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MegaMillions

By on 3.28.12 @ 10:08AM

How can I not buy some tickets in the MegaMillions lottery for the drawing this Friday? This game is in 42 states plus the District of Columbia. (It is not in Alabama, Alaska, Florida, Hawaii, Mississippi, Nevada, Utah, and Wyoming, so if you are in one of those places, call a friend in another state — a friend you trust — to buy a ticket for you.)

I admit it: I wasted $20 on yesterday’s drawing, when the jackpot was a paltry $363 million, understanding that lottery tickets are basically a tax on stupidity. Actually, I wasted $17, because one of my twenty lines of numbers included the “MegaBall” and one of the other numbers — a combination worth $3. Apparently 1.3 million other gamblers also won back $3 of their hard-earned money. Forty-seven people won the $250,000 price received for getting all 5 regular numbers, but not the MegaBall. Sooooooo close!

Despite the odds of losing all or nearly all of your wager, at some point it becomes what a friend calls a “utility bet,” using the word “utility” in its economic sense. In other words, the possibility, almost no matter how vanishingly small, of winning such an enormous prize makes it worth taking a flier with some modest amount of money.

And the odds of winning are indeed long, at about 175,711,536 to one.

But by the time the next numbers are drawn, on Friday evening, the grand prize will be over half a billion dollars; over $600 million would not be a surprise to see. (If you take the money all at once, you’ll get a little over 70% of the published amount.) The previous record, in 2007, was $390 million (which was split by two winners.)

Again, don’t you have to buy a ticket, even knowing you’re extremely likely to lose your money?

This reminds me of a question the above-mentioned friend likes to ask, and which I’ll ask you. There is no right answer; it’s just a reflection of your personality.

Imagine you’re given the opportunity to bet on a coin flip. You can take any real, government-issued coin out of your pocket for the bet, so you know that the coin is fair. You can bet any amount you want to bet. If the coin comes up heads, you lose your bet. If the coin comes up tails, you win ten times your bet. In other words, risk $1 to try to win $10, or risk $100 to try to win $1,000, etc. And you can only play once. How much would you bet?

I hope I don’t sound too much like Mitt Romney when I say that at ten-to-one, I’d probably bet $10,000. And I don’t have anything like Romney money…it would really bum me out to lose $10,000. But the chance to win $100,000 would probably be worth the risk.

An interesting thought experiment is to see how your answer, or your friends’ answers, change as you change the multiplier. In other words, what would your answer be if you could only win twice what you bet, and what if you would win 50 times what you bet? I know I would bet much less, probably not even one tenth as much, if the multiplier dropped to 2, and would probably only double my bet if the multiplier went to 50 because I just wouldn’t feel like I could afford to lose more.

I’d love to hear your answers…again, there’s no right answer; it’s a personality question, not a math question.

I guess I’ll be heading back to the shop at the gas station to waste another $20 on Friday’s MegaMillions drawing…

View all comments (48) |

Bill| 3.28.12 @ 11:37AM

SCAM!!!!!!!!!!!!!!!!!!!!!!!

Mike 3/505| 3.28.12 @ 12:07PM

Ross,

Killing time until after today's SCOTUS session?

Regards,

Mike

Ross Kaminsky | 3.28.12 @ 12:28PM

Something like that, Mike!

Mike 3/505| 3.28.12 @ 12:30PM

Busted!

buckeyeman| 3.28.12 @ 12:11PM

Ross, you don't really need to buy a ticket. You should enjoy the vicarious pleasure of viewing long lines of ticket buyers on television and knowing that you are underwriting most of those purchases through you tax "donations". Remember that money is fungible. I know that you know what that means but everyone else should look it up 'cause it's an important word. So don't worry, be happy (like Ben Stein, I guess) and know that literally millions of folks are buying tickets on your behalf with your (former) money. Of course, if one of them wins you won't get any of it, but statistically that's the about the same odds as if you stood in line yourself (ie, zero).

Ross Kaminsky | 3.28.12 @ 12:28PM

That's all right, except that I was able to buy a ticket without waiting in any line!

It does seem like Ben starts a lot of his notes feeling down, and ends them feeling better. I can relate, to some degree, with my business being a roller-coaster from time to time.

