I know you have a point, a good one, Lotteries cater to the vulnerable etc. - but you are wrong in one aspect: There are winners, in every lottery, and that's what fuels the hope.
Even small chances are chances. It's that simple ;)
When did I say there weren't any winners? I said people think there's a chance that they might win personally. And you can state the gamblers fallacy any way you like, the fact that there are winners in a lottery has nothing to with the chances of winning personally. Bad at math, bad at logic, too emotional, call it anything you like. Any hope is a result of these flaws, not the cause.