They would follow the same visible path as the degree of variation is tiny, but these variations can result in accumulated differences. My knowledge on this comes from a game development forum where a experienced developer was explaining one reason why physics simulations don't give the same result each time they're run. If you have an ODE simulation like the recently posted 'man-on-a-seesaw' code in the JV-ODE thread, each time you run it the result is different, even though the starting parameters are the same and the solving algorithm is the same.
As for how to keep a network game in sync, I've never written one, so will be interested to hear the ideas of those who have!
As for how to keep a network game in sync, I've never written one, so will be interested to hear the ideas of those who have!