There's also a conflict of interest. The state is responsible for math education while having an interest in people not doing the math.
I normally get a couple of tickets when the Euro lottery gets large - just for fun.
Just for fun, you could take the money you'd spend on a lottery ticket and hand it to the next person you see, just to see how they react.
If you're not just barely scraping together, dropping $25 on a negative EV lottery is not going to make one whit of difference to your finances. But it might change your life.
Dropping $25,000 on a positive EV lottery, on the other hand, is an incredibly dumb move.
Since most poor people will, in fact, miss that $25, the lottery is a really bad idea for them. Yet, they play it a lot more than the middle class do...
Since you'll almost certainly lose, I think the true value is in the fantasy of what you would do with a staggering amount of money. You could do this without buying a ticket, of course, but it feels more real when you have some skin in the game. Mathematically, your odds are still effectively zero, but mentally there's a big difference between effectively zero and actual zero.
Thinking of other consumables in that general price range that provide a short, quick fix of enjoyment (cup of coffee, snack, etc.), $1 for a slightly more vivid dream isn't so crazy to me.
Having said all this, I highly doubt it's the mentality of most lottery players.
Watching peaky blinders Is interesting and I a have a cousin who is an actor who is the direct descendant (and could probably do a better brummie accent)
As far as "illegal" goes, yes numbers games were and are illegal. Nobody cared because the cops got paid off. It's a big part of what made NY what it is. It was so successful that most every state now has a lottery system. The odds of winning in state lotteries are, well, you already know what they are. State lotteries are total rip off designed to fleece the public. State lotteries exist because the pols realized they could make bazillions of dollars running numbers on a large scale and they could chase the competition away, too. So, in a sense, numbers games became legal, but controlled by the usual suspects.