Abstract: I will study some of the most popular ways of shuffling cards; riffle shuffles, overhand shuffles and 'smushing". For each, sharp mathematical analysis is available. These have some surprises. For example, about seven ordinary riffle shuffles are necessary and suffice to mix up 52 cards, but it takes about 10,000 overhand shuffles (even though the two schemes have the 'same amount of randomness'/ shuffle). Analysis of 'smushing' needs different kinds of more continuous mathematics. A second theme of the lecture is to introduce the tool of 'coupling'. This has been developed in the probability community and seems unknown in the rest of mathematics. It's broadly useful (working for all three shuffles and Markov chains quite generally). I will try to explain all this 'in English' to a general mathematical audience.