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Math The Almighty Buck

The Mathematical Case For Buying a Powerball Ticket 480

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."
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The Mathematical Case For Buying a Powerball Ticket

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  • by Anonymous Coward on Wednesday February 11, 2015 @07:48PM (#49034435)

    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.

    • Actually the odds of you becoming a multi millionaire are significant higher forming a startup.

      There are 300 million people in the us. Statistics wise this means if every man, woman, and child bought a ticket 2 would win with these odds. Ask yourself how many self made millionaires are there? Lots!

    • The math so often quoted most often neglects to include taxes and often a shared jackpot. I always look at the ratio.

      I've done much better in the stock market. Unlike a non winning Powerball ticket, stocks rarely pay zero. If you refuse to sell at a loss, when you don't sell this week, your non winning stock is still in the game.

      I generally play the market for a 2:1 gain. Some stocks haven't doubled yet, but most have.

      Unlike a lottery ticket, none has gone to zero that I have.

  • by fish waffle ( 179067 ) on Wednesday February 11, 2015 @07:48PM (#49034439)
    I still maintain that by not buying a ticket my odds of winning are not significantly reduced.
    • by GrandCow ( 229565 ) on Wednesday February 11, 2015 @08:00PM (#49034547)

      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.

      • by Anonymous Coward on Wednesday February 11, 2015 @08:09PM (#49034633)

        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.

        • This whole topic is really weirding me out. My dad has always said (well, for at least 20 years or so) that he plays the lottery just for the fantasy of winning. In reply, I often make the same lame joke about being almost as likely to find the winning ticket in the parking lot. We're not so clever, me and my dad.

          • by swb ( 14022 )

            I must be as old as your dad, as I don't care for gambling (losing money, really, the games are fun) but I see buying 2-3 PowerBall tickets per year (when the jackpot is big) about like your dad does.

            I'm not buying a chance to win, I'm buying a chance to seriously dream about what I would do with all that money.

            I occasionally enhance it by plugging the expected winnings into a spreadsheet I built that lets me actually "spend" the money to see just how fabulously I could live. My spreadsheet is ridiculously

      • by lucm ( 889690 ) on Wednesday February 11, 2015 @11:03PM (#49035619)

        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.

        • 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.

          Are you daft or making fun at people who are bad at maths?

          So the first ticket means you get 1/2 of the jackpot. The second ticket only adds 1/6th of the jackpot. The third ticket adds the difference between 3/4 and 2/3 which is just 1/12th. The 99th ticket is worth 1/2500th of the first ticket. Your chances of winning haven't grown, the expected winnings have about doubled. For the same money you could have increased your chances of winning by a factor 99.

      • by LWATCDR ( 28044 )

        Your leaving out the entertainment factor.
        One ticket is less than a cup of coffee at Starbucks or a large soda at most restaurants. It is about the same as a song on Itunes.
        So is the fun of possibility of winning several hundred million dollars worth the cost of a cup of coffee?

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

      Precisely true. I've won $175 in lottery money from scratch tickets, but I've never bought one.

      Instead, some of my relatives have taken to giving a few of these as gifts at Christmas. I think it's ridiculous, but whatever. So, over the past few years, I've won something like 5 or 6 tickets for a total of $175, including one ticket that got me $50 and another that got me $100.

      No one else in the family has ever won more than $20-25 on a single ticket, despite some of them buying scratch tickets on a re

    • Old Joke (Score:4, Funny)

      by R3d M3rcury ( 871886 ) on Wednesday February 11, 2015 @11:05PM (#49035623) Journal

      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.

  • by yelvington ( 8169 ) on Wednesday February 11, 2015 @07:49PM (#49034447) Homepage

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

    • by rmdingler ( 1955220 ) on Wednesday February 11, 2015 @08:03PM (#49034581) Journal
      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"

      • by Marginal Coward ( 3557951 ) on Wednesday February 11, 2015 @09:48PM (#49035263)

        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?...

  • by chrism238 ( 657741 ) on Wednesday February 11, 2015 @07:50PM (#49034463)
    Not such a great proposition when you consider that your chance of being killed in a car accident on the way to the store exceeds your chance of winning the big one.
    • Only if you believe that like lotteries, car accidents are purely random events. It's the same reason why the airplane vs car argument doesn't resonate very well. In my vehicle, I am mostly in control of any life threatening event. In a plane or lottery you have zero input.
      • You have the illusion of control, but no actual chance to do anything about a drunk coming into your lane or t-boning you at a red light.

