Department of Mathematics

Address: Mathematics 253-37 | Caltech | Pasadena, CA 91125
Telephone: (626) 395-4335 | Fax: (626) 585-1728


Annual Charles R. DePrima Memorial
Undergraduate Mathematics Lecture


Tuesday, January 22, 2002
4:15 p.m.  22 Gates

The Mathematics of Perfect Shuffles
by Persi Diaconis
(Stanford)

Abstract: There are two ways to perfectly shuffle a deck of cards. Magicians and gamblers have carefully studied these. Mathematicians can add to the mix, and in joint work with Bill Kantor and Ron Graham, we have determined exactly what can (and cannot) be done. Applications to parallel processing, statistical physics and magic tricks will be presented.

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Persi Diaconis is a Professor of Mathematics and the Mary V. Sunseri Professor of Statistics at Stanford University. Prior to following an academic path, Dr. Diaconis had run away from home at age fourteen to work as a magician. He started out as a magician’s assistant to Dai Vernon, the founder of the Magic Castle, and later worked on his own as a professional magician.

A MacArthur Foundation Fellow, Dr. Diaconis works in probability and statistics, including asymptotic theory of Bayes estimates, finite de Finetti theorems, Markov Chain Monte Carlo, rates of convergence in the ergodic theorem for Markov chains, the statistics of vision, spectral analysis for ranked data, random matrix theory, applications of group theory in statistics, as well as the mathematics of card shuffling and the study of coincidences.

His background in magic linked with his advanced degrees in mathematics and statistics has given him an edge in debunking psychics and parapsychology. A magician is an expert in the subtle art of sleight of hand and deception, the same abilities that mark psychics. It takes a magician to spot another magician (or psychic), and Dr. Diaconis has found every psychic he has observed was either cheating or simply failed to perform.

As an expert on the mathematics of card shuffling and the perfect shuffle, Dr. Diaconis will give the Tenth DePrima Lecture, "The Mathematics of Perfect Shuffles." To shuffle a deck of cards perfectly, the deck is divided exactly in half and then interleaved so that the cards from the left-hand half of the deck end up in strict alternation with cards from the right-hand half; that is, every other card comes from one side. Dr. Diaconis derived a mathematical proof demonstrating that if a deck is perfectly shuffled eight times (emphasis on perfectly), the cards will be in the same order as they were before the shuffle. The two ways of perfectly shuffling have, respectively, ABABABAB... and BABABABA... configurations, where A = from the top twenty-six of the deck and B = from the bottom twenty-six. In addition to discussing perfect shuffles, the lecture will demonstrate applications to parallel processing and statistical physics.

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The Charles R. DePrima Memorial Undergraduate Mathematics Lecture was established by a gift from Charles R. DePrima and Margaret Thurmond DePrima. The Institute is privileged to honor the memory of Professor DePrima and his distinguished contribution to mathematics and Caltech, where he served as a faculty member for over forty years, with a lecture each year by an outstanding mathematician.