I've heard it put like this: the lottery is a tax for people who are bad at math.
That said, I do play occasionally.
My response to that is usually that those people are bad at economics. Value isn't linear. I don't play scratch offs because the max payout is usually in the thousands or tens of thousands. Certainly nice, but not life changing. The statistical odds are against you, anyway. So you throw away your money for what? Maybe a new car, at best? However, in the case of the big lotteries, you're paying for a chance (minutely small, but still there) at a completely life changing event.
Case in point, If you give 200,000,000 people $1, you've pretty much wasted $200,000,000. Congratulations. But if you give one person $200,000,000 or even 2 people $100,000,000, you've completely changed their lives forever. Now, whether you've changed them for good or not, that's another discussion.
It's the same reason that supply/demand and price point curves aren't linear. They might be linear within a certain range, sure. Let's say that you do an experiment. You have hamburgers for sale for $1. There are 100 people. All 100 people buy the hamburgers. You raise the price to $2 and only 75 people by the hamburgers. You raise the price to $4 and only 50 people buy them. You're losing 25 your customers with every 2x increase in price. But that doesn't mean, necessarily that at $8 you'll sill get 25 people to buy your hamburger. And it doesn't mean that at $16 nobody will buy your hamburger, either. When you start getting to the extremes of value questions, things get muddy.
So the same goes with monetary prizes. If you give me $50,000 I could do things like pay of car loans, student loans, etc. I would be in a lot better place financially, but certainly wouldn't feel like I'm living a different life. If you give me $500,000, would I be 10 times better off than $50,000? Could I then buy 10 more cars and get 10 more degrees to pay off my student loans with the money? Of course I wouldn't. I might, however, quit my job and take a couple year sabbatical to travel the world. Or I might start my own business, and finally get my dream job.
So, if there were 2 lotteries, one with a max possible payout of $50k, and one with $500k. And the $50k one cost $1 with certain particular odds of winning, and the $500k cost $10, with the same odds, I'd play the $500k one (assuming I'd play either of them). All other things being equal, mathematcially and statistically speaking, one has the chance to change your life forever. The other doesn't.
At least that's how I justify it in my mind.
