Persi Warren Diaconis (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.

Card shuffling

See also: Shuffling

Professor Diaconis received a MacArthur Fellowship in 1982. In 1992 he published (with Dave Bayer) a paper entitled "Trailing the Dovetail Shuffle to Its Lair"[6] (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. Interestingly, 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.).[7]

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.[8][9]


Diaconis left home at 14[10] to travel with sleight-of-hand legend Dai Vernon, and dropped out of high school, promising himself that he would return one day so that he could learn all of the math necessary to read William Feller's famous two-volume treatise on probability theory, An Introduction to Probability Theory and Its Applications. He returned to school (City College of New York for his undergraduate work graduating in 1971 and then a Ph.D. in Mathematical Statistics from Harvard University in 1974), learned to read Feller, and became a mathematical probabilist.[11]

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".[12]

Diaconis is married to Stanford statistics professor Susan Holmes.



  • Diaconis, Persi (1988). Group representations in probability and statistics. Institute of Mathematical Statistics. ISBN 0-940600-14-5. 
  • "Theories of data analysis: from magical thinking through classical statistics", in Hoaglin, D.C (eds) (1985). Exploring Data Tables Trends and Shapes. Wiley. ISBN 0-471-09776-4. 
  • Diaconis, P. (1978). "Statistical problems in ESP research". Science 201 (4351): 131–136. doi:10.1126/science.663642. PMID 663642. 


  1. ^ Persi Diaconis at the Mathematics Genealogy Project
  2. ^ Hoffman, J. (2011). "Q&A: The mathemagician". Nature 478 (7370): 457. 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". Retrieved 2011-10-27. 
  6. ^ 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. 
  7. ^ Trefethen, L. N.; Trefethen, L. M. (2000). "How many shuffles to randomize a deck of cards?". Proceedings of the Royal Society, Series A: Mathematical, Physical and Engineering Sciences 456 (2002): 2561–2568. Bibcode:2000RSPSA.456.2561N. doi:10.1098/rspa.2000.0625. 
  8. ^ "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 
  9. ^ Assaf, S.; Diaconis, P.; Soundararajan, K. (2011). "A rule of thumb for riffle shuffling". The Annals of Applied Probability 21 (3): 843. doi:10.1214/10-AAP701. 
  10. ^ Lifelong debunker takes on arbiter of neutral choices
  11. ^ Jeffrey R. Young, "The Magical Mind of Persi Diaconis" Chronicle of Higher Education October 16, 2011 [1]
  12. ^ Interview with Martin Gardner, Notices of the AMS, June/July 2005.
  13. ^ 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. 
  14. ^ 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
  15. ^
  16. ^ List of Fellows of the American Mathematical Society, retrieved 2012-11-10.
  17. ^