More like 1 man will have $18, 17 men with none will refer to him as "the honorable..." and the two men who still have a dollar will be "trouble-makers".

In the poorest areas there are strong incentives for the residents to spend any extra money on necessities such as housing, housing maintenance, utilities, food and clothing. Much of that work would be done by other residents or local businesses. As far as I understand money distributed this way gets cycled through the economy at a high rate, changing hands many times.

Unless the one man can physically dominate all the others, this will never happen. Capitalism as we know it requires state-controlled force.

You know what all the evidence says? Lock 20 people in a room, each with a dollar, and nobody will care about the dollars as there's no market to do anything with them. If they have food in the room, they will tend to realize that it's gonna be a terrible mess and have violent conflicts if there's anything far from equal share of the food. Everyone reasonable will gang up on any hoarder. At their core, human groups are actually communist: from-each-by-ability to-each-by-need. Check out the book Debt: The First 5,000 Years by David Graeber

Wanna bet? ;-)