When I was learning how to play Blackjack the "right" way, I often came across the name of Persi Diaconis in the books I was reading. The first few times I saw that name, I wasn't sure why he kept being cited as an authority but I eventually learned, he was the world's greatest expert on card shuffling. He's a magician-mathematician who, among other accomplishments, determined the number of shuffles it takes before a deck of cards is thoroughly randomized. If you shuffle cards the way most people do, that number is eight.
Roger Green sent me this link to an article about Mr. Diaconis and his amazing work. Thanks, Roger.