## Monday, December 14, 2009

### Lottery study zeros in on risk

Most people know they are not going to get rich playing the lottery. But if you just want to buy some tickets for fun, can you improve your odds? Is a bigger jackpot a better bet? How big is big enough?

When lottery prizes climb into hundreds of millions of dollars, these are the kinds of questions Emory mathematicians Aaron Abrams (above, right) and Skip Garibaldi (above, left) get from their students. The pair decided to conduct an analysis, applying math and economic theory 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.

You can read their paper, "Finding Good Bets in the Lottery -- And Why You Shouldn't Take Them," in the January edition of the American Mathematical Monthly. Their results showed that, while a lottery ticket could theoretically be a good bet, it is always a bad investment.

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.

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."

So most people already know this intuitively, right? What's the point of spelling it out in precise mathematical and economics terms?

"Most people don't fully understand risk," Abrams says. He points out that 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," Abrams 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."

To sum up the lesson in their lottery analysis for students: Math studies are a sure bet and a great investment.

Related:
Math's in your cards, so deal with it