The other day I drove past the headquarters of the South Carolina State Lottery and noticed that its official name is the “South Carolina Education Lottery”. In fact, they use this name in their advertising. Tonight the estimated jackpot is $20 Million (but, as they are required to say in the fine print “$9.4 Million Cash Value”). Sound good? Well, let’s have a little education.
The lottery is required to put at least 45% of the money paid by ‘players’ into the prize pool. Although it takes some looking around, one can find the odds of winning the various games on the lottery’s web site, and those odds confirm that the expected value per dollar spent is around -55 cents. (In other words, in the long run, for every dollar spent by a ‘player’, that ‘player’ will get around 45 cents back in ‘winnings’.) About 15 percent of the money spent by ‘players’ goes towards running the lottery. (Anybody else suddenly feeling tempted to go into the lottery business?) The remaining 40% of the money spent by ‘players’ goes towards education in the state of South Carolina.
Apparently, that education does not include a lesson on why you shouldn’t play the lottery. Let’s consider the two apparently best reasons one might have for playing the lottery.
First, you might play because you wish to support education (a noble sentiment). This reason is clearly stupid, because your gift is first reduced by 60%. You (and the state) would be far better off if you just gave what you can to the state, bypassing the lottery.
Second, you might play for the chance of winning a lot of money. Let’s compare how well you would do at the lottery compared with going to a casino. In 2003, the average household in the U.S. spent $372 on state lottery tickets. Shocking, I know, but the facts are there for all to see. On average, over 10 years spending this much money on the South Carolina lottery, a household will have lost $2046 (of that, $1488 will go to education). (All of the numbers that I will give here are rough, not taking inflation, etc., into account, but they are sufficiently close to the truth to illustrate the point.)
Suppose instead you went to a casino and played baccarat with your money. (Many games have worse house odds than baccarat; a few are better.) If you play correctly, and spend the same amount that you would have on the lottery, you should expect to lose about $39.50.
“But”, I hear you say. I don’t mind losing my money to the schools of South Carolina. I don’t particularly want to give my money to casinos. Plus, I would have to buy a plane ticket to get to a casino.”
Let’s be clear that this argument is awful. When you play the lottery for $372 per year for ten years, here is where your money goes (on average):
| Winnings: | $1674 |
| Schools: | $1488 |
| Folks who run the lottery: | $558 |
Suppose instead you spent $400 on a weekend trip to Atlantic City. (I just found a deal on the internet – flight plus hotel – for $400, and I only looked for 3 minutes.) Then your breakdown (on average), spending the same $3720, would be (playing Baccarat – again there are better (and worse) games):
| Winnings: | $3284.80 |
| Flight and hotel: | $400 |
| Casino: | $35.20 |
Take out $1674 for yourself, and you still have $1610.80 to give to the State for education. (Of course, your local Indian casino is likely to be closer than Atlantic City. Moreover, if you really must gamble, you can do it essentially for free on the internet, saving that $400 entirely.) And I haven’t even mentioned all of the free snacks and cocktails…
But maybe you play the lottery because of the chance to win ‘the big one’. So let’s finish off this argument by looking at the big one, the Powerball lottery. Let’s compare the chance of winning $200,000 by spending $3000 on lottery tickets, versus the chance of winning $200,000 by playing American roulette (which is far from your best bet if you are hoping to win money in a casino). Playing the lottery, your chance of winning $200,000 is a little better than 1 in 1200. In American roulette, if you simply bet all of your money on a 2-1 proposition (such as ‘1st 12’) every time until you reach your goal (or, as is more likely, bust), you have an approximately 1.2 in 1200 (i.e., 1 in 1000) chance of getting to around 200,000. In other words, your odds of winning a ‘big prize’ are about 20% better (and that was by playing a silly game in a silly way).
And what about the ‘really really big one’? Well, the payout changes from week to week. This week the real cash value of the payout is around $10 million, and your odds of winning that money are 1 in 146,107,962. You have a better chance of getting 27 heads in a row on a fair coin. It’s trite to say, but your odds of being struck by lighting are far better. (A common estimate is 1 in 600,000, or around 240 times more likely than wining the lottery.)
I can hear the response. “I play the lottery for the excitement of gambling. And I’d rather get a little excitement every week for 10 years than a lot of excitement for one weekend.” Well, there’s no arguing with taste – maybe some people do get excited about scratching numbers off of a card in a convenience store and then going home and watching some overdressed ‘TV host’ draw numbers from a bin (not to mention paying 55 cents on the dollar for the privilege). I’ll only suggest that there are better (more stimulating, longer-lasting, more productive) ways to get excited. And there are certainly better things to do with $372 per year.
This is an excellent entry. It will find a home in my lectures on probability in my Scientific Reasoning classes. Usually I use the example of Publishers’ Clearing House where the expected utility of winning is roughly -.37 dollars (unless you have a thing for licking stamps or sealing envelopes), provided you don’t purchase any publications. You example is better since most students are more familiar with Powerball, scratch-off lottery tickets, and education lotteries. I find it interesting that individuals who purchase lottery tickets come up with all sorts of reasons (post hoc, I might add) for why they play those silly games, and it is unclear that the reasons they cite in defense of their decision to play sometimes seem extremely unlikely to have been the actual reasons relevant to the decision to play. For instance, if the person does not know he is answering to a philosopher, he will say that he is playing to win. However, once you point out the “innumeracy” of his response, he will back off and claim that he is playing for the excitement of winning or he’ll claim (and this is my favorite) “well, *someone* has to win,” to which I usually respond, “yes, (depending on the lottery), but it won’t be you.”
Just out of curiosity, do you think that these lotteries are a bad thing? I once had a professor who claimed that they were since they take advantage of low-income people and people that are, frankly, not sophisticated enough to know that they should not play these games. (I know this sounds elitist, but a.) it is not my argument, and b.) these people exist.) Moreover, the education marketing gimmick fools people into thinking that they are doing the right thing by playing, when clearly, for reasons you enumerated, it is not. To what extent should one just be a libertarian about these matters and just let people throw away their income on these games? Does the state have a responsibility to look out for the polity and see to it that lotteries and the like do not take advantage of people?
Thanks for the comments, Brian.
Yes, I do think that these lotteries are a bad thing if they are run by the state. But I’m also not a libertarian!
I believe that, in part for reasons that you already mentioned, these lotteries are inherently misleading. They rely on — and indeed, in their advertising practices, encourage — widespread misperceptions about probability. It is a shame, of course, that such misperceptions exist, but they do. (And there is some psychological evidence to suggest that not much can really be done about it.) I do not believe that the state must protect citizens from themselves (one of the causes of an overly litigious society, in my amateur opinion), but I also believe that the state should not actively seek to take advantage of its citizens, and I believe that these lotteries do exactly that. It is probably also true that they take undo advantage of exactly those who can least stand it financially, but, while deplorable, that aspect of these lotteries is not my main argument against them. (And lots of dumb — and some smart — rich people in fact buy the lottery tickets as well.)
By the way, private gambling establishments are a different matter. If operated in ‘the right’ way (and I won’t try to elaborate on what ‘right’ might mean here), they are fine, in my opinion. True, they also take advantage of people’s misperceptions about probability, but they are different in some important ways. First, it is very clear that they are out to make money — there is no pretense whatsoever that they are operating for some charitable purpose. Second, there is, arguably, some actual entertainment value. Third, they are not the state. Citizens do not have a right to presuppose that a private entity is not trying take advantage of them. They do have a right, in my amateur opinion, to presuppose that the state is not trying to take advantage of them. (Another difference is that the odds of winning money in a casino are actually much higher than the odds of winning the lottery….)
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