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Finding Good Bets in the Lottery, and Why You Shouldn't Take Them

Award: Lester R. Ford

Year of Award: 2011

Publication Information: The American Mathematical Monthly, vol. 117, no. 1, January 2010, pp. 3-26.

Summary

Lottery operators make money - lots of it apparently - so on average, players must lose money. But do the operators make money on every single drawing? What happens with rolling jackpots, where winnings can reach staggering amounts (rolling jackpots are those games in which prize money is rolled over from one game to the next when no one wins the jackpot)? Does there come a time when playing such a lottery makes a good bet? If so, when is that? And does that make these drawings a good investment?


After constructing a model of a rolling jackpot lottery, the authors of this paper consider these questions. They develop an analysis of rate of return, from which they draw some surprising conclusions regarding bets. Two outstanding features of this work are the incorporation of concrete lotteries as examples and the mathematics (mostly elementary calculus) and statistics used. They do not end their analysis at bets, however, they explore the less familiar (to most readers) territory of investments. This necessitates considering risk, so economics and subsequently linear algebra get involved. This supports their ultimately unsurprising conclusion, namely that lotteries will almost never be good investments.

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About the Authors: (From the Prizes and Awards booklet, MathFest 2011)

Aaron Abrams was born in Winnipeg, Manitoba, and has been moving to successively warmer and warmer climates ever since. After growing up in Ohio, he made his way to California and earned mathematics degrees from UC Davis (undergraduate) and UC Berkeley (Ph.D.). Then, following postdoctoral positions at MSRI and the University of Georgia, he joined the faculty of Emory University, where he is an Assistant Professor. Where will he go next?

Aaron's mathematical interests span many fields, and he has published papers in the areas of topology, geometry, group theory, combinatorics, and probability. He especially enjoys collaborating with other mathematicians. In his spare time he plays and coaches Ultimate. He once won $18 in the lottery, without even playing.

Skip Garibaldi grew up in Fairfield, California. He dropped out of high school to attend Purdue University, where he earned a B.S. in mathematics and in computer science in 1992. After that, he studied at UC San Diego (Ph.D. 1998), held postdoctoral positions at the Swiss Federal Institute of Technology in Zurich and at UCLA, and held visiting positions at Université d'Artois and Université Paris-Nord in France. He is currently associate professor at Emory University. He received a Winship Professorship in 2009 and has been the speaker at two MAA State Dinners. While his research is primarily in algebra, he has also worked on applications of mathematics, such as making money.

MSC Codes: 
60-XX
Author(s): 
Aaron Abrams (Emory University) and Skip Garibaldi (Emory University)
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Publication Date: 
Sunday, August 21, 2011
Publish Page: 
Summary: 

Lottery operators make money - lots of it apparently - so on average, players must lose money. But do the operators make money on every single drawing? What happens with rolling jackpots, where winnings can reach staggering amounts (rolling jackpots are those games in which prize money is rolled over from one game to the next when no one wins the jackpot)? Does there come a time when playing such a lottery makes a good bet? If so, when is that? And does that make these drawings a good investment?

After constructing a model of a rolling jackpot lottery, the authors of this paper consider these questions. They develop an analysis of rate of return, from which they draw some surprising conclusions regarding bets. Two outstanding features of this work are the incorporation of concrete lotteries as examples and the mathematics (mostly elementary calculus) and statistics used. They do not end their analysis at bets, however, they explore the less familiar (to most readers) territory of investments. This necessitates considering risk, so economics and subsequently linear algebra get involved. This supports their ultimately unsurprising conclusion, namely that lotteries will almost never be good investments.

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