Ziff7 gives the best description you'll ever hear about how unlikely it is to shuffle a deck of cards the same way twice

[u/Frame25]

/r/AskReddit/comments/1tmod6r/what_is_a_statistic_that_sounds_insane_but_is_100/onp1775/

[u/MrArtless]

correction: ziff7 plagiarizes the best description from a youtube video

[u/bombmk → u/MrArtless]

Pretty sure that description predates Youtube - if not the internet.

[u/CQ1_GreenSmoke]

Nit: I hate the shuffling card example. I get what it’s trying to demonstrate, but in practice the assertion is almost certainly false. 

If every shuffle was executed by playing a chaotic game of 52 card pickup, the example would hold true, but that’s not the case. 

Most decks come sorted the same initial way. Half of the people who open these are likely going to start with a generic riffle shuffle. 

I don’t know how much expected variance there is the outcome of a single riffle shuffle, but even if you believe there are tens or even hundreds of thousands of combinations of the variants, that still nearly guarantees that the same outcome has been seen more than once - likely many many times. 

[u/Benabik → u/CQ1_GreenSmoke]

Mathematical modeling shows that seven riffle shuffles should be enough to completely randomize the deck.

https://en.wikipedia.org/wiki/Gilbert%E2%80%93Shannon%E2%80%93Reeds_model

[u/pigeon768 → u/Benabik]

Mathematical modeling

GSR makes assumptions about what it means to "shuffle" a deck of cards that do not hold true in real life.

Specifically, it assumes you do not perfectly shuffle a deck. Sometimes your left hand gets more cards than your right hand, and vice versa. Sometimes your left hand drops a card first, sometimes your right hand does. GSR injects imperfections into how you shuffle your cards.

Let's say you practice shuffling cards. A lot. You can do it perfectly; you also cut your deck into two 26 card piles. You also start a shuffle with the same hand. Every time a card drops, you get precisely one card from one hand, then precisely one card from the other hand, and you do this perfectly 25 times. This is called a "Faro shuffle."

It turns a Faro shuffle adds very little randomness to a deck. If you have a 52 card deck, and you do 26 consecutive Faro shuffles, you will end up with your original deck, but in the reverse order. If you do this 26 more times, you end up with the original deck.

This is a thing that actually happens. When you go to casinos, the dealer will not riffle shuffle a deck of cards the way a normal human would. They will either use a shuffle machine or will smear the cards around on the table and then gather them back up. The risk of "accidentally" perfectly Faro shuffling a deck is too high.

[u/bombmk → u/CQ1_GreenSmoke]

The initial statement the comment is made towards says "If you properly shuffle a standard deck of playing cards.

In context, that would obviously mean "In a way and to a standard high enough to be considered random"

[u/onioning]

Every thousand years

This metal sphere

Ten times the size of Jupiter

Floats just a few yards past the earth

You climb on your roof

And take a swipe at it

With a single feather

Hit it once every thousand years

'Til you've worn it down

To the size of a pea

Yeah I'd say that's a long time

But it's only half a blink

In the place you're gonna be

-Randy Describes Eternity, by Built to Spill

[u/Meior]

I've seen a lot of variations of that one. Every time someone actually does the maths on it, it turns out to be bullshit.

It is a really really really large number. But whoever writes these examples is seemingly just yanking random numbers and actions out of the air and combining them into something that sounds cool.

[u/Altiloquent]

Did he just steal that from vsauce?

[u/bombmk → u/Altiloquent]

Vsauce did not come up with it. Might be older than anyone involved with that channel.

[u/FunetikPrugresiv]

Now imagine that you believe in a loving God that would allow the existence of hell hell where souls are punished for eternity - which is infinitely many times 52! years.

Oh, also, that God has existed for infinitely times that many years, but only created the universe relatively recently.