I'm much better at card shuffling than math, but really enjoyed this piece about mathematicians tackling the problem of when a shuffled deck becomes truly disordered.

Seven Perfect Shuffles Randomize a Deck of Cards. But How Many Sloppy Ones? | Quanta Magazine
A decades-old proof showed that seven shuffles are enough to mix up a deck of cards. But it requires you to cut the deck with the precision of a professional magician. A new proof gets around that obstacle.
quantamagazine.org