think about first.













The chances that anyone has ever shuffled a pack of cards in the same way twice in the history of the world are infinitesimally small, statistically speaking. The number of possible permutations of 52 cards is ‘52 factorial’ otherwise known as 52! or 52 shriek. This is 52 times 51 times 50 . . . all the way down to one. Here's what that looks like:

80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000.

To give you an idea of how many that is, here is how long it would take to go through every possible permutation of cards. If every star in our galaxy had a trillion planets, each with a trillion people living on them, and each of these people has a trillion packs of cards and somehow they manage to make unique shuffles 1,000 times per second, and they'd been doing that since the Big Bang, they'd only just now be starting to repeat shuffles.

Many casinos use the child's approach to shuffling with new decks of cards, i.e. spreading all the cards out on the table and jumbling them before collecting them back into a deck. This is called 'washing' the deck or the 'Corgi' shuffle; casinos or tournaments often use it when introducing a new pack to initially randomise it. If you can riffle shuffle cards perfectly – i.e. ABABAB, as some casino dealers can – it actually makes the order slightly less random than if you shuffled the cards imperfectly.

To mix up a pack of cards thoroughly you need at least seven imperfect riffle shuffles. Any less and there is still a vestige of order; any more and the rewards of the extra shuffle are small. For some games like blackjack, where suits don’t matter, you only need about four shuffles.

Here's the link I got the above explanation from: http://qi.com/infocloud/playing-cards
 
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VirtualKnight

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Is that number more than there are grains of sand on the planet? The answer to this will keep me up at night.
 

RutgersRaRa

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Is that number more than there are grains of sand on the planet? The answer to this will keep me up at night.
I saw something recently that said it's more than the number of atoms in our galaxy, or something ridiculous like that. Here is another website's attempt at putting into perspective, which is of course impossible for us but fun nonetheless:

Start by picking your favorite spot on the equator. You're going to walk around the world along the equator, but take a very leisurely pace of one step every billion years. The equatorial circumference of the Earth is 40,075,017 meters.Make sure to pack a deck of playing cards, so you can get in a few trillion hands of solitaire between steps. After you complete your round the world trip, remove one drop of water from the Pacific Ocean. Now do the same thing again: walk around the world at one billion years per step, removing one drop of water from the Pacific Ocean each time you circle the globe. The Pacific Ocean contains 707.6 million cubic kilometers of water.Continue until the ocean is empty. When it is, take one sheet of paper and place it flat on the ground. Now, fill the ocean back up and start the entire process all over again, adding a sheet of paper to the stack each time you’ve emptied the ocean.

Do this until the stack of paper reaches from the Earth to the Sun. Take a glance at the timer, you will see that the three left-most digits haven’t even changed. You still have 8.063e67 more seconds to go. 1 Astronomical Unit, the distance from the Earth to the Sun, is defined as 149,597,870.691 kilometers.So, take the stack of papers down and do it all over again. One thousand times more. Unfortunately, that still won’t do it. There are still more than 5.385e67 seconds remaining. You’re just about a third of the way done.

And you thought Sunday afternoons were boring
To pass the remaining time, start shuffling your deck of cards. Every billion years deal yourself a 5-card poker hand. Each time you get a royal flush, buy yourself a lottery ticket. A royal flush occurs in one out of every 649,740 hands.If that ticket wins the jackpot, throw a grain of sand into the Grand Canyon. Keep going and when you’ve filled up the canyon with sand, remove one ounce of rock from Mt. Everest. Now empty the canyon and start all over again. When you’ve levelled Mt. Everest, look at the timer, you still have 5.364e67 seconds remaining. Mt. Everest weighs about 357 trillion pounds.You barely made a dent. If you were to repeat this 255 times, you would still be looking at 3.024e64 seconds. The timer would finally reach zero sometime during your 256th attempt. Exercise for the reader: at what point exactly would the timer reach zero?

Back here on the ranch
Of course, in reality none of this could ever happen. Sorry to break it to you. The truth is, the Pacific Ocean will boil off as the Sun becomes a red giant before you could even take your fifth step in your first trek around the world. Somewhat more of an obstacle, however, is the fact that all the stars in the universe will eventually burn out leaving space a dark, ever-expanding void inhabited by a few scattered elementary particles drifting a tiny fraction of a degree above absolute zero. The exact details are still a bit fuzzy, but according to some reckonings of The Reckoning, all this could happen before you would've had a chance to reduce the vast Pacific by the amount of a few backyard swimming pools.

