This week's fight at the Hemingways has been about whether to buy a Megamillions ticket. My view is that Lotto is a tax on people who don't understand statistics. His view is, and I quote, "Come on! It's over \$500 million! I had an uncle who won the lottery once."

It will not surprise you that my background is in math and his is in wishful thinking. (I kid because I love. And also because he is literally right about everything ... except this.)

I come from a long line of fighting about gambling. See, my dad is a pastor and really sees no moral value in gambling. My mom views it like others might view any other entertainment expense. You might spend \$100 a year on going to movies. When she's in Vegas, she plays a roll of quarters on the slots and stops when she runs out of money or time.

But I'm curious if we reach a point where the risk of reward makes the purchase of a ticket more reasonable. Scientific American says "No Matter How Huge, Mega Millions Jackpot Will Always Be a Bad Bet."

The prize is so high it exceeds the number of possible number combinations on a ticket, which is about 176 million. (In other words, the chance that any particular ticket is a winner is about 176 million to one.) The math seems to imply that a \$1 ticket has an expected value of \$500 million divided by 176 million, or nearly \$3. Yet a closer look at the math reveals that the Mega Millions jackpot is a bad bet no matter how large the prize. ...

Certainly, the threat of having to split is there, but does that really make it a bad bet—especially when the jackpot is so very high? According to the mathematicians, yes. As the number of tickets sold goes up, the chance that more than one person will share in the jackpot does as well, according to a well-known mathematical function called a binomial distribution. When Emory University mathematicians Skip Garibaldi and Aaron Abrams worked through the equations, they found that lotteries are generally a terrible bet—Mega Millions and Powerball particularly so. (I encourage you to take a look at their paper “Finding good bets in the lottery, and why you shouldn’t take them,” which was published in the American Mathematical Monthly in 2010.)

Even in the case of the current drawing, which offers a jackpot so large that Garibaldi and Abrams show how it should only occur on average every 22 years, the number of tickets that go out is correspondingly large. “I ran the numbers last night,” Garibaldi told me over the phone. “You can tell by the amount they estimate the jackpot to be what they estimate the ticket sales to be.” Based on the current jackpot, an estimated 380 million tickets have been sold this week. The estimated return on an investment of this week’s Mega Millions drawing? Negative 19 percent, per his calculations.

I wonder if there's a simply way to figure out when the estimated return on investment is not negative. Either way, considering the economic situation of our family and our country, I think our "win the lotto" retirement plan might be the best bet we have.

Joined
Sep '11

### Re: At \$540 Million, Is Lotto Still A Tax On People Who Don't Get Math?

If the buck is basically meaningless to you - then it actually makes sense to buy a ticket. It might not add up mathematically, but it can still add up personally.

Joined
Aug '10

### Re: At \$540 Million, Is Lotto Still A Tax On People Who Don't Get Math?

Whiskey Sam

 Whiskey Sam: I find it ironic that people who kick and fuss about government taxes being too high willingly hand over even more of their money to that government on an ill-advised get rich quick scheme that preys on the ignorance of the innumerate and the poor.

Hey, at least lotto tickets are voluntary. Taxes are coerced.

Just because someone's stupid does not mean we should encourage the government to take advantage of it.

Hey, just trying to look on the bright side.

Joined
Aug '10

### Re: At \$540 Million, Is Lotto Still A Tax On People Who Don't Get Math?

 Severely Ltd.:You claim (admit?) that this is the only thing your husband is wrong about?! That man hit the jackpot when he married you, Mollie.

Mmm-hmm.