So I guess you're going to follow your own advice and not buy a ticket?

Humphrey Dumfries| 3.28.12 @ 12:41PM

A friend on Facebook is in an office pool. Her co-worker (who's apparently in charge of buying the pool's tickets) keeps posting pictures of all of the tickets he buys, then tagging my friend and her co-workers. The result -- any of their FB friends get to see all of the pool's numbers. I keep thinking I should play all of their picks...

Another thought experiment: What would you throw in on your tax return ($2? $5?) for a chance for a lifetime reprieve from federal taxes?

An article in this month's issue of The Atlantic tells of a guy who secured nearly even odds in A.C., and walked with upwards of $10 million:
http://www.theatlantic.com/mag.....city/8900/

Tony| 3.28.12 @ 12:57PM

Ross,

I would not bother to pick up $20 worth of tickets if they were free. On the 10 to 1 odds on a coin flip, I also think that $10K seems about right. But don't tell my wife. I think that this is a statement of your economic standing in combination with your personality.

Tony

Bob| 3.28.12 @ 1:34PM

It's not 10 to 1 odds, it's 2 to 1. You're flipping a coin and have a 50% chance of calling it right, and if you do call it right you get back 10 times what you put in.

Tony| 3.28.12 @ 2:58PM

You are right. I understood it but wrote it wrong.

Thanks.

Jim Woodward| 3.28.12 @ 1:03PM

I've probably wagered $100.00 in the last thirty years or so on lottery tickets in MD, DE and GA, usually scratch offs. Never stood in line to buy one nor was it my intention to buy one when I entered the store.

I would buy one or two with change from a gas purchase on a whim. Usally hit for $2.00 or a free ticket. Every once in a while $5.00 and once in GA, $50.00. I may be even on my bets, or less, probably not on the plus side.

On the coin toss? No more than a buck regardless of payout.

LiveFreeOrDie| 3.28.12 @ 1:17PM

It is a tax on people who are bad at math. The odds of winning are roughly the same for one who doesn't even purchase a ticket. Then the multitudes buy even more when the amount goes up and the odds get worse.

That being said I'll probably buy a ticket as well.

Ross Kaminsky | 3.28.12 @ 1:20PM

So, I don't think the odds get worse as the amount goes up because even though more people are in, the number of possible numerical combinations (for the drawing numbers) doesn't go up, so I think your expected value increases, though that would have to be offset to some degree by the increased chance of having to split the prize.

I'll ask a math expert and get back to you...

LiveFreeOrDie| 3.28.12 @ 2:14PM

Doh! You're absolutely right about the odds, my mistake.

Bob| 3.28.12 @ 1:32PM

50-50 on getting back 10 times your bet? I would take that chance. Would be an even sweeter deal if you were allowed more than one chance, but then it would be too easy to win a lot of money.

Ross Kaminsky | 3.28.12 @ 1:35PM

That's why you can only play once, Bob! So how much would you bet?

SCM| 3.28.12 @ 1:53PM

I'm not above purchasing a tick when the jackpot gets high, but I know that gambling appeals to one of our worst instincts: greed.
That being said, Ross, if I win the half-billion, I'll give you a $100K so you don't have to make your coin flip bet.

Ross Kaminsky | 3.28.12 @ 2:03PM

A most generous offer, SCM...

Jon| 3.28.12 @ 2:04PM

Interesting question - everybody has that sweet spot where losing won't hurt TOO bad, but winning feels good...at 10-to-1 payout I'd wager $50, 2-to-1 I'd wager $5, and at 50-to-1 it'd be worth $200 to me. Craps or sports betting would still be more fun, though!

PJ| 3.28.12 @ 2:22PM

As a trained statistician, I know the odds are are very much against me to win.

As human beings, we have the natural propensity to take chances, hopefully calculated ones, resulting in some form of excitement. That's why we have entrepreneurs, athletes, & Navy Seals. So for me putting some skin in the lottery does create a little excitement.

DW| 3.28.12 @ 2:50PM

I'm with the ETrade baby who reminds his adult friend that his odds of winning the lotto are the same as his odds of being mauled by a Polar Bear and a regular Bear in the same day!

