Is it smarter to buy 10 Powerball tickets for $20 than a single $2 ticket?
Here's the theory: Buying more Powerball tickets increases your odds of winning. So buying more Powerball tickets would seemingly improve your investment.
But that's not the case. Despite your improved odds, your expected Powerball losses actually increase as you buy more tickets.
Here's why: Your expected return on a $2 Powerball ticket is equal to just $1.05, according to Victor Matheson, professor of economics and accounting at the College of the Holy Cross in Massachusetts.
Put another way, you can expect to lose 95 cents on every $2 Powerball ticket purchase.
That may not make obvious sense, but it is factoring in that one out of 25 tickets will win some kind of prize, which could be as low as $4 or even as high as $2 million. Or the jackpot.
"The best way to make money on the lottery is not to play," said Matheson. "The only way to make the Powerball a worse deal is to buy lots of tickets."
Buying 10 tickets increases your expected loss to $9.50. If you buy 100 tickets, you can expect to lose $95. That's not a sound investment.
There are two reasons why your expected loss wouldn't decrease with every additional Powerball ticket that you purchase: Your odds of winning don't meaningfully improve, and the size of the pot doesn't increase enough by buying 10, 100 or even 1,000 tickets.
That begins to change when you start buying really, really large amounts of tickets -- in the hundreds of thousands or millions, Matheson said. At that point, your expected per-ticket losses begin to fall, less so because your odds are getting better and more so because you're increasing the size of the jackpot by buying so many tickets.
Bigger jackpots are worse investments
As the Powerball jackpot increases, more people run out to buy tickets. Interestingly, bigger jackpots actually lower your expected per-ticket earnings.
That's because there are more people playing, increasing your odds of sharing the jackpot with someone else (or multiple people). With 550 million Powerball tickets sold so far, an average of 2.2 people are expected to win the $1.5 billion Powerball jackpot, according to Matheson.
On Monday, when the jackpot was $1.4 billion and 450 million tickets were sold, an average of two people were expected to win.
The $1.5 billion jackpot actually pays out $930 million in a lump-sum payment. Divide that by 2.2 winners, and the expected jackpot is actually around $420 million. Per $2 ticket, that works out to $1.43, plus 32 cents for the lower-tier prizes, minus 70 cents for taxes, totaling $1.05 in expected earnings per ticket.
Some lotteries pay off
So Powerball is not the lottery to play if you care about making a good investment. But there are actually quite a few lotteries that pay off.
Matheson and colleague Kent Grote researched 23,000 state lotteries and found that just over 1% represent a net positive investment. They're typically smaller lotteries with more modest jackpots of $1 million or less. In those lotteries, you're far less likely to have to share the jackpot, which is the biggest investment-killer.
There's no reasonable way to make a Powerball ticket a good investment. But if you insist on playing, Matheson says there's one way to improve your expected return, albeit by a miniscule amount: Choose obscure numbers.
When people choose their own lottery numbers, they typically pick digits that have some kind of personal meaning for them. Those numbers are typically between 1 and 31, since they represent dates like birthdays and anniversaries. If you pick numbers greater than 31 and large, obscure, prime numbers, you're less likely to split the jackpot if you win.
Good luck.