    • by AmiMoJo ( 196126 ) *

      Can't you play online? Most European lotteries allow you to buy a virtual ticket with an online account.

      I've always wondering what would happen if you had a winning online ticket. When you win smaller prizes you get an email saying "we have some good news about your ticket" but not the actual amount. You then log in and see "congratulations, you won â2.50!" Would it just say "congratulations, you won â25,000,000!" or what?

      Normally the money goes into your online account balance and you can withdra

  • I doubt they discount the expected value based on the possibility of a split pot.

    Without knowing how many people are playing this round, you don't have totally accurate estimates.

  • by rmdingler ( 1955220 ) on Wednesday February 11, 2015 @07:53PM (#49034485) Journal
    You are more likely to be struck by lightning twice in your life (100,000,000-1) than hit the six numbers.

    You probably have a better chance being eaten by a polar bear and a regular bear in the same day than winning the big prize on the lotto.

    • In my country there are zero bears (outside a zoo) and zero bear incidents. Yet people are winning lotteries every week. I don't have the figures, but I can't recall people dying each week from lightning strikes either. I challenge your maths.
  • by jd2112 ( 1535857 ) on Wednesday February 11, 2015 @07:53PM (#49034491)
    An unchecked lottery ticket in my wallet. That way i am both potentially broke and wealthy at the same time.
  • I buy tickets for the state lotteries each week. Relatively low payouts compared to Powerball, with a greater (but still infinitesimal, 1:6,000,000 or 1:2,000,000) chance of winning.

    It is entertaining, for an OCD-ish planner like me, to jigger with figures (inflation, taxes) and imagine what kind of lifestyle and payouts to relatives the week's jackpot would support.

    FWIW I'm an extremely aggressive saver, have a rigorous household budget, and live a modest lifestyle; there's a good chance I'll be able to re

  • The odds aren't appreciably closer to zero, the enjoyment is the same or greater, there is no chance of disappointment, and the cost is zero.

    If you invest the $104 a year you'd otherwise spend on lottery tickets then with interest at the end of 40 years (from age 20 to age 60) you will have accumulated about $9K, assuming 3.5% interest.

    • Where does one get those magical 3.5% interest? I wouldn't be surprised if government bonds pay less than that by now.

    • $9k in 40 years will be worth what, $500 bucks in today's money before taxes?
      • by Lumpy ( 12016 )

        Optomist...

        $9,000 US dollars in 40 years will be about $5.00 US value. In fact a large Coffee at starbucks will cost $10,000

  • As many have already pointed out, $2 won't even buy a decent cup of coffee, so most people (or, most people who post here anyway) wouldn't miss it. Regardless of how one might feel about the value received, the investment is pretty much down in the noise.

    But where this can do damage (to anyone, not only the minimum-waged) is the mistaken belief that one can acquire the prize by buying a *whole lot* of tickets. Every once in awhile you hear of people who have hocked their possessions and put every dime the

  • ..floats your boat, go for it. people spend stupider money on "fun".

    absent that type of reason, don't bother rationalizing, there's no rational point in buying lottery what-so-ever.

  • I'm one whose behavoir aligns pretty well with the article. I start playing the lotto when the jackpot gets north of $150 million. Statistically and historically it's wasted money, but I can blow $10 here or there without much consequence. If I saved and invested all the money I wasted on powerball, I'd have maybe $1,000-2,000- not a life changing amount of money for me.

    As I type this, a thought occurs to me- maybe I should double my lotto expenditures- every time I buy lotto tickets I deposit the same amo

  • When it gets over $350 million I spend $20 on 10 tries.

    I read the article, and it is interesting considering what one's initial expenditures would be.

    Of course I don't expect to win, I will check my numbers in the morning.

    I have, luckily, had much better performance with roulette, where I stand at about 300% above where I started all told (under $2000 in earnings total). Good times, I like Vegas every few years...

  • I can't back it up (I've never done that before on /., really) but I read somewhere that your odds of getting killed at the convenience store or on the trip to the convenience store to buy the lottery ticket are greater than your chance of winning the lottery jackpot.

  • If you buy the same powerball ticket after the lottery has been drawn, your chances of winning will go down infinitesimally from 0.5e-06 to 0.0e-06. But the price of the ticket will go down from 1$ to 0$. So it would take mathematical sense to buy the ticket tomorrow. If you really know more calculus you would apply L'Hospital's Rule to resolve the zero by zero division issue.