Scott| 3.28.12 @ 3:27PM

To the extent that any gambling makes sense, you should probably buy two tickets.

You should only gamble when the expected value is greater than zero. In the case of buying lottery tickets, the costs are fixed and the benefit (the winnings) need to be weighted by the probability of winning. If the cash value is about 70% of the listed amount, then the payoff will be about 350 million. The probability of winning (assuming you get the only winning numbers), is one in 175 million. Therefore the expected benefit is about $2. The cost of each ticket is $1, so two tickets will yield an expected benefit of zero, which is the dividing line between buy/don't buy. Since the final jackpot will probably be more than 500 million, that tips the equation into the net positive, so buying two tickets can be rationalized.

Ross Kaminsky | 3.28.12 @ 3:57PM

The problem, Scott, is your assumption that you get the only winning numbers...which becomes much less likely with so many people in the game.

Scott| 3.28.12 @ 7:55PM

Yes, I know, but I don't think there's any way to factor in the probability of more than one person getting the winning numbers.

Ross Kaminsky | 3.28.12 @ 8:23PM

There is definitely a way, but it's also definitely beyond my math skills! I've asked some smart friends if they have an opinion.

Oldefarte| 3.28.12 @ 4:05PM

Ross, people like you [or many of the rest of us] NEVER WIN LOTTERIES. It's always some poor out of luck, unemployed whoobegone individual that always seems to be awarded the prize. Maybe that's how it should be [but no doubt due to their predominent playing of lotto games also]. If I won such, I'd want to invest most of it and see if i could say double or triple the amount in the time I have left on this earth [just for the fun of it]. I'd also like to leave same as an structured inheretance. I've lived a pretty good life and don't feel neglected by life, and don't feel money buys happiness [but it would be fun to see if I'm incorrect in this]. Oh well!!!!!

Ross Kaminsky | 3.28.12 @ 5:05PM

Have you noticed how frequently the big winners seem to go broke in short order?

Scott| 3.28.12 @ 8:04PM

That's because they let it go to their heads. If I won (as if --hey, wait: my current job ends in May and I don't have another one lined up yet, so I'm sort of in the sob story category) I'd put most of it in savings accounts or CD's. Lousy rate of return right now, but even 0.45% (the return on a 9 month CD at my bank a couple of days ago) would be, what? $4,500 for every million? With 300 million thats about $1.2 million, and I think I could live on that every year without touching the balance.

Oldefarte| 3.28.12 @ 11:54PM

Absolutely, since they have no business education or experience. One doesn't necessarily have to know finance, but simply have the common sense to seek out those professionally qualified to provide honest financial advice and then to follow said wisdom. Unfortionately, most of these lotto winners lose their instant wealth through fraud and manipulative actions of crooks. Sadly, it happens!!!!!!!!!

SCM| 3.28.12 @ 6:17PM

One of our Wisconsin congressmen, Jim Sensenbrenner, (who is already wealthy), has won jackpots three times already. Not the huge ones, but nonetheless, an impressive record.
I say, good for him.

SteveM| 3.28.12 @ 8:00PM

>"people like you [or many of the rest of us] NEVER WIN LOTTERIES. It's always some poor out of luck, unemployed whoobegone individual that always seems to be awarded the prize. "

That's the perception, but I don't know how accurate it is. I have not researched all this in any great depth, but a few seconds on google says that one of the biggest jackpot winners of all time was Jack Whittaker, a businessman in West Virginia. He owned a construction company.

Ross Kaminsky | 3.28.12 @ 9:20PM

I'm guessing the poor people who win make for better news ratings.

Dai Alanye | 3.28.12 @ 4:15PM

"In other words, the possibility, almost no matter how vanishingly small, of winning such an enormous prize makes it worth taking a flier with some modest amount of money."

Pay attention to the foregoing quote, investors, and never, ever let Ross Kaminsky handle your funds, nor take his advice.

This goes double when it comes to electoral matters.

Ross Kaminsky | 3.28.12 @ 5:06PM

You're quite a bitter little person, aren't you?

For the record, I do not have clients and manage nobody's finances but my own.

Furthermore, was it not clear to you that I said that whatever I spent on lottery tickets was almost 100% likely to be completely lost?

