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Chutes and Ladders for the Impatient

Award: George Pólya

Year of Award: 2012

Publication Information: College Mathematics Journal, vol. 42, no. 1, January 2011, pp. 2-8.

Summary (From the MathFest 2012 Prizes and Awards Booklet)

After providing a brief review of the game, the authors extend a Markov chain model that uses the "official" \(1\)-to-\(6\) spinner to one that uses an arbitrary spinner labeled \(1\) to \(n\) in order to understand the relation between spinner range and the expected number of turns for the game. They discover that a spinner with range \(1\) to \(15\) will provide the impatient player with the shortest game on average (with an expected length of \(25.81\) turns). Readers are invited to consider additional variations on their own, and to model other childhood board games, aided by modifiable Maple code provided by the authors.

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About the Authors (From the MathFest 2012 Prizes and Awards Booklet)

Leslie A. Cheteyan received her B.S. in mathematics from Montclair State University in 2008, followed by her M.S. in 2011. From an early age she has had a love for math and its implications. Besides math, Leslie enjoys playing all types of sports, though basketball is her favorite. Her competitive nature helps to fuel her motivation in different areas of mathematics. She now works at Memorial Sloan-Kettering Cancer Center in New York as a research assistant.

Stewart Hengeveld received his B.S. in mathematics from Montclair State University in 2008 and his M.S. in 2012. He has enjoyed spending the last seven years as a mathematics and physics tutor at Bergen Community College, and the last four years as an adjunct professor there. During his time at Montclair, he worked as a fellow in the NSF sponsored GK-12 program. In his spare time, he enjoys astrophotography and playing games of all sorts. He now works for Blue Cross Blue Shield in New Jersey. Per aspera ad astra.

Michael A. Jones just completed his fourth year as an Associate Editor at Mathematical Reviews in Ann Arbor. Previously he held faculty positions at the U.S. Military Academy at West Point, Loyola University (Chicago), and Montclair State University. He is a graduate of Santa Clara University (B.S., 1989) and Northwestern University (Ph.D. in game theory, 1994). He likes the challenge of examining everyday observations through a mathematical lens and, when appropriate, writing about them. After eight years of living next to a piano teacher in New Jersey, he finally started taking lessons last year.

MSC Codes: 
60Gxx
Author(s): 
Leslie A. Cheteyan (Memorial Sloan-Kettering Cancer Center) and Stewart Hengeveld (Blue Cross Blue Shield in New Jersey) and Michael A. Jones (Mathematical Reviews)
Flag for Digital Object Identifier: 
Publication Date: 
Wednesday, August 8, 2012
Publish Page: 
Summary: 
After providing a brief review of the game, Cheteyan, Hengeveld, and Jones extend a Markov chain model that uses the "official" \(1\)-to-\(6\) spinner to one that uses an arbitrary spinner labeled \(1\) to \(n\) in order to understand the relation between spinner range and the expected number of turns for the game. They discover that a spinner with range \(1\) to \(15\) will provide the impatient player with the shortest game on average (with an expected length of \(25.81\) turns). Readers are invited to consider additional variations on their own, and to model other childhood board games, aided by modifiable Maple code provided by the authors.

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