What does it mean to shuffle a deck? Here are some of the slides I made for my @MathforAmerica talk at #MfAThursdayThinks last night. We did a simple example with a 3 card deck. (Thread) 
A state specifies what I know about the ordering (configuration) of a deck. (If you wish: a probability distribution on configurations of a deck.) 2/
A shuffle will move a deck from state to state. We did an example with a random-to-top shuffle, which picks a card at random (with equal probability) and moves it to the top of a deck. 3/
If you shuffle again, the probabilities mix again: 4/
Shuffling more mixes the deck more… approaching a random deck! This was a simple shuffle—the riffle shuffle is more complex (and I spoke about that as well)—but it gives you a sense of how we begin to understanding shuffling mathematically. (end)
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