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The Mega Millions jackpot is now over half a billion dollars ($540 million, to be exact). So is it time to buy a lottery ticket?
No, or at least not according to an analysis performed by computer scientist Jeremy Elson last year, when the jackpot was a “mere” $380 million.
It's actually not a crazy question. Sure, the lottery is a sucker's bet in general. But the odds of winning, per the official Mega Millions web site are about 1 in 176 million. A ticket only costs a dollar. So anytime the jackpot is worth more than $176 million, a $1 ticket is a good bet, right?
Not so fast. First, that eye-popping jackpot figure doesn't mean the winner gets an immediate check for $540 million. It's paid over 26 years as an annuity. You can take a lump sum now, but you only get $389 million. Taxes bite off another 40% or so, depending on what state you live in. Still, the jackpot should still be worth around $230 million in cold, hard, after-tax cash. That's still a lot more than $176 million. So the odds are looking — in true Hunger Games fashion — ever in your favor.
The problem, though, is that even if you win, there's no guarantee you'd be the only winner. According to economist Stephen Bronars , lottery officials figure there's about a 76% chance of someone picking a winner in tomorrow's drawing, and that if there's at least one winner, there will likely be two (or, more precisely, 1.9, on average). That would cut your likely winnings in half. Mr. Bronars actually still figures it's worth the gamble, but he doesn't appear to be factoring in taxes.
Still, let's say no one picks a winner tomorrow, and the jackpot keeps growing. At some point, it'd get big enough to be worth the bet, right?
Don't count on it. Mr. Elson notes that when jackpots go up, more people buy tickets, hoping for a shot at lottery riches. In fact, they seem to do so super-linearly — that is, the buying frenzy picks up pace as the jackpot grows. The more people who buy tickets, the greater the risk of multiple winners, and thus the lower the value of any payout. (Mr. Elson notes that there haven't been many cases of truly super-sized jackpots, so it's possible the sales-to-jackpot relationship breaks down at the upper reaches.)
Taking all this into account, Mr. Elson plots the expected value of a ticket against the size of the jackpot, and finds that it looks more or less like a bell-curve. That is, up to a certain point, higher jackpots mean higher expected payouts. But after a certain point, the risk of multiple winners overwhelms the higher jackpots, and the expected payout goes down. By Mr. Elson's calculations, the best time to buy a Mega Millions ticket is when the jackpot is $420 million. Even then, though, the expected value of a ticket is just 69 cents. So you'd still be better off keeping your dollar.
But hey, you never know.
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@John Hodgson: the WSJ article doesn’t mention it, but Elson’s analysis does take into account the non-jackpot prizes. They only add about 11 cents of expected value to a ticket.
The article has a major flaw. The jackpot is not your only chance to win in this lottery. If you only get a portion of the numbers correct, you will still win a prize. The prize is not nearly as much, but the odds are also much better than winning the entire jackpot. These winnings and any other intangibles (such as the fun of playing) should also be figured into the expected return of buying a ticket. Of course, if you really want to over-analyze this lottery, you could also consider who is buying the ticket and what their alternative investments are. The marginal utility of the $5 ticket versus hundreds of millions of dollars of winnings are very different to a poor person than they are to Bill Gates and the alternative uses for that 5 bucks are pretty different as well. I’d love to see an article explaining how much a corporation would expect to win if they were able to buy every ticket. I understand taxes take out a huge chunk in America, but does the decision change in Canada where this income would not be taxed?
Ya can’t win if ya don’t play!!
You don’t have to buy a ticket to dream about how to spend winnings. For non-dreamers, everyone knows the companies that run these games *always* come out ahead. Mega-millions never pays more than 50% of sales out in prizes. Winners lose half the remainder in taxes.
Give me a dollar and I’ll give you a quarter, all day long.
Write a BIG check to President for his reelection.
Real Time Economics offers exclusive news, analysis and commentary on the economy, Federal Reserve policy and economics. The Wall Street Journal’s Phil Izzo is the lead editor, with contributions from other Journal reporters and editors. Send news items, comments and questions to realtimeeconomics@wsj.com.
