The fraud: the government is using its advantageous position to aggressively market a get-rich-quick scheme that has a virtually zero chance of ever getting you rich. You could play a million times and not win. It then benefits from direct profits and taxation of winnings. This all has demonstrably negative effects on public health in the form of addiction and exacerbation of poverty.
I'm skeptical this has any effect on poverty. Poor people who buy lottery tickets wouldn't spend the money on job training if they couldn't buy lottery tickets. They'd find a bookie and bet on sports, or they'd play the horses.
And I don't find your argument characterizing lotteries as fraud persuasive in the slightest. People who buy lottery tickets are well aware they're chances of winning are pretty close to zero. Yes, they have to pay taxes if the do win, but that's not exactly an overriding concern.
