Why I’m playing the lottery

By Felix Salmon
March 20, 2012

Have you bought your lottery ticket yet? The jackpot’s up to $241 million!

An interesting thing happens, when the jackpot gets this big: if you actually believe the $241 million figure, the expected return on your dollar is positive. The mean player, it turns out, is going to get paid out to the tune of $1.553 for every ticket they buy. In reality, sadly, the cash option is $170 million, which brings the expected payout to $1.149 per dollar spent, which means that after taxes, you still have to expect to lose money.

But all of that is moot: realistically, your chance of winning the jackpot is zero. Technically, it’s one in 175,711,536, or 0.000000569%. Which is statistically the same as zero. But it’s not psychologically the same as zero — and that’s what counts. When you buy your lottery ticket, it’s impossible not to dream of all the things which might happen if you won. (My dream now has to include the inconvenient fact that my winning lottery numbers will have been broadcast on YouTube.) The dream is pleasant enough to be worth a buck — at least to someone with a buck to spare, like me. In fact, it’s so pleasant that sometimes I won’t even check my lottery numbers, because I don’t like the opposite feeling of finding out I haven’t won.

And the occasional wager on the lottery is a lot less expensive, and a lot less damaging, than attempts to get rich quick in the stock market.

Which doesn’t mean there isn’t a dark side to the lottery — there is. It’s a horribly regressive tax on poverty, for one thing. I’m one of those people who think that they should be paying more in taxes, and by far the easiest way to funnel more of your income back to the government is to buy lottery tickets. It really is a voluntary tax. But the problem is that it’s paid overwhelmingly by poor people who can’t afford it, rather than by rich people like me who can.

And if you move from lottery tickets to scratch cards, something else happens — they pay out with enough predictability that they can actually be used for money laundering. Take your dirty dollars, buy a bunch of scratch cards, redeem the winners, and you’ve got nice clean legitimate money. If the games weren’t so incredibly lucrative for the states, they’d be made illegal in no time just for this reason alone.

So from a public-policy standpoint, lotteries are a bad idea. Assuming that they’re here for the foreseeable future, however, I’m going to continue to buy myself a ticket now and again, if I ever find myself in a place selling lottery tickets when the jackpot goes above $200 million. I’m doing myself no harm, I’m doing the state and the vendor a little bit of good, and hey, you never know. This blog could turn into the diary of a lottery winner.


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I’ve never bought the statistical argument against the lottery. Isn’t there the exact same statistical argument for various types of insurance not making sense? Yet we pay insurance premiums to avert very unlikely disasters. What about paying a similar premium for a very small chance at success? I’m not saying the amounts paid by the people who pay them necessarily make sense but to a lesser degree, insurance can have the same problem.

Posted by bmozaffari | Report as abusive

One advantage of living in Australia – lottery & other gambling wins are tax free, unless you are a profressional punter (and the tax office has a high standard for that).

So we see a jackpot of $21million – 31 March 2012, then if you win it alone it is all yours in cash at once (about 2 weeks to do the paperwork and payout).

Right now am composing my resignation letter in my mind. :)

Posted by tqft | Report as abusive

Gosh, Mr. Salmon, sure hope you remember your loyal readers once in a while after you’ve banked (with GS, no doubt) your $170-million. Does the term “muppet” ring any bells?

Posted by MrRFox | Report as abusive

bmozaffari, because one is about making money and the other is about not losing money. If you can afford to pay any medical bill that comes along then it might make sense not to get insurance.

Posted by Danny_Black | Report as abusive

Danny_Black, the key there is that the marginal value of a dollar is asymmetric. Let’s say you are living happily on $60k/year, but you have to watch expenses carefully and don’t have much savings. (Plenty of people in this boat.)

If you buy lottery tickets every week, you need to cut back on other expenditures. There is a clear “opportunity cost” to each of those dollars that you spend. Hopefully the entertainment value is worth it.

You might “on average” get a little more than half your money back, but it isn’t returned in a useful fashion. The bulk is returned in a highly improbable jackpot that isn’t NEARLY as economically useful as an equivalent number of $10k payments.

If you drop insurance, however, all it takes is a single hospital stay to run up several thousand dollars of bills that you have no chance of paying off. Bankruptcy is unpleasant, so we are willing to pay a little extra to avoid it.

To summarize:
Bankruptcy = very unpleasant, willing to pay to avoid
A few marginal dollars at $60k = useful, not essential
Anything after the first million = limited marginal utility

The lottery doesn’t sell jackpots, it sells hope. And only the ignorant (or somebody like Felix who wants to make a point) buy into that false hope.

Also, how likely is it that there will be just one winning ticket? Usually participation spikes when the jackpot rises, often resulting in 2 or 3 winners. There goes your 15 cents of profit!

