The Best and worst ways to shuffle cards, according to math.

[Bryce Robinson]

A good watch on the different styles of card shuffling and how many times you need to do it to make the card order random.

https://www.youtube.com/watch?v=AxJubaijQbI&feature=youtu.be

[silent_rob]

Great video - I'm really becoming a fan of the Numberphile channel.

And it actually brought me back to my days of working in a magician's supply store as a kid. Specifically what reminded me of that is how he mentioned that doing 7 riffle shuffles will sufficiently shuffle a deck.

In magic there's a shuffle called the "Faro Shuffle." A Faro Shuffle is similar to a riffle shuffle but not quite. If you do a perfect Faro Shuffle you're dividing the deck into two equal piles and then when they're shuffled together you're alternating them perfectly so every card in one side alternates with the next card in the other side, perfectly "mixing" the deck. That's really difficult to do (especially the two-equal-piles part) so most magicians can't make a Faro Shuffle look like a riffle shuffle. They have to shuffle it in a way that would seem a little strange to get that effect. It'll still look like you're just shuffling the deck but another magician would catch it.

Anyway, the reason I bring up the Faro Shuffle is because if you do a certain number of perfect Faro Shuffles in a row, you'll restore the deck of cards back to its original order. How many perfect Faro Shuffles do you have to do in a row to do that? 8 of them.   

So there's a fine line between a deck of cards being "sufficiently mixed" and being back to where it started. 

Here's a Wikipedia article on the Faro Shuffle: Faro Shuffle

[Tempest]

I will now always do the 7x riffle shuffle.