Playing the Numbers

How to think about Powerball's record "$2 billion" jackpot like an economist

The world's largest lottery drawing ever was no accident
In the long run, you've already lost.
In the long run, you've already lost.
Photo: Dominique James (Shutterstock)
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This story was first published on Nov. 4, and updated Nov. 6-8. After an abrupt delay, the drawing for Powerball’s record jackpot on Monday, Nov. 7, produced a winner in California.  Follow the latest updates on the drawing here.

If you are actually an economist, then you probably aren’t playing in Monday’s Powerball lottery drawing, with an advertised jackpot of $1.9 billion, the largest in history. There are no checks big enough nor ping-pong balls bouncy enough for you to act irrationally.

But for the rest of America getting hyped for a potentially record-breaking Powerball drawing on Monday, Nov. 9, at 10:59pm Eastern Time, it’s time to start thinking like an economist. At least then you will have something to talk about while waiting on line for a ticket and ruing your loss the next morning.

So here is such a guide, but fair warning: The dismal science just makes the lottery even more depressing than it already is.

Bigger jackpots are not an accident

Eye-popping rewards generate higher ticket sales and, uh, media attention, which is free advertising that generates even more sales. So when Powerball faced slowing growth in 2015, the lottery responded by changing its rules, with the effect of creating fewer, but bigger, jackpots.

Powerball draws five white balls and one red ball, and you need to match all of them to win the jackpot. The rule change reduced the number of white balls, which made it easier to win smaller prizes by matching just some of the numbers, but increased the number of red balls, which made the jackpot more difficult. The odds of winning fell from 1 in 175 million to 1 in 292 million.

This was a particularly sinister change because it had the effect of creating more frequent, small winnings for regular lottery players, who are the most likely to be poor and to develop a gambling addiction. The occasional 10-figure jackpots draw infrequent players just having a little fun, which subsidizes the real business of the lottery, exploiting the desperate.

The “advertised value” is a lie

You probably know that if your lucky day actually does arrive, you will have to choose between taking the winnings in growing installments over 30 years (an annuity) or as one payment right away. The catch, of course, is that the lump sum will be less than the advertised jackpot: For Monday’s $2.04 billion jackpot, choosing the lump sum payment nets $997.6 million before taxes.

Deciding whether to take the annuity or lump sum is often presented as a fun personal-finance question (lump sum). What we should really take away is that Powerball, along with most lotteries worldwide, are grossly inflating their jackpots in order to advertise the largest possible number.

The reality is that the lump-sum payment, or cash value, is the prize for hitting jackpot. That’s how much money the lottery has in its prize pool right now from ticket sales, and if you win, the money is yours.

The much larger “estimated jackpot,” as Powerball calls it, is simply an estimate of the total payments the lottery will make over three decades, after the winnings are invested in a conservative portfolio of long-term, zero-coupon US Treasury bonds, and slowly drawn down until you’ve received $1.9 billion. In other words, the advertised jackpot is a simulation. You could take the lump sum, invest it the same way yourself, and end up with the same amount. You could also do other things that end up generating even more, or less.

So let’s be honest, the jackpot for Monday’s Powerball drawing is $998 million, which is nothing to sniff at.

Rising interest rates affect the lottery, too

Increases in borrowing costs driven by the US central bank’s recent rate hikes are affecting all parts of the economy, including the lottery. But unlike most businesses, Powerball actually benefits from rising interest rates because it can advertise higher jackpots even while having less cash on hand.

That’s because higher rates mean higher yields from the long-term US government bonds in which the lottery prize is invested. These securities are not particularly lucrative, in exchange for being extremely safe, but that dynamic has changed a bit recently as the Fed raises rates. Thirty-year, zero-coupon Treasurys are currently yielding 4.4%, up from 2.2% a year ago.

The result is that the actual, cash value of the Powerball jackpot, as a percentage of what Powerball advertises as the jackpot, is lower than it’s been in a decade. And that’s before adjusting for inflation!

In an era of higher interest rates and lower odds, we should expect to see even more 10-figure advertised jackpots.

The expected value of a lottery ticket

Perhaps you’ve read stories of math geniuses trying to beat the lottery by strategically hoarding tickets when the jackpot is large enough to make such a scheme profitable. The only instances of this actually working have involved rigging the system to produce numbers that weren’t random, but the dream is rekindled every time a jackpot gets large enough.

To simplify, the “expected value” of a lottery ticket is the average of all possible outcomes: Almost all of the time, you will lose the $2 ticket price, but when you include the possible outcome of a jackpot, and the jackpot is large enough, it can push the expected value of a $2 ticket above $2—guaranteed profit!

This is a very good way to learn statistics, but a very bad way to think about the lottery. You can’t buy every possible combination of numbers, and no one would give you the money to do it, anyway, because the scheme could fail in all sorts of spectacular ways, a lot of them having to do with taxes.

The most fun way it could fail is if more than one ticket had the winning numbers, forcing a split jackpot and no profit at all. Split jackpots are fairly common, and one reason is that lottery players are human, and humans think alike. By one estimate, half of all Powerball tickets are duplicates.

People tend toward certain numbers and avoid others, including patterns that don’t “seem” random. Letting your brain pick the numbers is the surest way to reduce the expected value of your ticket.

Lesson: You can’t beat the lottery, unless you cheat. The lottery, on the other hand, will always beat you, and cheats, anyway.