There are a lot of variations on the theme of "the lottery is a tax on people who can't do math"

Sometimes when people commonly say a thing, it's a myth, or a meme that they all got from the same place. Sometimes it's because the thing is plain for anyone to figure out who does the figuring.

but the fact remains it's the only form of gambling which has million-to-one payouts

All forms of organised gambling, whether a lottery or casino games, are rigged heavily toward the house. Let me put it to you this way: even under optimal condition, if you could buy the tickets only at the perfect times when the ratio of the jackpot verses the probability of winning most favours you, if you could buy every ticket sold, you would lose money even before you had to pay taxes on your "winnings". You would lose money every time, without exception. If the lottery were not run by the state, it would be criminal under various laws regarding fraud and other ways of taking advantage of gullible people.

With the lottery, I can put down a dollar and have the excitement of dreaming of winning a million.

I can dream for free about winning a million dollars, or about inheriting a kingdom, or about anything. Dreams are free. Convincing people to pay money for something that's free is one of the oldest and best-known scams in the book.

Also, my odds of winning it are infinitely greater than yours

Mathematically speaking, this is a wash. My expected returns, at zero, are a good deal higher than yours.

Look, the money is in your hands, and if you want to spend it on tickets that's your decision to make, but since you were talking about math, I just thought I'd bring up the mathematical side of the thing. If you want to buy dreams, hey, it's your money. Some people justify it by saying it's fun, and all forms of entertainment cost money. Sure, okay. But as far as the mathematics of the thing are concerned, it's an expenditure, not an investment of any kind. Ordinarily I don't trouble most people with this, because it just upsets them, but you were showing enough interest in math that I thought maybe you'd be interested.

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Look, the money is in your hands, and if you want to spend it on tickets that's your decision to make, but since you were talking about math, I just thought I'd bring up the mathematical side of the thing. If you want to buy dreams, hey, it's your money. Some people justify it by saying it's fun, and all forms of entertainment cost money. Sure, okay. But as far as the mathematics of the thing are concerned, it's an expenditure, not an investment of any kind. Ordinarily I don't trouble most people with this, because it just upsets them, but you were showing enough interest in math that I thought maybe you'd be interested.

Given that you won't participate in a lottery because math says that your expected winning is less than your wager, would you participate in a gambling if the expected winnings is higher than the wager? Or to be more concrete, give the following game: a coin is flipped until it comes up head, on the nth flip. You are then paid 2ⁿ dollars. How much are you willing to pay to participate in this game? Standard math will say "everything you own". Despite there's a 50% chance you'll end up with 2 dollars.

There's a solution to this problem http://rec-puzzles.org/sol.pl/decision/stpetersburg and part of it that involves the observation that one's desire for money isn't linear in the amount of money involved. Your first million dollars means more to you than your second.

But there are other things involved as well. Even if people don't win at a lottery, they get something out of it. Just the thrill of participating, seeing the numbers fall, or the dream of getting rich. It's not at all different from people paying money to get into a roller-coaster. The expected monetairy gain is 0. Yet people are willing to pay the price, because it satisfies some need. That's an economical explaination, but economics involves a lot of math as well.

Abigail

a coin is flipped until it comes up head, on the nth flip. You are then paid 2n dollars. How much are you willing to pay to participate in this game?

Depends. Do I get to participate on a regular basis, like one does in a lottery?

one's desire for money isn't linear in the amount of money involved

Yes, I know about the law of diminishing returns, but that's actually another argument against buying lottery tickets, because it further decreases the value of a chance at winning. There are additional factors as well that decrease it even further -- taxes, as I briefly mentioned, the tendency of most lottery winners to end up with nothing to show for it five or ten years later, and so on. I didn't feel the need to bring these things up because just calculating the expected return is convincing enough in itself, except for the people who aren't going to be convinced regardless.

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Well thanks again, but I can't help thinking you're being patronising. Despite the fact that this thread proves I'm not very good at math, I do know the math involved, and I do know that if I were to buy every ticket out there I would make a loss.

(Though there was a syndicate of people a while ago who waited until the cost of covering every possible combination was less than the jackpot, and went out and methodically covered every possible combination. Interesting story.)

But someone is going to win a million dollars tonight, and despite 7,000,000 to one odds, it might be me.

To put it another way, I have a piece of paper in my pocket that may or may not be worth a million bucks. You don't. I think the contents of my pockets are more exciting than the contents of your pockets.

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But someone is going to win a million dollars tonight, and despite 7,000,000 to one odds, it might be me.

Theoretically. However, if I were to bet money against its being you, I'd like my odds. Like I said, you spend the money however you want -- it's your money, and if buying lottery tickets is enjoyable for you, that's your business. I was only looking at it from a math perspective.

I think the contents of my pockets are more exciting than the contents of your pockets.

Well, I've still got the dollar... you do the math.

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Conversely the average lottery winner winds up a short time later with the winnings being only a fading memory. And most people live with a justified fear of uncontrollable financial crises due to uncontrollable outside circumstances.

But the potential lottery winner certainly gets more excitement than the plodding but fairly certain path to (modest) riches. Most people seem to find that worthwhile. At least that is how they behave.

Do I really need to say that I lead a quiet, industrious life, am buying property, investing, have insurance and so on, but I also play the lottery? It seems like you all think I must be some kind of vagrant or otherwise lead a completely dissolute life simply because I play the lottery.

I used to live, through an accident of fate, in a part of town that was just packed to the gills with millionaires. The average home would have been the other side of two million -- but believe me, those people did their lottery entries every week just the same as the poor people.

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I was making no accusation about you. Just commenting on generalities about people who save money, and those who play lotteries.

Oh. And I also intended that to be my way of pointing out that my odds of "winning" a million dollars are rather good, lottery or no lottery.