Here's that link: http://czep.net/weblog/52cards.html
 

RU4Real

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And you thought Sunday afternoons were boring
To pass the remaining time, start shuffling your deck of cards. Every billion years deal yourself a 5-card poker hand. Each time you get a royal flush, buy yourself a lottery ticket. A royal flush occurs in one out of every 649,740 hands.If that ticket wins the jackpot, throw a grain of sand into the Grand Canyon. Keep going and when you’ve filled up the canyon with sand, remove one ounce of rock from Mt. Everest. Now empty the canyon and start all over again. When you’ve levelled Mt. Everest, look at the timer, you still have 5.364e67 seconds remaining. Mt. Everest weighs about 357 trillion pounds.You barely made a dent. If you were to repeat this 255 times, you would still be looking at 3.024e64 seconds. The timer would finally reach zero sometime during your 256th attempt. Exercise for the reader: at what point exactly would the timer reach zero?

Here's that link: http://czep.net/weblog/52cards.html

Everest would be long gone by the time this experiment were concluded. On average, the lifespan of a mountain range is about 400 million years. Some are much shorter.
 

RU4Real

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Especially if @huskersalways is on the job. Dude levels stuff just by looking at it.

He's only rearranging what has been put there by other forces.

In the part of Nebraska shown in all those pictures of that spectacular hunting retreat, the basement rock of Nebraska lies about 3000' underneath what used to be the tops of the Rockie Mountains. You could make a very good argument that said cabin (ha) isn't really built on top of Nebraska at all, geologically speaking. It's very much on Colorado.
 

RutgersRaRa

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He's only rearranging what has been put there by other forces.

In the part of Nebraska shown in all those pictures of that spectacular hunting retreat, the basement rock of Nebraska lies about 3000' underneath what used to be the tops of the Rockie Mountains. You could make a very good argument that said cabin (ha) isn't really built on top of Nebraska at all, geologically speaking. It's very much on Colorado.
It really was unavoidable that the subject matter of this thread would point to one thing, and one thing only: Donovan's song.

 

Crazed_RU

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I'm sure we can somehow turn this into another bickering thread about global warming.
 

ScarletDave

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Start by picking your favorite spot on the equator. You're going to walk around the world along the equator, but take a very leisurely pace of one step every billion years. The equatorial circumference of the Earth is 40,075,017 meters.Make sure to pack a deck of playing cards, so you can get in a few trillion hands of solitaire between steps. After you complete your round the world trip, remove one drop of water from the Pacific Ocean. Now do the same thing again: walk around the world at one billion years per step, removing one drop of water from the Pacific Ocean each time you circle the globe. The Pacific Ocean contains 707.6 million cubic kilometers of water.Continue until the ocean is empty. When it is, take one sheet of paper and place it flat on the ground. Now, fill the ocean back up and start the entire process all over again, adding a sheet of paper to the stack each time you’ve emptied the ocean.

Do this until the stack of paper reaches from the Earth to the Sun. Take a glance at the timer, you will see that the three left-most digits haven’t even changed. You still have 8.063e67 more seconds to go. 1 Astronomical Unit, the distance from the Earth to the Sun, is defined as 149,597,870.691 kilometers.So, take the stack of papers down and do it all over again. One thousand times more. Unfortunately, that still won’t do it. There are still more than 5.385e67 seconds remaining. You’re just about a third of the way done.

And you thought Sunday afternoons were boring
To pass the remaining time, start shuffling your deck of cards. Every billion years deal yourself a 5-card poker hand. Each time you get a royal flush, buy yourself a lottery ticket. A royal flush occurs in one out of every 649,740 hands.If that ticket wins the jackpot, throw a grain of sand into the Grand Canyon. Keep going and when you’ve filled up the canyon with sand, remove one ounce of rock from Mt. Everest. Now empty the canyon and start all over again. When you’ve levelled Mt. Everest, look at the timer, you still have 5.364e67 seconds remaining. Mt. Everest weighs about 357 trillion pounds.You barely made a dent. If you were to repeat this 255 times, you would still be looking at 3.024e64 seconds. The timer would finally reach zero sometime during your 256th attempt.
Here's that link: http://czep.net/weblog/52cards.html

And then, Jim Delany will drop a beach ball from the international space station, and if it lands on the 50 yard line of Rentschler Field, UConn still won't be invited to the Big Ten.
 
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SkilletHead2

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Couple of related fun facts. You have about 100 billion neurons in your brain, about the same number as the number of stars in the Milky Way, or the number of galaxies in the universe.

We all know that we have iron in our blood. But did you know that that iron came from a supernova? The iron in your blood was created in a star or a supernova in the distant past (along with all the other heavy metals, with the possible exception Linkin Park).

If you're a bridge player, you might have once been looking at a bad had and asked yourself, "What is the probability of getting all spades as your hand?" Answer is: the same as the probability of getting the hand that you are looking at.
 

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