The Mathematical Case For Buying a Powerball Ticket

HughPickens.com writes Neil Irwin writes at the NYT that financially literate people like to complain that buying lottery tickets is among the silliest decisions a person could make but there are a couple of dimensions that these tut-tutted warnings miss, perhaps fueled by a class divide between those who commonly buy lottery tickets and those who choose to throw away money on other things like expensive wine or mansions. According to Irwin, as long as you think about the purchase of lottery tickets the right way — purely a consumption good, not an investment — it can be a completely rational decision. "Fantasizing about what you would do if you suddenly encountered great wealth is fun, and it is more fun if there some chance, however minuscule, that it could happen," says Irwin. "The $2 price for a ticket is a relatively small one to pay for the enjoyment of thinking through how you might organize your life differently if you had all those millions."

Right now the Multi-State Lottery Association estimates the chances of winning the grand prize at about 1 in 175 million, and the cash value of the prize at $337.8 million. The simplest math points to that $2 ticket having an expected value of about $1.93 so while you are still throwing away money when buying a lottery ticket, you are throwing away less in strictly economic terms when you buy into an unusually large Powerball jackpot. "I am the type of financial decision-maker who tracks bond and currency markets and builds elaborate spreadsheets to simulate outcomes of various retirement savings strategies," says Irwin. "I can easily afford to spend a few dollars on a Powerball ticket. Time to head to the convenience store and do just that."

Comments

Re:A tax on stupidity

[rmdingler]

I am constantly amazed by the difference in people's interest in the lottery when the jackpot is $500 million instead of $40 million.

"Shoot Honey, after taxes, forty million wouldn't make a dent in our lifestyle"

Re:Another silly decision

[FlyHelicopters]

And in the meantime you are shelling out for taxes, maintenance, and being rooted in one area.

Those are included in rent as well, just not broken out as line items, but they are there.

So, for a single family home that you live in, it is an expense. Yes, I know everyone in the media and our politicians calls home ownership an investment, but they are wrong. 2008 proved that.

It is both actually... the trick is not to move every 5-7 years...

I've been in my home for 10 years, at my current rate of payments, my mortgage will be paid off in the next 6 years. I'm not paying anything more per month than local rents for the same size house would cost, yet in 6 years, I'll own a $400k house free and clear.

That strikes me as an investment. Per month, I'm paying $3,000 including PITI and some extra towards principle. That $3K is about what the same house rents for.

Now it is true that I have to do repairs, replace the HVAC and water heaters, both of which I've done... but those rather pay for themselves when you're willing to buy the good units. My HVAC replacement was just over $17K for a pair of units (3,800sqft, so a 5 ton and a 3 ton unit). However they replaced a 15 year old 13 SEER single stage unit with a 16 SEER dual stage, dual speed unit. The savings in my electric and gas bills over 10 years makes the replacement free, vs. keeping the older units. Had a landlord done it, do you really think he would have put in such nice units into a rental house that he isn't paying the bills on?

Your equity? Let's put it this way, if Congress ever removes the mortgage interest deduction, attitude about homes being an investment will change. The people making money or I should say, making the decent returns, on your house are the banks.

Meh, at current rates, it isn't that big a deal... it is mostly in people's heads...

My current mortgage is 3.5%. The annual interest is less than $10K. It is a deduction, not a tax credit, so my actual savings from it is about $2,500 in taxes, give or take a few hundred. It is nice, but not the reason to own a home.

We have been programmed in our society to take on debt: cars, houses, education, etc ... And our tax system has also distorted how we "invest" our money.

Cars and education I agree with you, to a point... A car can be an investment if it lets you get to work. Leather seats and a V8 are not required for that however, those are luxuries.

Education? That can be an investment, if you pick the right major and go to cheaper schools and don't rack up stupid loan amounts.

Both can also be bad... it just depends...

Debt is a wonderful thing, if it makes you money, which it can... I've financed equipment and inventory purchases before and earned back many times the cost of debt. That is "good debt".

Putting a trip to Europe on the Visa that you can't pay at the end of the month? That is "bad debt".

It isn't complex, but debt can be both good and bad, depending on what it is used for.

Re:Another silly decision

[Obfuscant]

Under a "normal" system, the 2008 housing crisis should have caused all the banks holding the loans to go under. The threat of this happening is what is supposed to prevent the banks from making risky investments in the first place.

That's true. But the banks weren't allowed to properly evaluate the risks.

In this scenario, where you are essentially gambling with someone else's money (i.e. the tax payers)

Yes. And that's fair since it is the representatives of the taxpayer who forced the banks to ignore the risks and make the loans anyway. The Community Reinvestment Act was a legislative act that forced banks to make loans despite well-known and patently obvious risks. When a bank was required to include things like unemployment payments and ignore past credit histories when deciding which loans to approve (and how much money could be loaned), then those who forced the high risk loans should be the ones responsible when they fail.

That the "community activists" (ACORN, PUSH, etc.) jumped on the CRA bandwagon to threaten banks that didn't make enough risky loans with legal action is still a side-effect of the legislative regulations that our politicians enacted. Their actions led to the collapse. Be angry at them, not the people they forced to make the loans.

Read "Architects of Ruin" by Peter Schweitzer. It will open your eyes.

but get to keep the profits, the best move is to be as risky as you are able to get away with. In this light, the risky behavior of the banks makes a lot more sense.

Of course, businesses are in business to be as risky as they can get away with. Businesses that don't take risks don't remain in business -- the risk takers come eat their lunch. Heck, business that don't take risks don't become businesses in the first place.

But as ibid talks about, the environment of early bailouts was a contributing factor to the problem, but not the proximate cause. The fact that the US bailed out MEXICAN banks is, once again, a legislative failure that led to the collapse.

Re:I'll take the wine instead

[swillden]

You have insurance? Same thing: the expected return on insurance is also negative (insurers need to make a profit somehow, after all), and based on that value it seems silly to have it... until you ask the owner of the uninsured house that burned down.

Red herring. The expected value of your insurance is fairly close to its cost. More importantly, if the probability that your insurance would have to pay out were astronomically low, it wouldn't, in fact, make sense to buy insurance. But it's not. The probability that something will happen that causes you to need that insurance is non-negligible.

With that said, I find this conversation funny because both sides are ignoring the whole point of the article, which is that even if the cost of the lottery ticket exceeds its expected value (and it usually does), and even if the odds of winning are so small as to be negligible (for big prizes they always are), the lottery ticket often has net value for its worth as entertainment.

It's fun thinking about what you'd do if you suddenly had $200M. Really, it is. I can entertain myself for hours just thinking about strategies to manage it that wouldn't ruin my life by causing people to hound me for money, and yet still allow me to do the things that I want. I can do that (and sometimes do) without actually buying a lottery ticket, but paying the $2 for a ticket makes it dramatically more intense, and therefore entertaining. I don't buy many lottery tickets; I've probably purchased two or three in the last twenty years, but I've always felt like I got good value from them.

(Now we'll see if my AC stalker crapfloods responses to this post.)