A football field covered with M&M’s says don’t waste your money playing the lottery

| September 19, 2007 | 58 Replies

I’m sure you’ve seen the photos of many of those many delighted lottery winners! Yes, they do exist. 

As we all know, though, winning the Powerball requires a lot of luck. For every smiling winner there are millions of people with nothing to show for their money. 

How much luck does it take to win the lottery?  According to this Powerball site, the odds of picking all six two-digit numbers correctly is one chance in 146,107,962. This is bleak, but how bleak?  Some state lotteries show you how to do the mathematics, but I doubt that this complicated math can counteract the heavy advertising done by the lotteries–advertising that takes advantage of widespread innumeracy. How can the small chance of winning the lottery be conveyed in a visual and understandable way? 

I decided to use plain M&M’s (not peanut) and a football field for my thought experiment.  I didn’t really do this demonstration, but you could.  If you’d like to do it, just go out and buy 146,107,962 M&M’s.  Instead of actually buying the M&M’s, I used mathematics.

I decided to allow all six lottery numbers to serve as the coordinates for ONE M&M in a big pile of M&M’s.  I started by wondering whether 146,107,962 M&M’s might cover a football field (the field between the goal lines, not including the end zones).  A football field, between the goal lines measure 300 ft long x 160 feet wide = 48,000 square feet.  That equals 6,912,000 square inches.  Based on my experiments with M&M’s at home, I found that 17 M&M’s will cover about 3 square inches. 146,107,962 M&M’s would thus completely cover three football fields, from goal line to goal line.  

So . . . here’s the proposition.   Assume that ONE M&M was painted silver and mixed into the M&M’s that covered 3 adjacent football fields that had been completely covered with M&M’s. Then assume that a lottery company allowed you to pay $1 to walk out into those 3 huge fields blindfolded to pick up only one M&M with a tweezer–the silver one.  Would you do it, or would you rather keep your dollar?  Or how about this option:  would you scoop up one liter of M&M’s (enough to fill about one quart, which you could do by scooping up a bit more than a square foot) for $549?

BTW, I refered to this site to determine how many M&M’s there are in a specific volume.  It turns out that one liter (which is a little more than a quart) of M&M’s is about 1098 M&M’s.

This thought experiment helped me to understand the low odds of winning the lottery, but I’m curious.  Would this visual have the power to cure anyone else of the urge to spend their hard-earned money on the lottery? Could this serve as an “anti-lottery ad”?

If none of this cures you of the urge to play the lottery, consider this: coming into large sums of money will only temporarily change your happiness level. 


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Category: American Culture, Statistics, Whimsy

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  1. Dan says:

    I do win the lottery – the profits pay for my college.

    So by all means, the rest of you please keep playing, and I'll reap the benefits.

  2. Kevin says:

    Here's the thing:

    Yes: It is basically pointless to buy a lottery ticket.

    But that's not really what you're paying for. Think about it.

    When you buy a lottery ticket, you're paying for a fantasy. Between the time of buying the ticket and checking the numbers (and finding out you've lost) you get to fantasize about what you'd do with the money if you'd won, where you'd travel, what you'd invest in, who you'd help out, etc.

    All you have to do is pay a dollar and you get a few days to feel hopeful and fantasize. Then you lose and you pay another dollar and get to keep doing what you were doing before.

    Cheap hope is pretty hard to come by, after all. It might ultimately be naïve to buy lottery tickets of any form, but you could do worse. You could be spending your money on crack or PCP, for instance.

    And anyways, it's only a dollar. I'd pay a buck for hope–even the cheap, far-fetched kind.

  3. Erich Vieth says:

    Kevin: I largely agree with you. Playing the lottery can be a "cheap hope." I probably buy a lottery ticket once per year. I don't expect to win, but it is fun to bring it home and let the kids scratch it off. Truly, I can't think of any significant problem with this approach. It's morally no different than blowing a bit of money on any other form of entertainment.

    There are some people out there for whom hope is not so cheap, however, because they buy LOTS of lottery tickets when they can't really afford any.

  4. Vicktor says:

    There is another statistic to consider:

    The odds of winning are 0% if you don't buy a ticket

  5. anti-supernaturalist says:

    ** Brother can you spare a buck?

    The probability of winning the jackpot isn’t enough to declare every lottery game irrational. You need to consider the probability of winning multiplied by the “real” payout — in other words the expected value of the real payout.

    Sure it's rational to play: when the expected value of the real payout = $1. I assume that the player is risk neutral.

    Now assuming that you want "the real" payout to be a lump sum cash-in-hand less taxes, the nominal jackpot must grow to cover discounted cash flows (present value) and those pesky government tax predations.

    Once the *nominal payout* becomes very large, people flock to buy tickets. Thereby moving towards rational behavior in a game usually for dupes only.

    A state lottery board could use dynamic pricing — when the expected value of the *nominal payout* falls below $1, lower the price of each ticket so that it continues (more) rational to play. But, of course, the state bets on irrational behavior and usually wins.


  6. Kristy Wendt says:

    My boyfriend bought a scratch-off ticket a couple of days ago for one dollar. We scratched off three dog paws in a row, won ten dollars, and ordered crab cakes with dinner. My initial inclination when he'd asked for a dollar to buy the ticket was to yammer off the one about the statistical likelihood of being struck by lightening versus that of actually winning something in the lottery. I was glad I kept my mouth shut because, hey: ten dollars.

  7. Erich Vieth says:

    If you're lucky enough to avoid these things, you're not lucky enough to win the lottery.


  8. lottery says:

    Next jackpot is for me:)

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