This past weekend, I got into a small argument about the lottery. It was part of a larger discussion, but the key point was me telling the other person that playing the lottery is a very foolish thing to do if your intent is to actually win money at a reasonably fair rate, and that because a lot of poor people who don't know any better play the lotto regularly, it in effect functions as a tax against the lower class. My opposition in the argument was saying how the lotto is a good thing both because it's revenues help to fund public schools, and because it gives those same poor people some hope to win.
The point about state lotteries funding schools is true--they do--but so is the fact that a huge majority of people who play the lottery are low-income, so it's sorta impossible to argue that of the lotto income that funds schools, most of it is being paid by low-income people. That's a hidden but clear tax against anyone who plays the lottery. This has been said many times before, and I don't think my fellow arguer disputed this.
The point that bothered me as an analytical thinker was the one about how playing the lotto is a losing game, that the numbers are stacked against you. My assumption had been that of all the money coming in to the state for the lotto, they skim some off the top and pay out to the schools, then they skim a little more to cover the expense of running the lotto, and then the prizes constitute the rest. This is in fact how it works. What shocked me when I did some simple investigating this morning was how small the prize money is as a percentage of the intake. I'd assumed it might be something like 80-90%. Most sportsbooks will pay out around 91% of their income, keeping just 9% for themselves. Casino games have similar pay-out rates, if usually slightly higher (more fair to the player) even. Many slot machines actually pay-out much higher, up to 99% (mostly because the cost to operate them are so low--no dealers, etc).
According to the website of Mega Millions, the largest interstate lottery in the country, they pay out a ridiculous 50%. Stop and think about that for a minute. Playing the lotto is exactly like playing a 50/50 raffle, and those pretty obviously primarily exist as fund-raising tools. People who play them know that their buy-in is going to fund the school band, or the volunteer fire hall, or whatever else.
But people who play the lottery are not doing it to help fund others, in their minds when they buy the tickets, they are trying to win for themselves. Again, remember who buys most of the tickets. These people can't afford to be so charitable. Often, what they hope they're buying are literally tickets out of poverty.
And the system is only paying out 50%.
Let's do a math exercise to fully illustrate how stupid buying a lottery ticket is.
Assume one hundred $1 lotto tickets are sold. You buy one of them. Assume then that you're chance of winning is one-in-one hundred, or 1%.* Using the Mega Millions structure, the prize available to you is $50. You have a 1% chance of winning that prize, so your expected return for each $1 investment is 50 cents. On top of that, Uncle Sam will tax the winnings up to or around 50%. So your expected return drops to just a quarter. I don't need to tell you that this is epically bad.
Indeed, when you buy a lottery ticket, you do have hope to win a much larger prize. As a one-time, isolated occurrence, this could be considered a fun and harmless act. But done repeatedly, and spread out over millions and millions of people, it's just flabbergastingly stupid.
For the record, here is where the Mega Millions website says their ticket sales revenues go:
50% -- "goes back to the players as prizes."
35% -- "support government services in the member state." Here is your school funding.
15% -- "goes to retailer commissions and lottery operating costs." Here are bodega guys getting a tiny sliver, and the funding of all those terrible commercials, and rich people getting richer.
Finally, here is another factoid I encountered when searching. According to the Ohio state lottery website, the per capita play for all lottery games was $202. Let's guess that half of all people never played the lotto, so the share for those who did rises to $404. Let's then guess that half of those who played did so for less than $50 total (that's one per week still). The share for the remaining 25% of the population rises to over $750 per. And 25% is a horribly liberal guess as to the active lotto players. If there are 10% of the population that regularly plays the lotto, then those people are spending on average over $2,000 per year, even after subtracting out scratch-off winnings. If you want to pursue it more, you could guess that of these regular players, a lot are at poverty level and make less than say $20,000 per year, so that they're spending at minimum 10% of their gross income on lotto tickets.
This is not a small thing.
*I know that in big number-picking lotteries, the odds are independent of the number of entries, that you always have X% chance of getting 6 random numbers to match. I also know that multiple people can win the same prize in them. For the sake of the example, it will be easier to do it as though it's raffle-style. Anyways, the odds in my example above are far higher, since Mega Millions' odds of winning the jackpot are 1 in 175,711,536.
4 comments:
A while ago david brooks had a column on the lottery class v investing class..........Here you go.
"The agents of destruction are many. State governments have played a role. They aggressively hawk their lottery products, which some people call a tax on stupidity. Twenty percent of Americans are frequent players, spending about $60 billion a year. The spending is starkly regressive. A household with income under $13,000 spends, on average, $645 a year on lottery tickets, about 9 percent of all income. Aside from the financial toll, the moral toll is comprehensive. Here is the government, the guardian of order, telling people that they don’t have to work to build for the future. They can strike it rich for nothing."
Awesome. I love it when my rough assumptions turn out to be pretty accurate.
20% still seems kinda high, though I guess those low-income people would skew the whole group. I'm a bad test case, but I know exactly one person who plays lotto games: my dad, and even with him it's mostly just scratch tickets that he gives out around the holidays, or every once in a while for himself; plus then he gets overcome by the big numbers whenever the basic lottery gets over like $200million or whatever (though, as a hollow point of defending someone who doesn't actually carry out this thought process: not playing the lottery but then waiting and playing after the jackpot gets pretty high does in fact raise your odds, since all the prior entrants of un-won, rolled-over number drawings don't contribute to the denominator while their money does contribute to the numerator. The odds there would still be so bad as to be inexcusable, though.)
Btw, who is this Brooks guy?
Regarding your last point about people playing the lottery only when it gets to, say, $200 million - that is baffling to me.
If you actually win, there is no meaningful difference in your ROI whether you win a $50 million or $250 million prize. In both cases you've invested a dollar and won more money than you're otherwise likely to see in a lifetime. Sure statistically and mathematically there is a difference, but in terms of changes to your life, $50 million is closer to $250 million than it is to $0.
However, I've wondered if the denominator does change. Do enough additional people (like your dad) play once a jackpot hits $200 million that it significantly changes your odds of being a sole winner? So much so that the average prize to each individual winner is less at $200 million than it is at $150 million? Is there an optimal jackpot at which you should play? I've looked into that before and haven't found any relevant data.
Those are some excellent points, holtz. Especially about the life-changing aspect. The important thing to remember about a big jackpot like $250 million is that all the intake from selling tickets doesn't come just from that one drawing. Most of the pot is from prior ticket sales for prior drawings. You'd have to look and see what the opening jackpot amount is for first drawings. Let's say it's like $20 million. We know that they'd sell 40 million $1 tickets to get there. Given their constant jackpot winning odds of 175milion-to-1, there would be about a 23% chance that at least one of those 40 million tickets would hit. Every time it doesn't, all the money rolls over of course and they re-sell tickets for another drawing. By the time it gets to $250 million, the tickets bought per drawing would increase a lot, to like 100 million maybe, so that the odds of at least one person hitting go up to about 57%. You could definitely work out a graph to plot this stuff, but I'm not sure in the real world that the amount of tickets sold in an individual drawing would ever be so high as to create multiple winners and cause your individual odds to go down, simply because of all the untapped money in the pot from previous drawings. If 90% of the money in the pot is coming from tickets that have no chance of winning, and your ticket is only competing against the other 10%, then your return on just that last drawing multiply, enough so that it's not quite as dumb a proposition to play. The key to remember here is that the jackpot would have to contain a huge amount of rolled-over money and a relatively small amount of new tickets playing in the last drawing. BUT, in rare cases, it is definitely possible to have a positive expected return playing the lottery.
So to answer your question, the general rule is the bigger the pot the better the return (unless an ungodly number of people participate in that final drawing).
Of course, the "return" we are talking about here would be something silly like expecting $1.0000000000001 for every $1 invested. And with a return that small you'd have to buy tons and tons of tickets to have better confidence of getting it.
For the energy it takes to achieve that, you're better off standing in an unemployment line, or shoveling snow, or passing around a cup on the subway, or anything really.
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