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Xsyllman
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The following is from an article published in the 21 March 1999 edition of The Washington Post newspaper. I came across it the other day when going through some papers. There's not much that's useful for this trade/hobby/pursuit, but might make an interesting aside to mention when in the midst of presenting an effect. Enjoy.

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Improbable Probabilities

Want to do something that's probably never been done before --- something that's not illegal, expensive, or kinky weird? Just get a standard deck of 52 playing cards and shuffle them well.

The chances are very good that the exact order of cards in your just-shuffled deck has never, ever occurred before, said Virginia Postrel in a recent lecture titled "In Praise of Play" at the American Enterprise Institute.

That's because "an ordinary deck of 52 cards offers 10 to the 68th [power] possible arrangements [that's 1 followed by 68 zeros --- a really big number], which means that any order you happen to shuffle has probably never appeared before in the entire history of cards," said Postrel, who is the editor of Reason magazine.

Don't believe her? Here's one way to think about it. If 100 million card dealers each shuffled a deck of cards one million times a year for 1,000 years, they would exhaust no more than a quarter of the possibilities (10 to the 17th power) --- even if every shuffle produced a unique ordering, which is unlikely since all that shuffling would probably result in a few matches.

Still don't believe her? Start shuffling.

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The above, of course, excludes consideration of stacks or a new deck (which is a type of stack). And, it doesn't say that what you've just shuffled hasn't already occurred (i.e., a "match" of someone else's shuffle). What it does imply is that there are certain orders of a 52-card deck that may not yet have occurred. Whether that's true of not, and whether you believe this or any of the above, is another thing entirely. Still, it [u]can[/u] be something to mention at your next card presentation. That might give the fellow who says, "Let me shuffle the deck," something to ponder before asking to shuffle.
DanielSimu
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The example of the 100 million card dealers is incorrect, as it would not exhaust a quarter of the possibilities. 10 to the 17th power is not a quarter of 10 to the 68th! To get to 10 to the 68th you'd have to add another 51 zeros to the number of decks those 100 million card dealers came up with in their 1000 years of shuffeling one million times....

It is very very unlikely that a true shuffle has already occured. There is no need to "believe" the above, that there are nearly 10^68 different ways to order a deck of 52 cards is a mathematical fact.

I found this nice explanation on the internet:

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I've seen a really good explanation of how big 52! (factorial 52, which is the amount of orders a deck could be in -Daniel), actually is.
Set a timer to count down 52! seconds (that’s 8.0658*10^67 seconds)
Stand on the equator, and take a step forward every billion years
When you’ve circled the earth once, take a drop of water from the Pacific Ocean, and keep going
When the Pacific Ocean is empty, lay a sheet of paper down, refill the ocean and carry on.
When your stack of paper reaches the sun, take a look at the timer.
The 3 left-most digits won’t have changed. 8.063*10^67 seconds left to go. You have to repeat the whole process 1000 times to get 1/3 of the way through that time. 5.385×1067 seconds left to go.
So to kill that time you try something else.
Shuffle a deck of cards, deal yourself 5 cards every billion years
Each time you get a royal flush, buy a lottery ticket
Each time that ticket wins the jackpot, throw a grain of sand in the grand canyon
When the grand canyon’s full, take 1oz of rock off Mount Everest, empty the canyon and carry on.
When Everest has been leveled, check the timer.
There’s barely any change. 5.364*10^67 seconds left. You’d have to repeat this process 256 times to have run out the timer.

From reddit
Rachmaninov
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I love that ! Awesome ! I would like to use it in as a presentation frame for a coïncidence trick. Where did you find that text ? I need to check the calculations, which will be hard with all the estimations needed.
DanielSimu
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I found this on reddit Smile
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