Games run methodically by seat. So every seat at the table gets a game, in a regular pattern. Of course, people move around a lot and swap partners, so you might not get exactly the same number of games as the next person - but I don't think it's possible to ensure that, and certainly not under live conditions. It's hard to imagine if you're not there, but the game is pretty chaotic because people are moving constantly.
At the ends, if you would move off the table, you move as far as you can.