Do you have any sources for experiments ruling out our universe being deterministic? I'm not questioning you. I honestly have always been intrigued with the idea. Thanks.
(The result is that either which quantities we choose to measure must be deterministic, or physics must be nonlocal (i.e. what we do in one place can change what we measure in another place even if the two experiments happen simultaneously), or the results of our measurements must be nondeterministic)