Society & Culture - Posted by Beverly Clark-Emory on Thursday, December 17, 2009 13:56 - 6 Comments 
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EMORY (US)—Playing the lottery may be a good bet, but it’s almost always a bad investment.
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The text of this article by Futurity is licensed under a Creative Commons Attribution-No Derivatives License.
Using math and economic theory, Emory University mathematicians Aaron Abrams and Skip Garibaldi set out to analyze the rates of return and risks associated with lottery tickets.
“We wanted solid numbers to help explain why playing the lottery is not a good plan,” Garibaldi explains.
Their mathematical models for the interstate lottery Mega Millions and its competitor, Powerball, demonstrated that as the jackpots grow and more tickets are sold, the extra tickets nullify the benefit of the bigger jackpot. The study appears in the January edition of the American Mathematical Monthly.
Smaller, single-state lotteries like Georgia’s Fantasy 5 offered better rates of return, due to the larger ratio of jackpot size to total number of tickets sold, according to their analysis.
“To our great surprise, in some cases, single-state lotteries have had positive rates of return as high as 30 percent,” Abrams says. “That is, for these drawings a $1 ticket would give you back $1.30 on average. We didn’t expect this.”
So why not buy lottery tickets instead of stocks? Because the odds are you won’t win the lottery.
“The technical word for this is risk,” Garibaldi says. “The high rate of return is only an average for all lottery tickets for a particular drawing, and most people in that drawing will not win the jackpot.”
The two mathematicians applied modern portfolio theory, pioneered by economist Harry Markowitz, to compare the potential return and risk of a savings account, various stocks and bonds and lottery tickets.
“When we ran the analysis, the result was: don’t buy lottery tickets,” Garibaldi says. “It’s too risky. Even the enormous returns we found were not enough to counteract the enormous likelihood of not winning the lottery.”
Abrams says that people will still play the lottery, because “Most people don’t fully understand risk.”
Understanding risk goes beyond simply playing the lottery, Abrams says.
When people make decisions about how to allocate their money in an IRA, the prospectus gives the rate of return, but doesn’t attempt to quantify the risks.
“I strongly feel that mutual fund prospectuses should include the risk data,” he says. “It’s important for people to understand how they are spending their money.”
The recent collapse of the financial system illustrates the importance of driving home the fundamentals of risk, say the two mathematicians, who both teach probability theory to freshmen.
“The field of probability has developed rapidly during the past 50 years, and we have a tremendous understanding of how randomness works,” Abrams says. “But as our understanding of probability gets better, financial instruments keep growing increasingly complex.”
Emory University news: www.emory.edu/home/news/
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6 Comments
Duane
Actually, the return for lottery tickets is not completely monetary. For those not gambling-addicted, there as a certain rush that happens while waiting for the numbers to be announced. So buying one lottery ticket rewards the purchaser with that momentary anticipation while waiting to see what numbers will be drawn. It becomes a form of amusement.
S. MOHPAL
I am occasional lottery ticket buyer. I very well know chaces of hitting a jackpot is 1 in millions but spending 1$ a week is worth spending 5$ on cigerrette pack as 1$ might turn to millions but 5$ Cig pack will never.
Dan
S Mohpal – your argument is basically that buying a lottery ticket is a smarter investment than buying a pack of cigarettes. This may be true, but it doesn’t make either of them a good idea.
As usual, the economists totally, totally miss the point. Blazingly. So blazingly do they miss the point, that I find it surprising that folks are suprised when economists fail to predict any market behaviours with any accuracy beyond chance.
here i the magic key: what is the rate of return on buying a Starbucks Latte?
Did you get it yet? The answer is, of course, zero. You send a few bucks, you get nothing. nada, zip and yet, surprise of surprises, folks continue to spend huge amounts on Starbucks Lattes. Does it improve corporate productivity? No. Does it make them superhuman sex-machines that will out populate their eco-niche non-drinkers? No.
So what, pray tell, are they buying?
They are buying an experience! They are buying a bit of fun, a smooth nice taste that slips down their throat for a few minutes in a quiet exotic environment populated, often, with interesting people who discuss nothing profitable (usually) but it is fun, it is a ‘break’ and people line up to get in on the game.
Why then are lottery ticket sales suprising to economists? People do not buy tickets to invest in a portfolio! People buy tickets for that ride, that thrill of thinking that the impossible might happen, that dreams could come true, that a magic genie might grant their every wish. They know full well that even if they win there would be such a parade of sharks at their door they’d be lucky to escape with a dinner out and taxi fare, but it is the dream they are buying.
And for what, five bucks? sometimes ten? Ten dollars for a dream that may last a week (until draw time) or just until the last box is scratched, but that’s ten dollars for a trip to shangri la and that’s not a bad investment, I say. Fold into this the knowledge that the money you are spending on this thrill-ride is probably government controlled to constrain the profits into social charity causes, and I’d say that the Lottery Game is very, very very sensible economics.
Oh, but wait a sec! Back to Starbucks, back to that $0.03 worth of dilute coffee-bean diffusion with $0.10 of milked warmed in Italian by a minimum wage undergrad, let us not forget that while perhaps the material worth of our purchase may be (intentionally) minimal, as any good modern corp knows, there is good business plan sense in re-investing that obscene markup into societal worth which is, of course, exactly what we see in the Starbucks Love Project.
At Chrismas I give friends lottery tickets. For some reason they appreciate this more than anything else even when I explain they probably are not going to get anything. The field of probability and the field of rationality are at odds.