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