Persi Diaconis
Diaconis in 2010
Born (1945-01-31) January 31, 1945 (age 79)
New York City, US
EducationCity College of New York (BS)
Harvard University (MA, PhD)
Known forFreedman–Diaconis rule
SpouseSusan Holmes
Scientific career
FieldsMathematical statistics
InstitutionsHarvard University
Stanford University
Doctoral advisorDennis Arnold Hejhal
Frederick Mosteller[1]
Doctoral students

Persi Warren Diaconis (/ˌdəˈknɪs/; born January 31, 1945) is an American mathematician of Greek descent and former professional magician.[2][3] He is the Mary V. Sunseri Professor of Statistics and Mathematics at Stanford University.[4][5]

He is particularly known for tackling mathematical problems involving randomness and randomization, such as coin flipping and shuffling playing cards.


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]

According to Martin Gardner, at school, Diaconis supported himself by playing poker on ships between New York and South America. Gardner recalls that Diaconis had "fantastic second deal and bottom deal".[9]

Diaconis is married to Stanford statistics professor Susan Holmes.[10]


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:

His other publications include:

See also


  1. ^ Persi Diaconis at the Mathematics Genealogy Project
  2. ^ Hoffman, J. (2011). "Q&A: The mathemagician". Nature. 478 (7370): 457. Bibcode:2011Natur.478..457H. doi:10.1038/478457a.
  3. ^ Diaconis, Persi; Graham, Ron (2011), Magical Mathematics: The Mathematical Ideas that Animate Great Magic Tricks, Princeton, N.J: Princeton University Press, ISBN 0-691-15164-4
  4. ^ "Stanford University - Persi Diaconis". Retrieved 2011-10-27.
  5. ^ "It's no coincidence: Stanford University mathematician and statistician Persi Diaconis will serve as a Patten Lecturer at Indiana University Bloomington". Archived from the original on 2011-11-10. Retrieved 2011-10-27.
  6. ^ Lifelong debunker takes on arbiter of neutral choices
  7. ^ 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."
  8. ^ Jeffrey R. Young, "The Magical Mind of Persi Diaconis" Chronicle of Higher Education October 16, 2011 [1]
  9. ^ Interview with Martin Gardner, Notices of the AMS, June/July 2005.
  10. ^ O'Conner, J. J.; Robertson, E. F. "Diaconis biography". MacTutor. Retrieved 2 April 2018.
  11. ^ Bayer, Dave; Diaconis, Persi (1992). "Trailing the Dovetail Shuffle to its Lair". The Annals of Applied Probability. 2 (2): 295–313. doi:10.1214/aoap/1177005705.
  12. ^ Trefethen, L. N.; Trefethen, L. M. (2000). "How many shuffles to randomize a deck of cards?". Proceedings of the Royal Society of London A. 456 (2002): 2561–2568. Bibcode:2000RSPSA.456.2561T. doi:10.1098/rspa.2000.0625. S2CID 14055379.
  13. ^ "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
  14. ^ 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. S2CID 16661322.
  15. ^ Keating, Shane. How a magician-mathematician revealed a casino loophole, BBC, 20 October 2022.
  16. ^ Diaconis, Persi (1990). "Applications of group representations to statistical problems". Proceedings of the ICM, Kyoto, Japan. pp. 1037–1048.
  17. ^ Diaconis, Persi (2003). "Patterns in eigenvalues: the 70th Josiah Willard Gibbs lecture". Bull. Amer. Math. Soc. (N.S.). 40 (2): 155–178. doi:10.1090/s0273-0979-03-00975-3. MR 1962294.
  18. ^ Diaconis, Persi (1998). "From shuffling cards to walking around the building: An introduction to modern Markov chain theory". Doc. Math. (Bielefeld) Extra Vol. ICM Berlin, 1998, vol. I. pp. 187–204.
  19. ^ Salsburg, David (2001). The lady tasting tea: how statistics revolutionized science in the twentieth century. New York: W.H. Freeman and CO. ISBN 0-8050-7134-2.. Cf. p.224
  20. ^ "APS Member History". Retrieved 2021-05-25.
  21. ^ Kehoe, Elaine (2012). "2012 Conant Prize". Notices of the American Mathematical Society. 59 (4): 1. doi:10.1090/noti824. ISSN 0002-9920.
  22. ^ List of Fellows of the American Mathematical Society, retrieved 2012-11-10
  23. ^ "Graduation ceremony | 600th Anniversary | University of St Andrews - 1413-2013". Archived from the original on 2014-04-07. Retrieved 2014-04-05.
  24. ^ Review of Group Representations In Probability And Statistics:
    • Bougerol, Philippe (1990), Mathematical Reviews, MR 0964069((citation)): CS1 maint: untitled periodical (link)
  25. ^ Reviews of Magical Mathematics:
  26. ^ Peterson, Ivars (December 12, 2012), Magical Mathematics And Topological Barcodes, Mathematical Association of America
  27. ^ Reviews of Ten Great Ideas about Chance: