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

Odds are favorable in a way

[Anonymous Coward]

My odds of winning may be 1 in 175 million, but my odds of getting $337 million dollars any other way are 0 so it's not that bad.

Sure if I work hard and invest right I can earn a few million, but 175 million is just not going to happen any other way. I'm willing to spend a couple of dollars for that slim chance.

I'll take the wine instead

[fish waffle]

I still maintain that by not buying a ticket my odds of winning are not significantly reduced.

Re:I'll take the wine instead

[GrandCow]

Incorrect. Buying a *single* ticket is worth it, since it puts you on the playing field at least. It's buying 2+ tickets that aren't worth the money, Every ticket after the first raises your chances by such an incredibly small amount that it's not worth it. The first ticket raising your chances above a flat zero is worth it though.

Re:I'll take the wine instead

[Anonymous Coward]

Not buying a ticket alone does not leave your chances at zero. There is a miniscule probability that the winning ticket will be dropped in a parking lot and a non-purchaser will find it and claim the prize. The only way to make your probability zero is to not buy a ticket AND ignore all tickets found in the parking lot.

Re:I'll take the wine instead

[lucm]

It's buying 2+ tickets that aren't worth the money,

Unless you buy 2 tickets with the same numbers. Which could make sense because if someone else has the same numbers you will get 2/3 instead of 1/2. Even better: buy 99 tickets with the same numbers. Just the face of that other dude who ends up winning 1% of the jackpot would be well worth the $198 investment.

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.)

A tax on stupidity

[yelvington]

I figure the lottery is a tax on stupidity. And if it goes to $500 million I'm easily ten bucks' worth of stupid.

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"

I always keep

[jd2112]

An unchecked lottery ticket in my wallet. That way i am both potentially broke and wealthy at the same time.

Re: Another silly decision

[Anonymous Coward]

Indeed. And our apartment was raising the rent by $150. So we found a house, and are now paying $100 less (after mortgage and escrow) each month, plus the enjoyment of simple things like being able to paint or remodel, and plant a garden or have a bonfire in the back yard. Seems like a solid choice despite the social contract.

Re: Another silly decision

[aristotle-dude]

Definitely a good option in your case. In ours, we found a townhome that allows us to paint and do limited remodeling, and plant a garden. And if anything major goes wrong, we don't have to foot the bill. Oh, and there's rent control on the entire complex, so raising the rent is indexed against property taxes (meaning property tax would also be going up like this).

Other than as a financial investment, I really can't see the reason for buying a condominium though -- you pay just as much, and own no land (but still have conditions you must agree to about property use).

I'd buy land in a rural area if I could afford to live there -- but that's what retiring people tend to do, and it's bumping up the land value pretty much everywhere as the boomers retire.

The big difference between renting and buying is that instead of throwing away money to pay someone else's mortgage, you are building equity in your own property. You do "own" a portion of the strata if you bought a "freehold" instead of a "leasehold". The latter is rent free for a period that is usually 99 years and after that date, you lose whatever value you had and have to enter into a lease with the land owner.

I always keep

[Vraylle]

Schrodinger's Ticket?

Pure expected value analysis misses the point

[Anonymous Coward]

The expected value of a gamble being positive does not necessarily mean it is a good idea for a limited human.

Consider, for example, a lottery which cost $50K to enter, and returned 10e80 dollars with probability 1 in 10 billion.
Expected value dictates that it's an absolute home run, but 99% of individuals would not take that bet, because with near-certainty it will bankrupt them.

Similarly, for most, a $1 bet for a $1M jackpot with 1 in 1.1 million odds (e.g. negative EV) is better than a $1 bet for a $10M jackpot with 1 in 9.9 million odds (e.g. positive EV).

Why? Because of the nonlinear value money has to an individual.

Re:Another silly decision

[Obfuscant]

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

If you think that rental rates don't include the taxes and maintenance, you're naive.

And in many areas, house prices go down. So when you buy a house for an investment, you are really speculating

The question is not one of absolute values but of relative. "Buy instead of rent", not "buy for investment". When you leave a house, even if the value goes down, you still likely have some equity. When you rent you walk away with nothing.

The OP was saying that he was buying not for the investment but because he could install air conditioning and a hot tub even if he couldn't get his money back on them when he sells. He won't get his money back on them when he rents, either, so what's the reason to buy?

Yes, I know everyone in the media and our politicians calls home ownership an investment, but they are wrong. 2008 proved that.

2008 proved that people who bought houses they couldn't afford lost money. My house has doubled in value. When my bank offered me two options (fixed and ARM) I opted for the one I could afford. That meant looking five years down the road and seeing the balloon. There was no gun held to my head to pick the wrong option.

The people making money or I should say, making the decent returns, on your house are the banks.

Why yes, they make money off the loan (as they should -- they take a risk loaning money and they don't have it until I pay it back), but I will still have a good chunk of change should I ever decide to sell. Not as much money as I spent total, but nothing to sneeze at. And at no point in my loan was I ever upside down, simply because my eyes weren't bigger than my stomach.

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.

A Home Without Equity is Just a Rental with Debt

[lucm]

The big difference between renting and buying is that instead of throwing away money to pay someone else's mortgage, you are building equity in your own property.

This was common sense in the 1960s and 1970s. Now with debt consolidation, second/third mortgages and other similar schemes, home equity is frequently tiny or illusory.

there's an excellent report on this matter that was published more than 10 years ago.

A Home Without Equity is Just a Rental with Debt:
http://papers.ssrn.com/sol3/pa...

Re:Another silly decision

[afidel]

The CRA did NOT cause the financial crisis! This has been debunked many times. In fact in ~75% of communities CRA loans had lower default rates through late 2009 than traditional conforming loans (let alone crap like interest only, sub-prime, and liar loans) due to more stringent underwriting criteria. No, the cause was improperly rated securities comprised of crap that was sold in bundles to the big banks and through the back door to Fannie and Freddie.