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
Mar '12

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

 dittoheadadt: 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. · 42 minutes ago

A roll-over would be very cool.  If people are going nuts over \$640m imagine a prize over \$1 billion.  That's government-scale numbers!

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

I saw this on the Facebook Wall of a friend of mine.  Clever.

Joined
Aug '10

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

To understand why people buy lottery tickets (and why poor people tend to buy more lottery tickets), you can't just look at mathematical expectation - you have to look at the utility of money.  Utility theory says that as you gain dollars, the marginal value of each new dollar changes.  Not only that, but the utility of money is situational.

For example, let's say that my rent is \$500, and I have \$450.  If I don't come up with \$50, I will be evicted.  So along comes a gambler who offers to flip a coin with me - Heads, he gives me \$50.  Tails, I give him \$60.  From an expectation standpoint, this is a terrible bet for me to take.  But the utility of winning \$50 is much greater to me than the utility of losing \$60, because if I lose I'm evicted regardless of whether I lost \$20 or \$450, but if I win I get to stay in my home.

So, the bet has positive utility even if it has negative expectation, and I'd be smart to take it if I had no other way of raising the money.   The lottery is no different.

Joined
Aug '10

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

 Mark WilsonKind 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."

I've always thought, though, that if the drunk isn't sure that he dropped his keys in the alley -- he thinks he did, but there's a chance they could be elsewhere, like under the street lamp  -- then starting his search under the street lamp might be a good idea. It could be the easiest place to eliminate from the search.

Joined
May '10

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

 Mark WilsonKind 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."

I've always thought, though, that if the drunk isn't sure that he dropped his keys in the alley -- he thinks he did, but there's a chance they could be elsewhere, like under the street lamp  -- then starting his search under the street lamp might be a good idea. It could be the easiest place to eliminate from the search. · 3 minutes ago

What?!  A mathematician speaking practically?!

Joined
Aug '10

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

Mark Wilson

 Midget Faded RattlesnakeI've always thought, though, that if the drunk isn't sure that he dropped his keys in the alley -- he thinks he did, but there's a chance they could be elsewhere, like under the street lamp  -- then starting his search under the street lamp might be a good idea. It could be the easiest place to eliminate from the search.

What?!  A mathematician speaking practically?!

Well, this mathematician has lost so many keys that she became an expert at jimmying locks and forcing windows.

Never quite had the patience (or need) to learn to pick a deadbolt, though. Though I knew a chemist who did, and for the same reason.

Joined
Oct '10

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

Numbers are in, I'm hoping for a rollover.

2, 4, 23, 38, 46  with Megaball 23

Joined
Mar '11

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

I've changed my mind... playing the lottery is stupid.

### 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. · 22 hours ago

Well, it can actually be quite frustrating. Though not as frustrating as what a friend of mine has to go through. Her husband is a saint. He always treats her perfectly. She wants just once to be able to be righteously indignant about his behavior or attitude and she's still waiting after 45 years of marriage. What's funny about this is that she's actually not joking -- it really, truly is difficult to be married to someone so perfect. Although it always makes me laugh when we discuss.

Joined
Aug '10

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

Apparently there were three winning tickets.

I bet those three people are really upset that they're oh so bad at math.

Joined
Mar '11

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

Mollie Hemingway, Ed.

 Severely Ltd.:

What's funny about this is that she's actually not joking -- it really, truly is difficult to be married to someone so perfect.

Yeah, my wife has a hard time with it too.

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