Magician Turned Professor Talks About the Math Behind Shuffling Cards

An anonymous reader writes with this story about magician and professor of mathematics and statistics at Stanford University Persi Diaconis. "Now a professor of mathematics and statistics at Stanford University, Diaconis has employed his intuition about cards, which he calls 'the poetry of magic,' in a wide range of settings. Once, for example, he helped decode messages passed between inmates at a California state prison by using small random 'shuffles' to gradually improve a decryption key. He has also analyzed Bose-Einstein condensation — in which a collection of ultra-cold atoms coalesces into a single 'superatom' — by envisioning the atoms as rows of cards moving around. This makes them 'friendly,' said Diaconis, whose speech still carries the inflections of his native New York City. 'We all have our own basic images that we translate things into, and for me cards were where I started.' In 1992, Diaconis famously proved — along with the mathematician Dave Bayer of Columbia University — that it takes about seven ordinary riffle shuffles to randomize a deck. Over the years, Diaconis and his students and colleagues have successfully analyzed the effectiveness of almost every type of shuffle people use in ordinary life."

Comments

Numberphile interviews

[myrrdyn]

Brady Haran on Numberphile has a series of interviews with Persi Diaconis: https://www.youtube.com/playli...

Perfect shuffle

[Anonymous Coward]

If you do 13 perfect shuffles (deck cut in exactly half, one card from each half going on top of the other), you will end up with the same deck. So it's not surprising that 7 "shuffles" would maximize entropy, by how they are measuring it (where does the top card end up, are there adjacent cards still "stuck"). You do end up with interesting pattern on a perfect shuffle using a sorted deck.

--sf