
Address: Mathematics 25337
 Caltech  Pasadena, CA 91125
Telephone: (626) 3954335  Fax: (626) 5851728
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.
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 lefthand half of the deck end up in strict
alternation with cards from the righthand 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 twentysix of the deck
and B = from the bottom twentysix. In addition to discussing perfect shuffles, the
lecture will demonstrate applications to parallel processing and statistical physics.
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.
