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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."

24 of 480 comments (clear)

  1. Odds are favorable in a way by Anonymous Coward · · Score: 4, Insightful

    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.

  2. I'll take the wine instead by fish+waffle · · Score: 5, Insightful

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

    1. Re:I'll take the wine instead by GrandCow · · Score: 5, Insightful

      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.

      --
      "Well kids, you tried your best, and you failed. The lesson is, never try." -Homer Simpson
    2. Re:I'll take the wine instead by Anonymous Coward · · Score: 4, Funny

      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.

    3. Re:I'll take the wine instead by j-beda · · Score: 3, Informative

      I think the lottery is a win in general. Yes, you have people who become addicted or can't afford to spend the money, but that's life. On the plus side a lot of people sincerely enjoy playing and much of the cash goes to public works and schools and such. It's practically an optional tax, and the idea of taxes being optional I find fantastic.

      Except for the fact that the lion's share of money raised by the lottery is from people purchasing multiple tickets. And for the fact that money raised by lotteries does not typically add to the tax base, it just allows governments to decrease the amount of money they send to the schools from out of general revenue.

      http://stoppredatorygambling.o...
      "80% of Lottery Profits Come From 10% of the Players"

      http://www.cpjustice.org/stori...

      "...What we found, however, was that lotteries did not enhance the funding of public education. Lottery states actually used a smaller percentage of their wealth for education than did non-lottery states...."

    4. Re:I'll take the wine instead by lucm · · Score: 4, Funny

      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.

      --
      lucm, indeed.
    5. Re:I'll take the wine instead by JaredOfEuropa · · Score: 3, Insightful

      You know the joke about the statistician who tried to cross a river with an average depth of 1 meter (3 feet ish)... and drowned. Just looking at the expected return in lotteries is just as silly, you also have to consider the potential actual return. If you don't believe me, ask the previous Powerball winners. 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.

      People don't gamble for a guaranteed payout of the expected return. If that were the case, casinos would consist only of a teller window where you'd hand in a $100 bill and get $70 in return. People gamble in hopes of being an outlier when it comes to the actual return. Some gamble in small stakes game, for them it's mostly about the thrill of the game itself; most games are more fun when there's actually something at stake, even if it's a candy bar. Others gamble in lotteries, in order to increase their chances at riches from a flat zero to some tiny probability. That's a poor decision only if you look at averages.
      My advise: gamble away, as long as you don't gamble with money you don't have or can't afford to miss, and don't count on a positive outcome. That goes for lotteries as well as insurance (or more accurately: not having insurance)

      --
      If construction was anything like programming, an incorrectly fitted lock would bring down the entire building...
    6. Re:I'll take the wine instead by swillden · · Score: 4, Interesting

      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.)

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      Note to ACs: I usually delete AC replies without reading them. If you want to talk to me, log in.
  3. A tax on stupidity by yelvington · · Score: 5, Funny

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

    1. Re:A tax on stupidity by rmdingler · · Score: 4, Interesting
      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"

      --
      Happiness in intelligent people is the rarest thing I know.

      Ernest Hemingway

    2. Re:A tax on stupidity by Marginal+Coward · · Score: 3, Funny

      Let's assume it's all about the entertainment value of the fantasy of winning. Then, it's perfectly logical: for the same $2, a $500 million jackpot provides 12.5x the entertainment of a $40 million jackpot.

      Or as Dirty Harry might say:

      I know what you're thinkin' - is it 500 million or only 40? You just gotta ask yourself one question: do I feel lucky? Well, do ya' punk?...

  4. I always keep by jd2112 · · Score: 5, Funny

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

    --
    Any insufficiently advanced magic is indistinguishable from technology.
  5. Re: Another silly decision by Anonymous Coward · · Score: 4, Insightful

    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.

  6. Re: Another silly decision by aristotle-dude · · Score: 4, Insightful

    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.

    --
    Jesus was a compassionate social conservative who called individuals to sin no more.
  7. I always keep by Vraylle · · Score: 4, Funny

    Schrodinger's Ticket?

    --
    Mutant Freaks of Nature: "Frighteningly Addictive"
  8. Pure expected value analysis misses the point by Anonymous Coward · · Score: 5, Insightful

    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.

