There's an interesting theory that the solution to this is to subsidize the lottery and improve the odds significantly. Take to the extreme and you could essentially implement UBI this way.
I also don't think poor people are wrong to think a chance of getting a life-changing amount of money is a worthwhile luxury spend compared to the other available options. They may be wrong about the probability, but instead of fixing that with education, we could fix it by making the probability closer to people's intuition.
Given the well-known issues with means testing, randomly assigning the payouts instead might be a significant improvement.
I also don't think poor people are wrong to think a chance of getting a life-changing amount of money is a worthwhile luxury spend compared to the other available options. They may be wrong about the probability, but instead of fixing that with education, we could fix it by making the probability closer to people's intuition.
Given the well-known issues with means testing, randomly assigning the payouts instead might be a significant improvement.