Powerball Jackpot Hits $1.3 Billion—But Is Your $2 Bet Worth It?

Should You Spend $2 to Win $1.3 Billion? Inside Powerball Math

By Mark Fischetti edited by Dean Visser

No one has won the Powerball lottery jackpot in many weeks, which means the next drawing (slated for Wednesday) is worth an estimated 1.3 billion—one of the largest payouts in U.S. history. The question, of course, is whether a $2 bet on something like this is “worth it.” Here’s the math.

Chance of Winning

For Powerball, you pick five random numbers out of the digits 1 through 69, plus a “Powerball number” from 1 to 26. This math is simple: With a single ticket, your chance of winning is one in 292,201,338. If you buy two tickets and run different numbers, your odds are two in 292,201,338—not much better!—and so on. You may think, “Okay, I’m going all out this time. I’m spending $50 to buy 25 tickets.” Your chance is now 25 out of 292 million, which is still, sorry to say, infinitesimal.

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Playing Different Numbers

What about the idea that you should play different numbers week to week? People like to use their birthday or the date of an anniversary or other special numbers. Go for it. A set of any six numbers for Powerball has exactly the same chance of winning—or, well, most likely losing—this week as that same set of numbers has next week. Each draw is a new day and has nothing to do with prior draws. Perhaps the most famous case of this happened in reverse: In 2009 the Bulgarian national lottery randomly selected the winning numbers 4, 15, 23, 24, 35, 42. Four days later, when the next drawing was held, the same six numbers came up.

Massive Ticket Buy

You can try to guarantee a win if you can find a whole lot of people and coordinate your buying. But the math here is daunting. Consider the “guaranteed win” that happened in the Virginia Lottery in 1992, which we covered years ago: Players had to pick six numbers out of 44, so there was a one-in-seven-million chance of winning. To play every possible combination, which would guarantee a win, someone would have to buy seven million tickets, which, at $1 per ticket, would cost $7 million. The jackpot had grown to $27 million, so 2,500 people formed a consortium. Each person paid about $3,000 in an attempt to cover all the possible combinations. The group scrambled to buy tickets and tried to make sure each purchase was a different set of numbers. These individuals ran out of time and “only” purchased five million different tickets. But that was enough. They won! For Powerball, though, the winning chance is not one in seven million—it’s one in 292 million, and tickets are $2 each. So within a couple of days, you’d need enough friends to physically go buy 292 million tickets and to somehow know that each set of six numbers you picked was unique. And you’d have to spend almost $600 million. Good luck with that.

High Payout, Greater Worth

The one counter to these remote possibilities is the “worth it” factor. As the jackpot goes up, is spending $2 more “worth it”? In 2023 our resident mathematical whiz Jack Murtagh, who writes our Math column, offered a cool mathematical assessment of this emotion-based question in one of his articles. He wrote that the “Expected value of a bet = (Probability of winning) × (Winning amount) – (Probability of losing) × (Losing amount).” If you roll a six-faced die and bet $1 on one number for a $1 payout, the expected value is –$0.667. Translation: the bet is not worth it. But if the payout is $100 for a $1 bet, then the expected value is about $16, well worth a shot. For Powerball, with a $2 bet and a $20 million payout, the expected value is –$1.93—really bad! As Murtagh wrote, “You’d get more value out of those two bucks if you traded them for a dime.” But if the payout is $1 billion—hmm. Do the math and see. (Okay, okay! My back-of-the-envelope calculation says the value is around $1.42.) Of course, this expected payout is a philosophical exercise. It doesn’t raise your chances of one in 292 million.

Fun Factor

But maybe that doesn’t matter. Sure, you can hope against hope to win the big one. In the meantime, you’re spending $2 to live out a fantasy that might last at least a day or two. To quote Murtagh: “We all make frivolous purchases, and most of them have zero probability of netting us a fortune.” The excitement of playing the game, of the remote but grand possibility of winning big, he added, “makes people happy regardless of the outcome.”

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