10 February 2010

Bad at math

I've been on a run of good luck lately, and I thought to myself that I should capitalize on it and buy a lottery ticket.  Lotto's a pretty rare indulgence for me, maybe one or two tickets a year at most.   I've always joked about it as the tax on people who are bad at math.  (There's a bitter truth in there, by the way.)  But occasionally I do buy a ticket -- the one-dollar daydream about exactly which airplane I would buy if money was no object.  (An EADS Socata TBM 850, if you're curious.)

So when my wife was checking out the results of the local school levy vote, I noticed a banner ad for our state's lottery, and clicked through for no particular reason.  What I saw took me aback: the breakdown of the actual odds of winning.


I already knew the lotto was a sucker's game, but I had no clue that it was that bad.  40:1 of winning?  Yikes.  Just for reference, slot machines in Vegas will pay out 98 cents on the dollar over the long run, and the roulette table pays out 95 cents on the dollar.  The lotto pays out 2.5 cents on the dollar if I'm doing my mental statistics right.

So, I admit, I'll still buy my one-dollar daydream the next time I'm at the grocery store, and I'll feel all the more foolish about it now that I know exactly how terrible the odds are.  But then I think about the poor lower-income/lower education souls who are pooling their money and buying $20 worth of tickets a week.  That's real retirement money they're spending on their daydreams, and it's our own government that's bilking them out of it.  At least when I go to Vegas I have a fun time and free booze. 

Update: Eric the Pragmatic Caregiver says it's better than 1:40 payout.  I don't really know what the definition of paramutual wagering is and am too lazy to Google it.  But he says the payout for lotto is more typically 50-60 cents on the dollar.  I'll assume he knows what he's talking about because I sure don't.


  1. The odds never stop me from going in with other guys at work for the "big payout." I do that about once every other year. It's nice to dream.

  2. If every win was precisely $1, you'd be correct, but since it's parimutuel wagering, with a variable top win depending on the number of players and the previous history of the game....

    MegaMillions is, like most lotto games, actually designed to pay off at 50% in aggregate. About 60% of the total payoff (30% of action) goes out in the biggest prize) with a 56,000,000 jackpot. The biggest jackpots increase the total return to about 60% for the participants in that drawing, but the return *never* reaches 75%.

    It's late and I've got a raging viral syndrome, so I'm not going to explain all the math, but http://www.durangobill.com/MegaMillionsOdds.html has a reasonable explanation of the paytable.


  3. If you feel stupid for hoping to win money for a better life, remember
    people play the reverso lottery (a worse life) of winning cancer from smoking, it's a crazy world.

  4. The math gets a little fuzzy as multiple people can (and will) win payouts at different levels (there are always people that win sub jackpot amounts). Generally if the lotto is above 60 million (one time payment) it's not too terrible from a payout prospective (probably like 60-70 cents on a dollar). It's the scratch offs and small lottery that are dumb.

    Why would I want to play a lottery where, even if I did win I'd still be working? Thus I only buy if it's 100+ mil annuity. If I ever do win though first thing I am getting is a new car (likely an insanely powerful european estate/avant) and a plane (single engine turboprop).

  5. Just re-read your post and noticed you would also get a plane, an TBM 850? good choice. My dream has always been the slower/bigger/$1 mil more expensive PC-12, which will never happen, but is fun to think about.

  6. Actually, that site that Eric linked to suggests that the before tax return on $1 is in the order of 90c. This isn't too bad; it's not as good as a roulette wheel, but given the nonlinear returns (a dollar lost in real money may be worth the chance at 90c in potential money) it may be not too bad a game.


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