Determinism versus Free Will or Non-deterministic.
Well, in closed systems we can prove small cases of determinism. However, in cases where the system is not closed we can't prove it. Also it's very hard to prove as 'reading' the 'information' change's the result, hence the Cat Paradox. So the only way to predict this is if we had a complete model of particle physics (which we are near with CERN, a few years away probably) and a change in most of our Physics based Calculus; because it is based on the Kinetic side of the equation and not the potential or 'information' side. Although, I know of changes coming soon by a certain Physicist about to publish in the 3 largest journals about a different model for calculus, which is interesting as a lot of approximations go away doing so.
Sadly, in the end, I predict their is no true Free Will, just the appearance. However, that does not mean we are not responsible for our actions, as at this level their is no way to calculate what is going to happen because we can't get a good Snapshot because of the Cat Paradox again and and the very idea of proving true Free Will wrong will change how you think again, and everything changes again. So, in effect as X approaches infinity our equation looks like when we are racing against something to infinity but it had a head start.