The interactions themselves are inherently undeterminable. To reiterate; according to our best understanding of quantum physics, the world
does not operate like Dwarf Fortress, where you plug a seed into some black box and get the same result everytime (well, macro scale it
almost does, but not on the quantum scale).
If you run the exact same interaction a thousand times (literally rewinding time so that EVERY single number is the same), everything we know about QM suggests you will still get a probabilistic distribution of results. You can model the out come of each option, but you can't say whether one option wil be chosen over the other.
If we go with your many worlds theory
1, then there is still the issue that what you described is a probabilistic system, only 2 fold.
If you're using one of the many-worlds variants, where there are multiple worlds and you find yourself in a world with probablity equal to the squared modulus of the amplitude, then the sum across all of the many worlds is deterministic. It's deterministic in a way where everything that can happen, quantumly speaking, does happen, but that's still determinism - stuff is just happening where you can't see it, giving the superficial appearance of nondeterminism.
To explain; after an event, instead of one universe, we have x many branches. We can observe an event that can give A or B yielding A with 70% probability. Since the universe is the same, except for this quantum result, during the split from 1 to x universes, we can assume there is no preference for which universe branch the hypothetical observer recording this goes down, it can be anything from universe 1 to universe x. Thus, what dictates whether A or B is seen would ultimately be the ratio of universes created (e.g. approximately 70% of the created universes are A, 30% B).
2Thus, we just chose a universe at random. We can't say which one, beforehand, our hypothetical observer was going to take, hence not deterministic. There can't be some predefined 'hidden variable' that does, either, because that variable would be inherited by all branches from a given progenitor universe. Either that, or there is a probabilistic function in the number of universes created with A, and the number created with B.
1I personally dislike Many-worlds theory; we're talking the endless creation of new universes from a prior one here, but without a corresponding input of energy. Since thermodynamics is pretty well one of the most fundamental laws of phsics, that's just painful.
Before anyone says "but what about this universe", yes, I don't know what caused the big bang. However, suggested possibilities include both this universe being a black hole from another earlier one, or collisions between multiversal membranes; basically some large event that could conceivably impart the necessary energy. A complete replication of the universe because an electron in the 2nd orbit of a H atom decided to drop then and there into the 1st just doesn't make mathematical (or common, for that matter) sense.
2 Alternatively, there are 2 worlds produced, strictly A and strictly B. However, there is a weighted chance that A or B is observed. Then you still have a probabilistic choice, because, as discussed above, whatever the starting conditions (hidden or otherwise) that lead to universe A, they are also the ones that lead to universe B.