For instance, let's take the simplest example:
we hit the white ball with a force on a billiard table so then it hits the rest lf the balls. After a brief period of time all balls will have a certain position.
So the question is, if we (could) repeat the action in the same way as before, with the same starting state of the board, will we get the same results or will it be always sligthly different?
But since we have the exact same starting states, the exact same physical laws, and a closed system with constant, homogen outer forces (gravity), the outcome should be the same, shouldn't it?
Since we are talking about a closed system, and were pretty much assuming a virtual environment governed by a mathematical principal, then it will most definitely yield the
exact results, with each trial. A mathematical equation will always come up with the same answer.
Uncertainty only really exists on the quantum level and even then we're not 100% sure of that.
Cause y'know, uncertainty
But on the macro level (subatomic particles -> atoms -> molecules -> things comprised of trillions of molecules) that uncertainty is effectively irrelevant, kind of like how playing a slot machine in the short term could be profitable but in the long term you're practically guaranteed to lose more than you win. The probability of the white ball being off by even a fraction of a degree is so astronomically low that (and this is a conservative estimate) you're more likely to win the lotto a thousand times in a row.
I agree with cog. If we are to consider the implications at a quantum level, then an interesting question would be if the differences made at a quantum level really are
truly random?
Assuming that they are, it could be like cog said, the mass quantity of states that pass by in a certain period of time could amount to almost absolutely no difference. If you were to flip a coin 10^99999 times, there would almost be an absolute 50% result for each side of the coin. Perhaps the particles in a quantum level do reach an absolute. Then the whole trial could be considered deterministic.
However, if it were even the slightest bit off, then we could say we have something truly random. (that is, if we assume the physics of quantum particles are random) It could be an indication of a multiverse with slightly different alternate realities!

(sorry, had to throw that in).
Scenefinale brought up another interesting thought. Are the choices that humans enact (and possibly other forms of life) truly random? To me, it would be ultimately incredible if the exact way we move about and do things was all determined since the start of our existence. Too incredible to seem plausible. But perhaps, in the long-term, grand scheme of things, certain generic events (like the invention of vehicles) had a great likelihood to happen. And the specific detailed events of life were indeed very random.
So going back to the simple billiard ball example, you would have to determine air pressure, seismic activity, and the forces of astral bodies, etc, and how they effect the measurements. And also take account how the random acts of life influence those things as well.
Because of the random acts of living things (and maybe the random properties of quantum particles), if we could rewind time, and attempt to simulate the experiment exactly, there may be a certain degree of difference. Maybe. If the choices living things made were random, and/or particles act in random ways.