> This bet either has a positive EV or a negative one and if it’s positive it’s going to tend to infinity when repeated.
This is wrong. The bet as described has a positive EV and the time average for a single player tends to zero as the bet is repeated.
> There is one assymmetry at the zero point (assuming people can’t recover from bankruptcy by borrowing another dollar) ...
The result is not due to zero being an absorbing value. In the setup you can go arbitrarily small and come back without issue. The result is the same.