  9. Re:Another silly decision by Obfuscant · · Score: 4, Insightful

    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.

  10. Re:Another silly decision by FlyHelicopters · · Score: 4, Interesting

    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.

  11. A Home Without Equity is Just a Rental with Debt by lucm · · Score: 4, Informative

    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...

    --
    lucm, indeed.
  12. You don't decide, the market does by lucm · · Score: 3, Informative

    According to Numbeo, the buy/rent ratio in Seattle is 10. That'sobscenely expensive (Boston is 3), but that's still pocket change compared to Geneva, Switzerland, where it's 35!!! Look at the numbers, the price *per square meter* in Geneva is 2x the average monthly disposable income.

    --
    lucm, indeed.
  13. Old Joke by R3d+M3rcury · · Score: 3, Funny

    So this woman goes in to church and prays to God.

    "God, you know our situation. My husband is in the hospital. I can't find a job. Our kids are hungry. Our house is in foreclosure. We have no money to pay the bills. Please, God, if you would let me win the lottery, all of our problems would be solved."

    Lottery comes and goes and the woman doesn't win. So she goes back to church and prays again.

    "God, our situation has gotten worse. My husband is home from the hospital but is sick. All of the kids are now sick as well as hungry. The bank says they're going to kick us out of the house. The power and gas have been shut off. Please, God, let me win the lottery so that we can be happy and we will only take what we need to get back on our feet and then donate the rest to the church!"

    Lottery comes and goes and the woman doesn't win. So she goes back to church and prays some more.

    "God, we're in desperate straits. The police have kicked us out of our home. They bank has taken all of our posessions to pay off the debt. My husband and children are living in the park, but the police have threatened to kick us out of there. Please, God, don't forsake us! Help us by letting me win the lottery!"

    Suddenly, she hears a booming voice say:

    "Meet me halfway! Buy a ticket!"

    Thanks. I'll be here all week.

  14. Re:Another silly decision by afidel · · Score: 5, Informative

    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.

    --
    There are 4 boxes to use in the defense of liberty: soap, ballot, jury, ammo. Use in that order. Starting now.
  15. Re:A Home Without Equity is Just a Rental with Deb by swillden · · Score: 3, Informative

    Did you read the report before talking about short-sighted comments?

    For those who don't want to read a 30-page report just to decide if you have a valid point (or if the report you linked is even relevant), I'll provide the summary that you should have provided, and try to guess at the argument you were trying to make (but didn't):

    The report argued (in 2001, before the bubble and collapse) that much of the growth in housing was driven by relaxed lending which allowed more segments of the market to buy homes, and that this growth was driving an increase in prices. It further argued that if we saw a significant economic collapse, particularly a large rise in unemployment, that this effect could collapse.

    Your argument, I presume, is that buying a house is risky because the price could collapse, leaving the borrower "upside down", holding a large debt they can't pay.

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

    --
    Note to ACs: I usually delete AC replies without reading them. If you want to talk to me, log in.
  16. Re:A Home Without Equity is Just a Rental with Deb by werepants · · Score: 3, Insightful

    It's silly to say that it made more sense in the 60's and 70's than today, because nothing about the economics have changed, only the behavior of mortgage holders.

    Even so, whether one is a better decision depends on the interest rates, the length of the mortgage, realtor fees, and what the market is doing. This calculator lets you figure it all out, and is actually a pretty impressive applet in terms of presenting information and allowing you to quickly get a grasp of all the variables in the problem: http://www.nytimes.com/interac...

    The big thing that changes the equation the most IMO is going with a 15-year mortgage. Especially considering that rates are generally 1% lower on the shorter mortgage, it makes a dramatic difference in how your equity builds. For instance, on my home I could've taken a 30-year at 4.75% and paid $1100 a month, with maybe $100 of that going to principal. Instead, I'm paying $1400 a month on a 15-year @ 3.75% interest rate, with $700 going to principal every month. Think of it this way: would you pay $300 a month to get $600 more in equity every month?

    Of course, the scenario changes as you get farther along in the mortgage, but conventional wisdom I've seen says that short mortgages are only for people who are intending to pay off a house and retire in it. Seems to me that short mortgages are best for anybody who doesn't like being a slave to the bank.