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Physics engines are rarely deterministic, which means most of these games use what you would call the "animation deciding results"
It is very rare that it works the other way around contrary to what others have commented it is non trivial to make weighted deterministic random in this manner
While technically possible, only very specialised games with reasons good enough to budget the programming required will go the route you describe as "result calculated before the animation"
I just want to say, having worked in the lottery industry and having made one of the first predetermined pachinko games, it's actually fairly easy.
It may be considered easy, and for sure this one probably is, but it doesn't compare in complexity to normal physics engines. The whole thread read like it was, so I felt I should provide a better perspective on it.