Malintent
Veteran Member
It has been said that if you shuffle a deck of cards, the resulting arrangement of 52 cards will be unique... in that the odds are extremely high that never in the history of card-shuffling has that particular arrangement of cards ever existed. I thought that was pretty cool, so I looked more into it.
52 factorial, noted as "52!", represents the odds of there being a particular arrangement of 52 randomly ordered items. i.e. (52 x 51 x 50 x 49... x 2 x 1) = 52!
This is a large number. "How large?" is the focus of this.
52! is approximately equal to 8.066x10^67
The Universe is approximately 4.4x10^17 SECONDS old.
If you were to start arranging cards at a rate of 1 deck per second (you are a very fast shuffler) starting at the Big Bang, by now you will have not even scratched the surface of the number of possible arrangements of a deck of cards. This is how we know that is it incredibly unlikely that a deck of shuffled cards has ever been seen before.
So how long IS 52! seconds, to put it into perspective?
Try this experiment, if you have the time:
Pick a spot on Earth's equator.
Start a timer that counts the seconds to 52!
Stand in that spot for 1 BILLION YEARS
After 1 billion years, take a single step East
Wait another 1 billion years, and take another step...
After you have walked all of the way around the world, take 1 drop of water out of the pacific ocean and discard it (*poof*)
Repeat this process of taking 1 step every 1 billion years and removing a drop of water after each complete trip around the world.
Once you have completely drained the Pacific ocean, take a sheet of paper and place it on the ground.
Now, the ocean is magically refilled, so you can repeat all of the steps above, placing another piece of paper on top of the previous one after completely draining the pacific one drop at a time as you make it around the world again (1 step per 1 billion years).
Once you have stacked up enough sheets of paper to reach THE SUN, do you think you will have run out of time?
Nope. At this point, you are not quite 5% there. Repeat all of those steps from the very beginning approximately 250 more times, and you will then have lived long enough to have created every possible arrangement of cards, as long as you arranged them non-stop 1 time every second.
Large numbers are... really large.
52 factorial, noted as "52!", represents the odds of there being a particular arrangement of 52 randomly ordered items. i.e. (52 x 51 x 50 x 49... x 2 x 1) = 52!
This is a large number. "How large?" is the focus of this.
52! is approximately equal to 8.066x10^67
The Universe is approximately 4.4x10^17 SECONDS old.
If you were to start arranging cards at a rate of 1 deck per second (you are a very fast shuffler) starting at the Big Bang, by now you will have not even scratched the surface of the number of possible arrangements of a deck of cards. This is how we know that is it incredibly unlikely that a deck of shuffled cards has ever been seen before.
So how long IS 52! seconds, to put it into perspective?
Try this experiment, if you have the time:
Pick a spot on Earth's equator.
Start a timer that counts the seconds to 52!
Stand in that spot for 1 BILLION YEARS
After 1 billion years, take a single step East
Wait another 1 billion years, and take another step...
After you have walked all of the way around the world, take 1 drop of water out of the pacific ocean and discard it (*poof*)
Repeat this process of taking 1 step every 1 billion years and removing a drop of water after each complete trip around the world.
Once you have completely drained the Pacific ocean, take a sheet of paper and place it on the ground.
Now, the ocean is magically refilled, so you can repeat all of the steps above, placing another piece of paper on top of the previous one after completely draining the pacific one drop at a time as you make it around the world again (1 step per 1 billion years).
Once you have stacked up enough sheets of paper to reach THE SUN, do you think you will have run out of time?
Nope. At this point, you are not quite 5% there. Repeat all of those steps from the very beginning approximately 250 more times, and you will then have lived long enough to have created every possible arrangement of cards, as long as you arranged them non-stop 1 time every second.
Large numbers are... really large.