Laplace's demon requires being able to tell velocity vectors of individual molecules, and tossing a coin predictably takes being able to throw it with equally enormous precision, correcting for the net effect of all collisions with molecules of air along the way, etc.

So in the end of the day posessing such knowledge, or rather having a mind with this much focus, depth and resolution would indeed mean a win of determinism over entropy. How can a cup break irreversibly if we know how to put back all of its shards so that they click in place at atomic scale without gaps and lost pieces?

But our reality is a battlefield between pure will/determinism and pure chance/entropy, and it's depicted vividly in The Matrix as the battle between The Architect and The Oracle. And we seem to be cursed/blessed to be Neos trying to balance that out or escape that Sisyphean task altogether.

Now I think we're having two different conversations again? If I understand your point about the "battlefield between pure will/determinism and pure chance/entropy" correctly, you're talking about more of a psychological, individual, "is there a meaning to life, the universe and everything" type direction?

What I was trying to drive at was really more of a "in the framework of Laplace's Demon, your choices in the present can be 100% predicted, no different from the movements of molecules. It follows that you have no more options of choosing than the molecule does and your future has been set in stone from the beginning of time."