Joined
Jul '10

### Re: At \$540 Million, Is Lotto Still A Tax On People Who Don't Get Math?

 RB: Well, there's that age-old saying about the lottery:Someone's going to win, and it won't be you.· 31 minutes ago

Joined
Oct '10

### Re: At \$540 Million, Is Lotto Still A Tax On People Who Don't Get Math?

George Savage

 Mollie Hemingway, Ed. Certainly, the threat of having to split is there, but does that really make it a bad bet—especially when the jackpot is so very high? According to the mathematicians, yes. As the number of tickets sold goes up, the chance that more than one person will share in the jackpot does as well, according to a well-known mathematical function called a binomial distribution. · · 3 hours ago

Does this mean that my plan to borrow \$175,711,536 and play every possible combination won't guarantee me a profit?  Rats. · 17 minutes ago

Edited 17 minutes ago

Not only will it not guarantee a profit -- it's also physically impossible to accomplish the task of buying tickets with every possible number combination (which would have to be manually entered) from various outlets with limited ticket supplies in the few days between drawings.

Learned that one the hard way.

Just kidding.

Edited on March 30, 2012 at 8:42pm

Joined
Aug '10

### Re: At \$540 Million, Is Lotto Still A Tax On People Who Don't Get Math?

Great article from Lileks on this subject.  Money quote;

The Mega Millions website asks "What's Your Dream?" and the first one that pops up is "Saving for Retirement." The odds of winning the jackpot are 1 in 175 million. Buying lottery tickets to prepare for retirement is like burning a bushel of dollar bills to reduce your winter heating bills.

Joined
Mar '12

### Re: At \$540 Million, Is Lotto Still A Tax On People Who Don't Get Math?

If it isn't affordable entertainment, then it's wrong.  But it can be entertainment, and that is a legitimate purchase.

Joined
Oct '10

### Re: At \$540 Million, Is Lotto Still A Tax On People Who Don't Get Math?

 Frozen Chosen: Great article from Lileks on this subject...0 minutes ago

That old curmudgeon?  Optimism is James's kryptonite.

Now I'm off to buy more lottery tickets...because my kryptonite is rationality.

Joined
May '10

### Re: At \$540 Million, Is Lotto Still A Tax On People Who Don't Get Math?

My office has a pool.   Many of us kick in only because there is some microscopically infinitesimal chance that they *might* win and anyone not in the pool will be left on Monday morning to do all the work and recruit the replacements.

We consider it a job creation plan  - 30+ potential openings - with as much chance for success as  ... investing in near bankrupt solar panel companies.

Joined
Apr '11

### Re: At \$540 Million, Is Lotto Still A Tax On People Who Don't Get Math?

While some people would find great satisfaction in dismantling the fortune of a disgustingly wealthy individual and doling it out in tiny parcels to everyone...nobody would stand for the opposite redistribution of wealth: Taking tiny bits from everyone to create one brand new fabulously rich individual.   And yet...

Joined
Mar '12

### Re: At \$540 Million, Is Lotto Still A Tax On People Who Don't Get Math?

I know they say that money can't buy happiness, but winning this prize would give me a chance to try and prove the saying wrong.

Joined
Aug '10

### Re: At \$540 Million, Is Lotto Still A Tax On People Who Don't Get Math?

 Frozen Chosen: Great article from Lileks on this subject.  Money quote; The Mega Millions website asks "What's Your Dream?" and the first one that pops up is "Saving for Retirement." The odds of winning the jackpot are 1 in 175 million. Buying lottery tickets to prepare for retirement is like burning a bushel of dollar bills to reduce your winter heating bills.

In case anyone's wondering... a single dollar bill has about 12.44 BTU, with a lot of assumptions for an idealized physical setup to capture all the energy.   This compares with 1,015 BTUs in a cubic foot of natural gas, 91,700 BTUs in a gallon of propane, and 3,413 BTUs in 1 kW of electricity.

To raise the temperature 10 degrees in a 10x10 room, using a rough heating calculator, it would require burning roughly \$402 in dollar bills every hour.  Or \$8040 in \$20 bills, or \$40200 in \$100 bills. [edited to fix copy/paste errors in calculations]

Those lottery tickets are starting to look like a better investment all the time...

Edited on March 30, 2012 at 10:24pm

Joined
Oct '10

### Re: At \$540 Million, Is Lotto Still A Tax On People Who Don't Get Math?

No more than buying a movie ticket is a tax on people who don't get math (buying that movie ticket isn't going to make you rich).

