"Your entire argument is predicated on the existence of land that is free to use by others."
No it isn't. It's predicated on the fact that the government prevents people from starting small businesses. Why do you idiots think the only two possible systems are "Nazi boots on your face at all times" and "OMG ANARCHY"? Did the Nazis crush your head a little more than average?
"If everything is privately owned and they have nothing to offer but labor, which is devalued or valueless in our hypothetical robot-run world, where do they get this money?"
Where do people get money from now? Surely everyone can afford to spend $2.50 for 24 water bottles and sell them for 25 or 50 cents each? If you can't afford that, go to a food pantry.
"If he's starting with nothing,"
Why do you make retarded assumptions? Fuck, he can go sell some plasma and feed himself while making a little stand out of a discarded cardboard box. Just sell sealed, prepackaged stuff that you can buy in minor bulk.
If you want to discuss things, you would do well not to strawman people and go full retard with the reductio ad absurdum.