EMORY (US)—Playing the lottery may be a good bet, but it’s almost always a bad investment.

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.”

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