Hm… If anything, Dinah’s power suggests a sort of probabilistic approach, but I can’t be sure yet whether the numbers she gives are the cosmic probabilities for a particular outcome, or if she sees all the possibilities and just can’t be certain which one is predetermined to happen.
I disagree with your definition of determinism, though. I personally consider myself an atheistic determinist and materialist, with the view that everything that happens has a cause, and if you follow the chain of causes backwards, you always wind up at physics, and from there it all goes back to the state of the universe at the big bang. So in theory, anything could happen, but they will turn out a certain way based on the initial state of the universe.
I’ve had lengthy discussions with a friend about whether this means no free will. I think we do have free will in that we can choose whatever we want, but what we’re going to choose was always inevitable due to simple cause and effect.
(Quantum mechanics kinda messes with my view, but I think there’s a good chance we just don’t understand it well enough yet.)