That's an excellent point. The lottery aspect does bug me a lot. (Though my "regular" grocer also has lottery, tobacco, and beer/wine, so I don't think the bodega is worse than the other grocers in that regard.)
It's not primarily that people are bad at math. It's that they don't see any other way out. I've seen data that show that people play lotteries "for money" at higher rates the lower their income is. I can't find the exact citation, but here's a CMU article about study that shows something similar: http://www.cmu.edu/news/archive/2008/July/july24_lottery.sht...
We really just need to end state-run lotteries. The problem is that the states depend on this regressive tax for revenue.
But at the very least the states shouldn't be advertising the damn things!
Basically, every so many dollars that are in a savings account for a set period of time counts as one ticket, and so of course the way to increase your chance of winning is to "buy more tickets". Winnings are paid out in lieu of interest, but in the end averages to about the same.