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Intransitive Dice

by Brian Conrey, James Gabbard, Katie Grant, Andrew Liu, and Kent Morrison

Year of Award: 2017

Award: Allendoerfer

Publication Information: Mathematics Magazine, vol. 89, no. 2, April 2016, pp. 133-143.

Summary: (adapted from the MAA Prizes and Awards booklet for MAA MathFest 2017) The fundamental question asked in Intransitive Dice is: how rare is this? In other words, given a random set of dice, how likely is it that one could put them into a cycle that is intransitive? The question is a tantalizing one, and the authors deftly move from the concrete to the abstract in their search for the answer.

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About the Authors: (From the MAA MathFest 2017 MAA Prizes and Awards Booklet)

Brian Conrey is the Executive Director of the American Institute of Mathematics in San Jose, a position he has held since 1997. He has taught at the University of Illinois and Oklahoma State University. He received his B.S. from Santa Clara University and his Ph.D. from the University of Michigan. His research interests are in analytic number theory and random matrix theory.

Kent Morrison received his B.A. and Ph.D. degrees from the University of California, Santa Cruz. After thirty years on the faculty of Cal Poly, San Luis Obispo, including nine years as department chair, he is now Professor Emeritus. Since 2009 he has been affiliated with the American Institute of Mathematics, where he helps in various capacities and directs the AIM Open Textbook Initiative to encourage the development and use of open source and open access textbooks for undergraduate mathematics courses. He has found it difficult to stick to one area of mathematics but in recent years his interests have been in combinatorics, probability, and game theory, and especially in mixtures of these areas. “Intransitive Dice” is his fifth article in Mathematics Magazine and his third to have student co-authors.

James Gabbard is an undergraduate at the University of Southern California where he is majoring in mechanical engineering and applied mathematics. In his spare time he enjoys backpacking and performing with the USC marching band.

Katie Grant is pursuing a B.S. in management science and a minor in computer science at the University of California, San Diego. Her favorite classes have been Decisions Under Uncertainty, Econometrics, and Introduction to Probability. In addition to her studies she has worked in an internship with TD Ameritrade and is a registered investment advisor.

Shang-Chi Andrew Liu attends the University of California, Los Angeles, where he is majoring in political science with a double-minor in philosophy and cognitive science. In his spare time he enjoys playing tennis and exploring the city of LA with his friends.

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