    Idea stolen from here [dilbert.com]

  • ...Some BS that everyone has read 18 times before.
    Yes, the Powerball is 175 million to 1 against winning, being $15 million or $450 million. The odds don't change. There are only so many numbers.

    But so what? The cost of 'a' Powerball ticket, $2, is trivial. If $2 really makes that much difference in your budget....even $2 a week, every week....then you do not need to do it, whatever the percentages say.
  • I almost never buy lottery tickets but every once in a while when the pot gets big I'll spring for some quick picks on the off chance I'll win. It's money I can easily afford so why not take the chance. Now if I was spending every week on the lottery that would be stupid but every once in a while isn't that big a deal. It's kind of like when I go to Las Vegas and play blackjack. I'll take maybe $250 in to play with and I quit if I loose it all.

    If by some strange chance I do win I'll reserve enough to li

  • by Anonymous Coward on Wednesday February 11, 2015 @08:30PM (#49034791)

    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.

  • If spending $2 on a lottery ticket is so good, why not use every dollar you've got to buy lottery tickets. That will give you a much bigger chance of winning.
  • by g01d4 ( 888748 ) on Wednesday February 11, 2015 @08:39PM (#49034857)
    Mathematical case implies a relation to the probability of winning which is definitely not the case here. What's really meant is that there's a utilitarian [wikipedia.org] case that, w/the usual hand waving, you can apply some dollar value to.
  • Yes, the odds of winning are 1/175M. But the odds of winning without a ticket are exactly zero, which is inifnitely smaller than 1/175M. Also, they run these lotteries until someone wins, which means SOMEONE has to win. That someone could be you if you buy a ticket. It CAN'T be you if you don't.

    Me? I never buy lottery tickets. My life is pretty good. Not wealthy, but rich.

    RS

  • because it gives the working class a false sense of hope. It's a buffer. A fake safety net that keeps the poor from asking too many questions about things like wealth inequality and declining wages. We do similar things with racism and classes/casts. And before anyone asks, yes, I am comparing racism and the lottery. From the ruling classes standpoint they serve the same purpose. Distractions to keep plebs us from asking for things like stable incomes and health care. Maybe it's not like this in the rest of
  • by geantvert ( 996616 ) on Thursday February 12, 2015 @06:20AM (#49036921)

    3, 33 or 333 millions. Would that make any difference? I don't think so.
    It you want to calculate the expected gain then you should only consider the useful gain.
    For me, 1 or 2 millions would be enough for the rest of my life so if I had to choose a lottery, I would pick one that maximize the probability to gain that amount. Any lottery with a smaller maximal gain (e.g. a few millions) but a higher probability is a better choice.

  • by gurps_npc ( 621217 ) on Thursday February 12, 2015 @10:16AM (#49038067) Homepage
    Look, when the jackpot gets very high, then it becomes an actual investment.

    If the odds are 1 in 175 million, then a $2 breaks even when the after tax, instant profit exceeds $350 million. In this particular jackpot was $564 million. Instant payment of $381 million. Now, taxes (and the chance of splitting it with others) makes this not a real investment, but it got pretty darn close.

    But if the jackpot got to say $800 million, buying a ticket becomes a mathematically good bet.

    But there are other things going on. Honestly, if you hit the jackpot for anything over 20 million, it won't make that much of a difference. It will radically change your life in pretty much the same way. Most likely you will gain somewhere between six months to one year of happiness, a year or so of realizing that things are going poorly and then the rest of you life with a CRAPLOAD of depression and anger about how everything went to hell.

    Why? Because if you gain something too quickly and easily, you neither value it nor do you know how to maintain and keep it.

    Chances are very high you will want to help out a few people you know that really need it, which will cause a bunch of people that don't really need it to come begging for help. If you turn them down, suddenly your friends turn on you. If you don't turn them down, suddenly you are broke.

    Your leisure activities will dramatically change and your friends won't be able to afford to go with you unless you pay for them. Which turns the relationship from friends to hanger-ons. It's hard enough to keep family from disintegrating, let alone your friendships.

    Honestly, my advice to anyone that wins is to REFUSE TO TELL ANYONE YOU WON. At most, tell them you won a smaller amount. Don't sign anything giving up your privacy, instead keep it a secret from EVERYONE you are not married to. Set up a Trust that will anonymously help people you think truly need it, and do NOT take credit for it.

    You can't 'bring your friends' along for the lifestyle, but you can occasionally show them a fantastic time.

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