In one of Vsauce's videos he suggested a good visualisation of the number of unique shuffles of a deck of cards that was originally suggested by Scott Czepiel.

Imagine you have a friend that is shuffling a deck of cards and ordering the deck uniquely every second. Also imagine that every action you take is completed instantaneously.

You stand on the equator. Wait a billion years. Then take a step. Wait another billion years. Then take another step. Continue this until you have got back to where you started.

Then take 0.02ml from the Pacific Ocean. Wait another billion years. Then take a step. Continue until you get back to where you started and take another drop out of the Pacific Ocean.

Repeat this process until the entire Pacific Ocean is empty. Then place a sheet of paper on the ground at sea level.

Refill the ocean and repeat - wait a billion years between steps as you walk around the equator, take a drop of water out of the Pacific Ocean every time you get back to where you started and place a piece of paper on the ground in a tower before refilling the Pacific Ocean and repeating.

When the tower of paper reaches the sun do you think that your friend has managed to produce each, unique ordering of the cards?

Nope! Not even close...

If you were to repeat all of the above 3000 times, then he'd be pretty much done.

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