A lottery ticket (not that I would buy one) is an entertainment expense and should be compared to other entertainment expenses. Spending $2 on a lottery ticket and having a nice half an hour imagining what you would do if you won is just as much of an entertainment value as spending $8 on a ticket to a two-hour movie, even if your chance of winning is zero. Since your chance of winning something is a hair better than zero, it is arguably better.
While it may be better still not to make either purchase, looking it as an entertainment expense explains it.
This is the only way I can look at purchasing a lottery ticket (BTW at least Mega Millions is $1 a ticket, but your logic holds). You get to day dream about all the things you could do living off of 4 percent of such a large windfall (at least for the intelligent). If you are lucky you might get more than half an hour out of it; after all you day dream, if it is a big lottery there is conversation at the office, and I imagine some people get a little thrill out of checking their ticket.
I agree that lotteries, including scratch tickets, are a scam but I would not call it a Tax.
Taxes are mandatory payments levied for services. This includes property taxes, vehicle taxes, sales or income taxes, etc. You can argue that these taxes are too high, improperly used, etc. but they are all clearly Taxes.
Lotteries are completely voluntary. No one is forced to buy a lottery ticket. They are not taxes on the poor or mathematically challenged. They are just a scam people fall for.
I fine it interesting that when the mob ran numbers games (lotteries) it was evil and against the law but now that the government runs it everything is fine. The government was not opposed to the numbers game scam, they just didn't like the competition.
I agree that technically a the lottery is not a tax, but if we are going to be technical . . . the lottery is not a scam as it is not a dishonest scheme; pretty much every aspect from the methods to the odds are disclosed and procedures are in place to ensure the "integrity" of that system.
Are the advertisements confusing: sure and are the disclosures often buried in the fine print of course like everything else in our society.
Calling it a tax on the poor and stupid is shorthand for not-a-tax-but-augments-tax-revenue-through-a-voluntary-system-which-primarily-comes-from-minorities,-the-poor,-and-the-underprivileged.
Just like calling it a scam is shorthand for not-dishonest-in-that-all-relivant-information-is-disclosed-but-not-easily-accessed-execpt-by-those-who-are-looking-for-it-and-advertised-and-distributed-in-ways-to-target-the-most-vulnerable.
I do agree it is odd that our government runs what could easily be called a social evil, but there are difference from a secretive and illegal operation; such as procedures, disclosure, and accountability and recourse if the system is violated.