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The sneaky math that made the lottery more alluring — and harder to win

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As lottery jackpots climbed to new highs earlier this year, including the Powerball’s historic $1.5 billion jackpot in January, followers of Salil Mehta’s blog began writing him to ask if there were strategies they could use to improve their odds. Mehta is a statistician who has worked on Wall Street and uses his math gifts to explore entertaining topics on his blog, Statistical Ideas.

Mehta found that there are strategies to increase your odds in the lottery — but you shouldn’t use them. Mostly, his research uncovered the absolutely stunning amount of money many Americans will lose playing the lottery over the course of their lifetimes.

He also found that recent changes to the games are exacerbating those losses. Winning the lottery has always been far-fetched, but in recent years, popular lotteries have been re-engineered to make their contests more appealing, but also further decrease your odds of hitting the jackpot.

Mehta spoke with me last week about his research and the real cost of the lottery. This interview has been edited for length and clarity.

What did you find when you started researching the numbers behind the lottery?

One, how few people actually win. I don’t mean just the jackpots, but actually make any money on their tickets. Only 2 percent of regular players will break even. Even if you win, it's taxed, so fewer than that win money on a net basis.

Next, the sheer volume of spending that goes into the lottery system. It comes to $73 billion and it’s growing each year. Proponents say people will spend money anyway — they should be allowed to spend it on entertainment. But the amount spent on other forms of enjoyment, like football games, pizza and Coca-Cola, pales in comparison. For example, total annual spending on Starbucks in the U.S. and on gambling in Las Vegas combined comes to about $20 billion.

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The final thing is how much people are playing. Regular players, roughly the top 5 percent of people who play the lottery, are spending a few thousand dollars a year, or more than a hundred thousand dollars on average in their lifetime, assuming no interest. The irony is that 98 percent are blowing this for the chance to make say a million dollars, which would then be taxed, so it would be reduced to about $500,000. Meanwhile, if they invested at a conservative 2 percent return, they could have had a guaranteed nest egg of hundreds of thousands of dollars. More than 50 million Americans are playing at least a thousand dollars annually for life.

What were your thoughts about the lottery after doing all this research?

I’ve spent a lot of time in the government, working to get people in a more comfortable position financially. So when I see something that’s so asymmetric, where people are throwing their money away on this promise that is funded by state governments, it’s very sad.

The lottery optimizes its game to draw the most money out of people. In the last few years, two of the big multi-state lotteries, the Powerball and the Mega Millions games, have both been re-engineered so the odds of winning are lower, but when a win actually happens, it’s a larger jackpot. The average lottery jackpot is around twice what it was a couple years ago. If you look at the top 10 jackpots of all time, four of them have happened so far in 2016 alone. Meanwhile, the odds are lower, meaning the vast majority of gamers are walking away with a gargantuan loss.

The associations for Powerball and Mega Millions both made these changes at roughly the same time. They were concerned that, without the eye-catching jackpot levels, they wouldn’t be able to reinvigorate sales they thought were otherwise slumping.

How did they actually create these big jackpots?

What they’ve done, essentially, is change the number of balls to pick from. It’s a bit of trickery. With Powerball, for example, you need to match five white balls and one red ball to win the jackpot. There were 59 white balls to pick from, and they jacked that up to 69. And then they reduced the number of red balls by 10. The total number of balls stayed the same, so people might think the probability also stayed the same. But the odds of winning are more greatly influenced by the number of white balls. Because of what they did, the odds of winning Powerball went up from 1 in 175 million to 1 in 292 million, nearly twice as difficult.

Because it’s twice as difficult, it should take twice as long on average to win, assuming the same amount of play is occurring. But we’re actually seeing that the games are being won a little more frequently. So they’ve gotten people to play more. From my modeling, when the jackpot starts rising above the $500 million range, people who would otherwise be on the sidelines suddenly see this very large amount and say, "Well, maybe I’ll go ahead and try this go around."

How rational is that thinking?

In one sense, the value of your ticket is a bit higher when the jackpot is bigger, because your probability of winning stays the same regardless of the size of the jackpot. You could say, if I have the same probability of winning, I might as well win a bigger jackpot than a smaller one. But on the other hand, the probability of multiple people sharing that larger jackpot increases as more people get off the sidelines. And when it gets above the $500 [million] to $600 million level, you get people who institutionally buy a larger swath of tickets. Any one individual couldn’t possibly buy tickets in all combinations. However, with enough people buying large swaths, you get to the point where virtually every ticket combination has been purchased.

You said people asked about winning strategies. Did you find any?

There are some strategies that give people slight edges. For example, avoiding lucky numbers: Everyone picks 7, so you should not pick 7 or 17, 27, 37, etc. But those faint enhancements are dwarfed by the sheer likelihood you’re going to lose nearly all your spending. You can play around on the edges of increasing your odds a bit, but it’s a colossal risk-reward in the best scenario.

Lottery money goes toward support public education. What did you find about whether this money is actually used for good?

About 40 percent of the revenue gets redeployed back to the educational system. But it’s gotten to the point that, because the lottery money is coming in, the money that was originally earmarked for education is being deployed to other parts of the state government.

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Also, the lottery draws out money from the percentage of the population who are having the hardest time saving for retirement. Yes, the money as a whole does get spent on something good, but it’s not clear if the money is coming from the right people at the right levels.

Who is playing the lottery in the United States?

Roughly half of Americans over the age of 18 have never played the lottery. Roughly 5 percent play every drawing, multiple drawings a week, every week for their entire lives. The other 45 percent are somewhere in between.

More than 10 million Americans literally play all the time. And if you look at their overall lifetime spending on the lottery, again it’s a hundred thousand dollars on average. Relative to the net worth of those individuals at retirement, it’s not small. The typical net worth of the bottom 90 percent of American households where the breadwinner is at retirement age is less than $50,000.

Is there any data about whether most people who are playing the lottery are rich or poor?

The lottery has purposefully not collected that information. There are ways to triangulate it. In New York City, for example, you can survey volunteers where the lottery kiosks are. And you can see the amount of spending that’s happening in Harlem is a lot higher than the amount in midtown on Park Avenue. It’s implausible that somebody on Park Avenue is jumping over a bunch of lottery kiosks to go to Harlem and buy their ticket. But you can’t prove it. The lottery has been very careful not to provide that information, for obvious reasons.

To state the obvious, what are those reasons?

Let me phrase this a different way. We have tens of millions of Americans who are spending over a thousand dollars a year. If you add 2 percent interest over 45 years, this comes to hundreds of thousands of dollars over a lifetime. What fraction of Americans can actually afford that?

No one can possibly say that the tens of millions of Americans who are spending on the lottery are wealthy enough to afford it, because there aren’t that many wealthy people. Only the top few percent of Americans could actually afford this, yet more than that portion are draining their nest eggs in regular play. And they’re spending in poor neighborhoods. I don’t have the answer, but it’s far-fetched that the story would yield a good result if you had data.

Here's how some recent Powerball winners said they'd spend their winnings. (Video: Claritza Jimenez/The Washington Post, Photo: HANDOUT/The Washington Post)

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