The problem is, this view really doesn't match with our experience of what it means to live as human beings. We experience deciding. We become convinced that things are actually true. We love and are loved. We know, from direct experience of living as human beings, that this is not who we are.
This leaves a dilemma. Either our experience is wrong, or our initial starting point is wrong. Either the laws of physics are not what is "furthest back" (in Francis Schaeffer's term), or else we really are determined and our lived experience is an illusion.
Choice is deterministic, but that doesn't make it less real - on the contrary, it gives your choices meaning! They have causes, reasons, justifications! It would hardly be preferable if your "choice" were the outcome of a fair dice roll, would it? What kind of choice would that be?
I think the problem arises from a confusion of of abstraction levels. At the level of atoms and chemical reactions, you are completely deterministic and "choice" isn't a meaningful concept. 10 stories up, at the level of thoughts and ideas, it is. This is no different than how "pressure" is a meaningful concept for a tank of air, but not a single air molecule.
If your view is that Brownian Motion is not deterministic then does that not contradict the idea 'that cause and effect holds in a closed system' as any sort of absolute?