As one fair way of allocating insufficient resources. The lottery is evidence a lot of poor people would rather have a chance at radically improving their life than a small amount of money.
Do you have any real evidence that poor people would prefer a 1/300M chance in winning the lottery versus a guaranteed paycheck for their monthly expenses? I would love to see the proof for your assertion.
No, that sounds highly implausible to me. A guaranteed paycheck of $1,000/month to every American (in current USD) would be way better than what I suggested. This idea presumes scarcer resources.
I'm talking about something more like the difference between a 1/10 chance of $1,000/month for a year with a new drawing in a year vs $100/month for a year every year.
Even with those odds, I still don’t believe any poor person would prefer a lottery over guaranteed income. Your scenarios sound like projection/speculation than realistic to me.