Liked Nelson's answer and I appreciated learning "clinamen" as the name for the Lucretian swerve. I don't disagree with his points but I feel it is not representative of most physicists understanding. Like Wittgenstein argued definitions matter, and most don't really understand which ones they are using. At it's heart determinism is either partial or absolute. if partial most would consider that evidence of either randomness or agency (free will, not necessarily ours).
Physics calls absolute determinism super-determinism (though I suspect philosophers would just call it determinism). Bells inequalities are satisfiable via super-determinism as well as non-locality and randomness.
In summary the universe is either completely deterministic or it has some element of unpredictability which may be randomness or free will. The locality question links to this. The more loopholes are closed the more complex and distant in time this entanglement must be (totally predicted by a deterministic universe) or some faster then light hidden variable must exist (no real evidence for this as I understand it) or the nature of randomness/unpredictability emerges at the quantum level. Most physicists dismiss superdeterministic erroneously as they assume ruling out loopholes lowers its likelihood. The universe is under no obligation to be understandable to us and we assign probability based on the knowledge of an ensemble of outcomes. We don't have that data for the nature of reality.
With the exception of a non-local variable (which actually pushes the determinism argument back a level rather then resolving it) the other two options are the same one philosophers proposed thousands of years ago. What physics has done is make it clear which descriptions are currently lacking. Both classical mechanics and quantum mechanics currently fall into that category. I suspect it was a backlash against the false assumption of determinism in classical mechanics that biased QM in the opposite direction.