No more than going to DisneyWorld is a tax on people who don't get math (going to Disney isn't going to make you rich).

Entertainment dollars are spent in myriad ways.  Lottery tix are taxes on the math-challenged only if they expect it to be their income or retirement plan.

For everyone else, it's just entertainment dollars.  Why is that seemingly so hard to grasp?

Joined
Oct '10

### Re: At \$540 Million, Is Lotto Still A Tax On People Who Don't Get Math?

 Christopher Bowen: It is also surprising how so few people seem to understand that picking 1-2-3-4-5-6-7 is just as likely to win as any other combinations. · 2 hours ago

Or how many think getting a quick pik gives them a better chance than picking the numbers themselves...or vice versa.

I once got a quick pik that was 32-33-34-35-36.

Joined
May '10

### Re: At \$540 Million, Is Lotto Still A Tax On People Who Don't Get Math?

 Mollie Hemingway, Ed.I wonder if there's a simply way to figure out when the estimated return on investment is not negative.

Expected return on investment is not always a useful concept.

Joined
May '10

### Re: At \$540 Million, Is Lotto Still A Tax On People Who Don't Get Math?

 Christopher Bowen: It is also surprising how so few people seem to understand that picking 1-2-3-4-5-6-7 is just as likely to win as any other combinations. · 2 hours ago

If more than one person believe this, you would have a greater chance of having to split that jackpot than one where you selected the numbers randomly.

Kind of like asking the drunk why he's searching for his keys under the street lamp when he dropped them in the alley.  "The light's better over here."

Edited on March 30, 2012 at 9:35pm

Joined
Oct '10

### Re: At \$540 Million, Is Lotto Still A Tax On People Who Don't Get Math?

I don't know about the rest of you, but I love seeing one-ticket winners of these big jackpots.  Here's hoping for another one-ticket winner...or a rollover.

Joined
May '10

### Re: At \$540 Million, Is Lotto Still A Tax On People Who Don't Get Math?

 Severely Ltd.:Your husband's uncle won the lottery. What are the odds of two people in an extended family hitting the jackpot?

A professor of basketweaving was traveling by air to a conference.  He had never flown before out of a terrible fear that the airplane would be blown up by terrorists.

When he got to the security checkpoint, his luggage set off all the alarms and he was taken to the back room for questioning.

"We found a bomb in your luggage.  What do you have to say for yourself?" asked the interrogator.

"I can explain," said the professor.  "You don't have to worry, I was not going to blow up the plane."

"Then why did you try to bring a bomb on board?" asked the guard.

"My friends told me not worry, the chances there is a bomb on the plane are 1 in a million.  So what are the chances there are two bombs?"

Edited on March 30, 2012 at 9:55pm

Joined
Aug '10

### Re: At \$540 Million, Is Lotto Still A Tax On People Who Don't Get Math?

 Not only will itnotguarantee a profit -- it's also physically impossible to accomplish the task of buying tickets with every possible number combination (which would have to be manually entered) from various outlets with limited ticket supplies in the few days between drawings.

It's not impossible - just really hard.  And when jackpots get high enough, you can sometimes find situations were buying all the tickets will guarantee a profit, or at least make it highly unlikely that you will share with so many people that you won't make a profit.

There was an Australian syndicate that did just this - watched for lotteries where the jackpot went high enough to be statistically very likely to generate a profit if all ticket combinations were chosen.  Then they would send teams of people into the region to buy as many tickets as they could.  They did this with a U.S. state lottery, but the logistics of buying all the tickets got the best of them and they only managed to purchase something like 60-70% of all ticket combinations before the deadline.  Nonetheless, they won the lottery and made a huge profit.

Joined
Dec '11

### Re: At \$540 Million, Is Lotto Still A Tax On People Who Don't Get Math?

Who says people are risk-neutral?  A lottery ticket could be a good investment for a particularly risk-loving individual.

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