Powerball reality check: Fuzzy math advice abounds before colossal drawing

Cooler heads don’t always prevail when $1.4 billion is on the line.

Ahead of the next Powerball drawing, with millions clamoring to get their hands on the world’s biggest jackpot, doubtful math and questionable advice have been metastasizing. The odds of winning are overwhelmingly against you, but that message frequently gets lost in the hype.

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On Monday, Media Matters for America (MMfA), a liberal watchdog of conservative media, flagged some dubious advice that flashed across Fox News: “Buy as many tickets as you can afford.”

Sure, purchasing as many tickets as you can afford would improve your odds, but they would still be infinitesimal — you would just be deeper in the red.

“It’s bad advice because, believe it or not, there’s essentially no meaningful improvement in your chances of winning if you were to buy $1 million worth of tickets instead of $2 worth of tickets,” Craig Harrington, the economic policy program director for MMfA, said to Yahoo News. “So, urging people to buy as many tickets as they can won’t really do anything for them, unless they’re able to buy about $300 million worth of tickets" (which would give them a 50-50 chance of picking the winning numbers).

Harrington said Fox News has many devotees who would see something like this and act upon it, especially since the segment was introduced with assurances that it would “try and make you rich” with supposedly “proven strategies.”

“Bottom line,” he continued, “Fox News urging viewers to buy as many lottery tickets as possible is irresponsible and embarrassingly bad advice.”

Ronald Wasserstein, the executive director of the American Statistical Association, the nation’s main professional organization for statisticians, said people have trouble understanding the absolute chance of something happening and the relative chance of something happening — not because they’re stupid, but because probability in general is not intuitive to people.

“It’s absolutely true that if you buy 10 tickets for this drawing instead of just one, you increase your chances of winning by [a factor of] 10. But instead of that being 1 in 292 million (the total number of combinations), it’s 10 in 292 million,” Wasserstein told Yahoo News. “It’s still a ridiculously small chance of winning. That’s a really bad strategy because it just means you’re going to lose more money. You spent $20 on 10 tickets instead of $2 on one ticket.”

Some people have been arguing that a potential lottery player’s “expected value” would be higher if he or she only plays when the jackpot is gigantic, according to Wasserstein.

“That’s arguably true but practically nonsense,” he said.

In statistics, an expected value is an average that helps determine how helpful or harmful a particular action might be. Gamblers use it to determine if they would win or lose on a given turn, on average, over an extended period of time.

Steve Horwitz, a professor of economics at St. Lawrence University, broke down for Yahoo News how playing the Powerball is a losing proposition from a purely economic standpoint.

“We know about all these cognitive biases that people have. If we are playing strictly by the economics, no one should ever buy one of these tickets if we are being utterly rational,” the economist said in an interview with Yahoo News.

Tickets are $2 each. The odds of winning the Powerball are 1 in 292 million. If you divide $1.4 billion by 292 million you get an average return/expected payout of $4.79. If everything stopped there, you would have a positive net expected value and buying a ticket would be worthwhile — but it does not.

The $1.4 billion payout is spread out over 29 years; the lump-sum cash payment is $868 million, reducing the expected value to $2.97. The likelihood that someone else picks the right combination and splits the prize (conservatively placed at 25 percent for this experiment) would bring the jackpot even lower, to $651 million, and the expected value to $2.22.

“Better odds than Vegas. But now we’re forgetting another part. Government takes a huge hunk of that. And they are likely going to take 40 percent of it depending on exactly the details,” Horwitz continued.

After adding up all of the factors, he said, you’re spending $2 today for an after-tax expected value of $1.33. Nevertheless, many people are willing to enter a losing scenario for the faint glimmer of hope for something extraordinary.

“We are attracted by the large prize if we win, and the loss of that small amount for even that fraction of a chance seems worth it,” Horwitz said.

Many turned to Twitter to comment on just how unlikely it is for any one person to win the Powerball.

A meme circulating on social media claims that if the Powerball winnings ($1.3 billion at the time) were evenly distributed among the United States’ population of roughly 300 million, everyone would receive $4.33 million, solving poverty. But that does not add up: 1.3 billion divided by 300 million would actually leave $4.33 per person. (Side note: The country’s population is currently estimated at 325 million).

Members of the Multi-State Lottery Association, which runs Powerball and other multijurisdictional games like Mega Millions, give a portion of the ticket sales to a variety of beneficiaries.

“This is the biggest jackpot in the history of the world as far as lotteries go — no question about it,” Gary Grief, executive director of the Texas Lottery, said in an interview with Yahoo News. “About 40 cents of every dollar spent on Powerball goes right back to the states involved to whatever good cause their lottery is dedicated to.”

Grief said people in the lottery industry take great pride in the amount of money that is raised for good causes. Since the last Powerball jackpot on Nov. 4, he said, more than $700 million has been generated for causes in all the states that sell Powerball.

Funds raised by the Nebraska Lottery are supposed to benefit the Nebraska Environmental Trust, educational funds (like the Education Innovation Fund and the Nebraska Scholarship Fund), the Nebraska State Fair — and the Compulsive Gamblers Assistance Fund.

“Since 1993, when the lottery first began, we’ve been able to raise $581 million for those beneficiary funds,” Neil Watson, a spokesperson for the Nebraska Lottery, told Yahoo News.

The next Powerball drawing is scheduled to take place at 11 p.m. on Wednesday.

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