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If the animations look realistic, it's almost certainly not predetermined. That's by far the simplest way to get the desired effect. However, that doesn't mean it's fair. It could easily use a real physics engine, but still subtly rig the system. For example, bounces off of the pins could have an elasticity factor of 0.4 for bounces towards the big prize, but 0.5 for bounces away from it. Or maybe the hitboxes on the center pins are just a little bit bigger. Stuff that will noticably affect the large-scale statistics, but that you're not gonna notice with your eyes.
You could do a perfectly realistic simulation, record the path for each outcome and then play one of them.
Or, if the physics simulation is deterministic, you could store a set of starting positions and their outcomes.