You're so humorless, you sound like a liberal.

Dai Alanye | 3.29.12 @ 3:36PM

Kaminsky scores again! An "own goal," as is to be expected.

A. I'm not "little" but all too well fed. Further, my concepts are large -- I contain multitudes.
#2. I'm not "bitter" but a genuine optimist.
Third, I have a keen sense of humor, tending toward irony and satire.
IV: I admit, however, to being a "person."

My problem with the Ross-man is that he says and apparently does so many foolish things, seemingly with little sense of self-awareness. Wasting money on a sure-loser bet like the lottery sets a bad example for the underclass, when he could have donated to his hero, Willard "Mitt" Romney.

[Note: The last sentence is an example of "humor."]

Oldefarte| 3.28.12 @ 11:57PM

Obviously you've never heard or applied the old saying of NOTHING VENTURED, NOTHING GAINED!!!!

Kingofthenet| 3.28.12 @ 5:16PM

Protip: ALWAYS take the annuity, or start a foundation, you will get creamed on taxes if you take a lump sum.

Ross Kaminsky | 3.28.12 @ 5:22PM

But what if you take the annuity and then tax rates go up? If the prize is big, you'll always be in the top bracket. I'd rather take the lump sum, I think.

Rich Rostrom| 3.28.12 @ 5:37PM

What if hyperinflation reduces the effective value of your future payments to nothing? If you take the immediate payout, you can hedge into precious metals and foreign currencies (also, of course, into equities, realty, and so on).

Kingofthenet| 3.28.12 @ 11:39PM

You will always be in the top bracket, but just for example lets talk a 100 million lump sum, 99,900k will be at the highest rate. if instead you took 2.5 million over 25 years(It will be more actually, the full amount) every year you would get some of it taxed at lower rates, with the rest at the highest.It adds up, besides what happens you go nuts, and spend like a crazy person, at least NEXT year you get a check, something to look forward too!

Scott| 3.28.12 @ 7:57PM

I have to think you can get a better rate of return by getting the lump sum and investing it that you could get with the annuity.

TheCoolah| 3.29.12 @ 1:52AM

$10k at 10 to 1? Ross, I enjoy gambling as much as the next man. But this isn't about odds, it's about the size of the pot. Sure, I'd take a flier on a $600m payday. Probably anyone would because the size of the payout is so large that it makes the odds irrelevant.

But your coin flip wager, even at 10 to 1, is ridiculous. I live in Las Vegas, and you can come here any day of the week, pick a number on the roulette wheel, and get 35 to 1 if it hits. You're really going to risk $10k on that?

Jon| 3.29.12 @ 12:35PM

No, Ross' example is a great bet - he's getting a 10-to-1 payout at 2-to-1 odds, which is awesome. The roulette example is a 35-to-1 payout at 38-to-1 odds (assuming an American roulette wheel), which will send you to the poorhouse over the long run.

Mike Stein| 3.29.12 @ 1:00PM

@The Coolah - Statisticians use a term called "expected value." If I get 10-1 payout on a fair coin flip, the expected value of a $1 wager is $5. This is less risky than the stock market. A Las Vegas roulette wheel with both 0 and 00 has a 1 in 38 chance of hitting your number. If it's only paying 35-1, it is a losing proposition in the long run. In order to give the roulette wheel the same expected value as the coin flip, the payout would need to be 190-1.

When the cash value of the jackpot is double the odds of winning the jackpot, the expected value of a ticket is greater than the cost of the ticket. In the long run you will show a profit. The one small flaw in this strategy is that "the long run" is approximately three million years, give or take a million.

TexasMom43| 3.29.12 @ 4:50PM

Have to buy one ticket when the prize is so high. Yes, the odds are terrible but the fantasy is great until the drawing. It's worth a dollar to get such a great day-dream!

Quartermaster| 3.29.12 @ 9:27PM

Ross, please don't say your gong to waste your money. Tell your wife you are going to invest in your retirement fund.

Julie Rovner| 3.30.12 @ 12:51PM

Just googled how realistic of a chance I had of winning. Depressing...www.megamillionssimulator.com

More Blog Posts by Ross Kaminsky

http://spectator.org/blog/2012/03/28/megamillions

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