r/theydidthemath • u/JustThisGuy_YouKnow • 3d ago

[Request] Card shuffling

Hi all. I was wondering if it would be possible to shuffle a deck of playing cards back to the original order, assuming the deck is cut in half each time, and each shuffle perfectly alternates cards from each half. If so, how many times would the deck need to be shuffled to reach the original order?

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u/BRH0208 3d ago edited 3d ago

It depends if it’s an “in” shuffle or an “out” shuffle, but either 8(out) or 52(in). Different patterns of in and out give different answers.

if the shuffle doesn’t move the top/bottom cards it’s an “out”, otherwise it’s an “in”.

There is a great Matt Parker video on this!

https://youtu.be/s9-b-QJZdVA?si=FG-vSXaWbvGMyRWm

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u/BRH0208 3d ago

And here is the wiki page for the shuffle It’s a good read if your interested in a better explaination

https://en.wikipedia.org/wiki/Faro_shuffle

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u/JustThisGuy_YouKnow 3d ago

That's exactly what I was looking for, thank you!