Posted by TFF | Report as abusive

Is the math on a lotto ticket any different than buying an extremely out of the money option? (besides being harder to hedge)

Thing that annoys me the most with anti lotto economists is that they assume money is mathematically consistent, despite the fact that they damn well know a dollar today is not the same as a dollar tomorrow. And a two million dollar day, that’s definitely not the same as a million two dollar days…

Posted by AbeB | Report as abusive


Your analysis is flawed of the average payback because as the jackpot increases, so does the number of players and thus the expected number of winners because multiple winners split the jackpot. Using the Poisson distribution, as np increases, the expected payout never goes above 1 dollar.

Posted by mwwaters | Report as abusive

Also wanted to comment on this line, “by far the easiest way to funnel more of your income back to the government is to buy lottery tickets.”

The lottery is a grossly inefficient way to return money to the government. First, they distribute roughly half the money to people who don’t need it. (A lottery jackpot winner almost by definition doesn’t need the money, or at least doesn’t need THAT much money.) Second, the system comes with hefty overhead. The lottery sales agents get their cut, the lottery management siphons off a hefty chunk, and part of what remains gets fed back into advertising.

If you want to give something back, then volunteer. Or contribute to a charity. Or write the Treasury a check (they will accept it). Buying lottery tickets gives back just a few cents on the dollar, with the majority spent on feeding the monster.

Posted by TFF | Report as abusive

The lottery is not a “horribly regressive” form of taxation, because it is voluntary. Nobody will file a tax lein on your property for not buying a lottery ticket. Those in poverty would best spend their money doing something more productive with the money they spend on tickets.

Posted by zotdoc | Report as abusive

If you buy a bottle of wine and enjoy it, then you consider that money well spent. If you buy a lottery ticket and can imagine for a few days what you’ll do with all that money, then you consider that money well spent.

To say a lottery is a tax on the poor does 2 things. First, it treats the individuals who are poor as an aggregate. Yes, the lottery doesn’t pay off as a monetary investment so you can measure that. But the second thing is that poor people lack the one thing a rich person has: money. So the chance to have what they otherwise can’t have is worth something to them, whatever the payoff.

While some people have gambling problems and spend irresponsibly on lottery tickets – and richer people spend irresponsibliy on other things – many poor people buy what they can fit into their budgets. It’s a ticket of hope. They know it doesn’t pay off. They’re poor. They already know life can suck really hard.

Posted by jomiku | Report as abusive

There is a way to get a positive expected return, but not sure Felix gets it right (for example, random number generation is good, but numbers that specifically avoid the popularly-chosen numbers would be better).

http://blogs.scientificamerican.com/gues t-blog/2012/03/06/a-fun-diy-science-good ie-how-to-get-a-positive-expected-rate-o f-return-on-a-lottery-ticket/

It’s also worth emphasizing that the idea of ‘expected rate of return’ breaks down any time the chances of getting any return at all are tiny, and matched with a huge variance in rate of return.

Posted by dmcdougall | Report as abusive

I find that buying a lottery ticket to get the cheap thrill of imagining my life as a multi-millionaire never lasts long enough to provide enough intellectual satisfaction. So I’ve migrated to another justification that I find more satisfying – a lottery ticket is insurance against fate actually having a material influence on me. Given the absurdly small likelihood of winning a material lottery jackpot, I’ve concluded that I probably place a higher (but still absurdly small) likelihood on fate actually having a material influence on my success in so-called random events like the outcome of a lottery ticket. So I can proceed along assuming that the events around me are in fact random, but just in case they aren’t, the occasional lottery ticket acts as my insurance policy.

Posted by Colossus | Report as abusive

And yet many people buy more than one lottery ticket, some many times per week. I would submit to you that this fact is inconsistent with the “just buying a happy dream” explanation.

Posted by Displacement | Report as abusive

mwwaters, your analysis is also flawed. There are many prizes beyond the jackpot, which raises the payback amount. So the payback goes down due to small chance of splitting the prize but is higher than just winning the big prize concludes. Feel free to do the math, but I’ll estimate that a wash.

Posted by markmatson | Report as abusive

Investing beats Lotto every time.

For instance if you know the trend of the market is going up, your buy Put options in VIX etfs or ETNs example in the recent uptrend VIIX shares have fallen from over $100 to just $36.48 , had you bought PUTS when it was $100 you would have hit the lotto.

Same thing is true if the market trend is down, in that case you buy Calls of VIIX and watch them goe up dramatically another Lotto Hit.

Posted by InvestingLotto | Report as abusive

Very interesting post! I never really looked at the lottery this way! I don’t see them going away anytime soon, plus they do a lot of work in our local comunity which is also good!


Posted by Luke123 | Report as abusive

Very fantastic post. I really love to play lottery and win it mostly.

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