[Baron Munchausen]

It seems to me that re-running the turn over and over would give slightly different results each time, but I just don't know if that is true.

Absolutely. There are many 'pseudo random' factors in the workings of the game. These probably run off the system clock but there are other ways of generating random numbers. So yes, re-running the same turn will always produce slightly different results, and sometimes produce drastically different results.