So, I had thought I had done a post on lottery math, wherein I demonstrated that lotteries were stupid mostly. But I seem not to have, or at least I can't find it. That's a shame, because while almost always, the math works out that the lottery is unwise (maybe the Mega-Millions lottery is +EV when Jackpot > $200M, but not much lower, and may have to hit $300M before it gets clearly +$EV)
On the other hand, there are 2 other ideas that should be brought in here.
Some folks say that lotteries are not actually games about winning. What you're buying with a lottery ticket is the dream of millions. Since we naturally suck at probabilistic math, we think there's a real chance (as opposed to a pretend [infinitessimal, but pretend sounds so much better] chance) of winning big. This illusion allows many happy dreams that are purchased with the $1 ticket. Thus, one should not treat Lotteries as probabilistic mistakes...one should just not be so silly as to think that $EV is what's being bought.
The other idea is thtat there are discontinuous utility values for $. 1 dollar is worth ... a cup of coffee at 7-11. A lottery win ($100K/Month for 30 years) means you NEVER have to work again in your life. The incommensurable values people would say: It is worth MORE than $300M cups of coffee to never have to work again. Indeed...no quantity of cups of coffee, cars, houses, etc. could make up for that. So people place the lottery win in a different category. In math terms: (-1 Coffee x 99.99999999999%) + (Not working again * 0.00000000001%) is positive in a way that winning $50000 isn't.
The theory doesn't hold up well under investigation, but it's a nice think.