The Best (and Worst) Ways to Shuffle Cards - Numberphile

[Dieter]

You will see dealers who shuffle near perfectly, interlacing most every card,

A perfect riffle is a bad shuffle.

I have never seen a random shuffle, ever. I have seen some effective shuffles.

The purpose of a shuffle is not to randomize the deck. The purpose of the shuffle is to reorder the deck, ideally in an unpredictable* way.

If you paid attention to what Diaconis said, 7 riffles is not the pinnacle of randomness in reordering the deck. It is the lower threshold of reasonably unpredictable reordering of a 52 card deck, based on the top & bottom cards moving to other positions in the deck.

The summary of the video should be: "When shuffling cards, if all you can do is riffle, do it at least 7 times." They didn't touch on what happens when you add other operations into the shuffle (hint: they help a lot, when combined with riffles).

*Now if you're going to go and say that unpredictable is random, maybe - but there's a lower threshold for "I'm pretty uncertain about what the next 3 cards are" vs "enough reordering has occurred such that every possible permutation is equally likely".