That's not the point. Of course it doesn't - but that unexpected $35 copay for the urgent care visit would've wiped you out, whether you'd bought the $1 lottery ticket or not. At least you had a little burst of "man, if I won, I'd..."
We know from studies that poverty dramatically changes short-term vs. long-term decision making.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5641572/
> How are those events handled without savings?
Be hungry the week after, pawn a possession, payday loan.
> How would giving them more money resolve this problem?
How would having money solve money problems? That's really the question?