Is Ticket for $600 Million Powerball Jackpot a Good Bet?
he Powerball jackpot is up to $600 million, with a day still to go before tomorrow’s drawing. Which means it’s time once again to ask the question: Is this the rare time where it makes economic sense to buy a lottery ticket?
Spoiler alert: No. No it is not.
But before we explain why, let’s take a step back. The last time we asked this question was just over a year ago, when the Mega Millions jackpot hit $640 million. At first blush, that looked like a good bet: A $1 Mega Millions ticket earns you a 1 in 176 million shot at the jackpot, which in theory means any jackpot bigger than $176 million should be worth the gamble. Even after adjusting for the smaller lump-sum payout option (the full jackpot is paid out over time as an annuity) and the effect of taxes, the jackpot was worth around $275 million.
The trouble with that math, though, is that it assumes there can be just one winner. In fact, there are often multiple winners — and as computer scientist Jeremy Elson noted , the bigger the jackpot gets, the more people buy tickets, further driving up the odds of a split jackpot.
Sure enough, last year’s mega-jackpot (which eventually totaled $656 million) ended up getting split three ways . That still comes out to more than $100 million per person after taxes — not bad for a $1 bet. But in strict net-present-value terms, the lottery still wasn’t a good investment. (Though as economist Stephen Bronars noted at the time, the expected return was better than in many other long-odds gambles.)
That brings us back to today’s question, which turns out to be a good deal simpler. The odds of hitting the jackpot are ever-so-slightly better in Powerball than in Mega Millions: 1 in 175 million vs 1 in 176 million. (The chance of winning a prize of some sort is about 1 in 38, vs 1 in 40 for Mega Millions.) But there’s a critical difference between the two games: A Mega Millions ticket costs $1. A Powerball ticket costs $2.
The higher price means that for a Powerball ticket to be “worth it,” the pot has to be twice as big as for in Mega Millions, or about $350 million. The cash value of the current pot is a bit better than that, at $376.9 million, but that’s before taxes. Assume a 40% marginal tax rate, though, and tomorrow’s pot is worth a mere $226 million.
And that’s before taking into account the risk of a tie. Mr. Elson notes that the higher ticket price in Powerball means there are fewer tickets sold, which somewhat reduces the chance of a split pot. But the same basic logic applies. He calculates that the best time to play is when the advertised pot is at about $493 million, the point that best balances a big jackpot against the odds of a tie. But even then, the net present value of a ticket is just $0.85, less than half the cost of a ticket. (That figure takes into account 21 cents of value from non-jackpot prizes.)
In other words, play or don’t play. But don’t expect to get “ that kind of rich .”
