How to distinguish "chance" from simulation events?

Question

People often like to think that given a certain probability of a dataset explaining results, like say 90%, then it implies if you "reran" events 10 times, 9 times they would return the same outcome.
From a classical view this is not the correct interpretation since the results leading up to the event in question have already been determined, so "rerunning" the same simulation should have no effect on the outcome. However, I don't know if that distinction has a name or exactly how to explain it or how to distinguish it from the intrinsic randomness implied by the standard model.
Chaotic behavior is not mutually exclusive with determinism, but the standard model doesn't prove intrinsic randomness one way or the other, but entropy and intrinsic randomness should also break time symmetry which means the results going backwards in time are not necessarily per-determined.

gandalf61 · Answer

In a deterministic scenario, assigning a probability to an outcome only makes sense if the initial conditions are allowed to vary (with some known distribution) or if there is some uncertainty in the initial conditions.
For example, it only makes sense to say that the top card of a deck of cards is a spade with probability $1$ in $4$ if the deck is randomly ordered, or if we do not know the order of the deck. But if the deck has a fixed and known order then the top card either is or is not a spade - there is no probability involved here.

How to distinguish "chance" from simulation events?

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