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Digg
The Mega Millions jackpot is now over half a billion dollars ($540 million, to be exact). So is it time to buy a lottery ticket?
No, or at least not according to an analysis performed by computer scientist Jeremy Elson last year, when the jackpot was a “mere” $380 million.
It's actually not a crazy question. Sure, the lottery is a sucker's bet in general. But the odds of winning, per the official Mega Millions web site are about 1 in 176 million. A ticket only costs a dollar. So anytime the jackpot is worth more than $176 million, a $1 ticket is a good bet, right?
Not so fast. First, that eye-popping jackpot figure doesn't mean the winner gets an immediate check for $540 million. It's paid over 26 years as an annuity. You can take a lump sum now, but you only get $389 million. Taxes bite off another 40% or so, depending on what state you live in. Still, the jackpot should still be worth around $230 million in cold, hard, after-tax cash. That's still a lot more than $176 million. So the odds are looking — in true Hunger Games fashion — ever in your favor.
The problem, though, is that even if you win, there's no guarantee you'd be the only winner. According to economist Stephen Bronars , lottery officials figure there's about a 76% chance of someone picking a winner in tomorrow's drawing, and that if there's at least one winner, there will likely be two (or, more precisely, 1.9, on average). That would cut your likely winnings in half. Mr. Bronars actually still figures it's worth the gamble, but he doesn't appear to be factoring in taxes.
Still, let's say no one picks a winner tomorrow, and the jackpot keeps growing. At some point, it'd get big enough to be worth the bet, right?
Don't count on it. Mr. Elson notes that when jackpots go up, more people buy tickets, hoping for a shot at lottery riches. In fact, they seem to do so super-linearly — that is, the buying frenzy picks up pace as the jackpot grows. The more people who buy tickets, the greater the risk of multiple winners, and thus the lower the value of any payout. (Mr. Elson notes that there haven't been many cases of truly super-sized jackpots, so it's possible the sales-to-jackpot relationship breaks down at the upper reaches.)
Taking all this into account, Mr. Elson plots the expected value of a ticket against the size of the jackpot, and finds that it looks more or less like a bell-curve. That is, up to a certain point, higher jackpots mean higher expected payouts. But after a certain point, the risk of multiple winners overwhelms the higher jackpots, and the expected payout goes down. By Mr. Elson's calculations, the best time to buy a Mega Millions ticket is when the jackpot is $420 million. Even then, though, the expected value of a ticket is just 69 cents. So you'd still be better off keeping your dollar.
But hey, you never know.
« Previous Fed’s Plosser: Additional Stimulus Would Be Bad Idea Next » Like It or Not, Fed’s Actions Raise Its Profile Real Time Economics HOME PAGE Email Printer Friendly Share:MySpace
Digg
del.icio.us
StumbleUpon
Error message
@John Hodgson: the WSJ article doesn’t mention it, but Elson’s analysis does take into account the non-jackpot prizes. They only add about 11 cents of expected value to a ticket.
The article has a major flaw. The jackpot is not your only chance to win in this lottery. If you only get a portion of the numbers correct, you will still win a prize. The prize is not nearly as much, but the odds are also much better than winning the entire jackpot. These winnings and any other intangibles (such as the fun of playing) should also be figured into the expected return of buying a ticket. Of course, if you really want to over-analyze this lottery, you could also consider who is buying the ticket and what their alternative investments are. The marginal utility of the $5 ticket versus hundreds of millions of dollars of winnings are very different to a poor person than they are to Bill Gates and the alternative uses for that 5 bucks are pretty different as well. I’d love to see an article explaining how much a corporation would expect to win if they were able to buy every ticket. I understand taxes take out a huge chunk in America, but does the decision change in Canada where this income would not be taxed?
Ya can’t win if ya don’t play!!
You don’t have to buy a ticket to dream about how to spend winnings. For non-dreamers, everyone knows the companies that run these games *always* come out ahead. Mega-millions never pays more than 50% of sales out in prizes. Winners lose half the remainder in taxes.
Give me a dollar and I’ll give you a quarter, all day long.
Write a BIG check to President for his reelection.
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