Diaconis left home at 14[6] to travel with sleight-of-hand legend Dai Vernon, and was awarded a high school diploma based on grades given to him by his teachers after dropping out of George Washington High School.[7] He returned to school at age 24 to learn math, motivated to read William Feller's famous two-volume treatise on probability theory, An Introduction to Probability Theory and Its Applications. He attended the City College of New York for his undergraduate work, graduating in 1971, and then obtained a Ph.D. in Mathematical Statistics from Harvard University in 1974, learned to read Feller, and became a mathematical probabilist.[8]
Diaconis received a MacArthur Fellowship in 1982. In 1990, he published (with Dave Bayer) a paper entitled "Trailing the Dovetail Shuffle to Its Lair"[11] (a term coined by magician Charles Jordan in the early 1900s) which established rigorous results on how many times a deck of playing cards must be riffle shuffled before it can be considered random according to the mathematical measure total variation distance. Diaconis is often cited for the simplified proposition that it takes seven shuffles to randomize a deck. More precisely, Diaconis showed that, in the Gilbert–Shannon–Reeds model of how likely it is that a riffle results in a particular riffle shuffle permutation, it takes 5 riffles before the total variation distance of a 52-card deck begins to drop significantly from the maximum value of 1.0, and 7 riffles before it drops below 0.5 very quickly (a threshold phenomenon), after which it is reduced by a factor of 2 every shuffle. When entropy is viewed as the probabilistic distance, riffle shuffling seems to take less time to mix, and the threshold phenomenon goes away (because the entropy function is subadditive).[12]
Diaconis has coauthored several more recent papers expanding on his 1992 results and relating the problem of shuffling cards to other problems in mathematics. Among other things, they showed that the separation distance of an ordered blackjack deck (that is, aces on top, followed by 2's, followed by 3's, etc.) drops below .5 after 7 shuffles. Separation distance is an upper bound for variation distance.[13][14]
Diaconis has been hired by casino executives to search for subtle flaws in their automatic card shuffling machines. Diaconis soon found some and the horrified executives responded, "We are not pleased with your conclusions but we believe them and that's what we hired you for."[15]
He served on the Mathematical Sciences jury of the Infosys Prize in 2011 and 2012.
The books written or coauthored by Diaconis include:
Group Representations In Probability And Statistics (Institute of Mathematical Statistics, 1988)[24]
Magical Mathematics: The Mathematical Ideas That Animate Great Magic Tricks (with Ronald L. Graham, Princeton University Press, 2012),[25] winner of the 2013 Euler Book Prize[26]
Ten Great Ideas about Chance (with Brian Skyrms, Princeton University Press, 2018)[27]
^Amason, Cassidy. "Deterministic And Probabilistic Approaches To Card Shuffling", Georgia College & State University, November 30, 2016. Accessed February 14, 2023. "Diaconis attended George Washington High School in NYC and found himself at home as a member of the magic club.... Regardless of not being in high school, Diaconis’ teachers decided to give him grades for exams he had not taken - and he ended up graduating high school."
^Jeffrey R. Young, "The Magical Mind of Persi Diaconis" Chronicle of Higher Education October 16, 2011 [1]
^"Shuffling the cards: Math does the trick". Science News. November 7, 2008. Retrieved 14 November 2008. Diaconis and his colleagues are issuing an update. When dealing many gambling games, like blackjack, about four shuffles are enough
^Assaf, S.; Diaconis, P.; Soundararajan, K. (2011). "A rule of thumb for riffle shuffling". The Annals of Applied Probability. 21 (3): 843. arXiv:0908.3462. doi:10.1214/10-AAP701. S2CID16661322.
Watkins, John J. (2012), Mathematical Reviews, MR2858033{{citation}}: CS1 maint: untitled periodical (link)
Van Osdol, Donovan H. (2012), Notices of the American Mathematical Society, 59 (7): 960–961, doi:10.1090/noti875, MR2984988{{citation}}: CS1 maint: untitled periodical (link)
