Ultimately, probability must be real, because if you zoom in to a low enough level, the movement of particles is basically random, and this randomness is enough

Ultimately, probability must be real, because if you zoom in to a low enough level, the movement of particles is basically random, and this randomness is enough to poison any deterministic explanations for which side a coin flip will land. You could calculate which side a coin will land if you knew all the variables and thus arrive at a higher probability that it will land on a certain side, but it’s still a probability, because the particles that make up the coin could all move in such a way at any point that causes the coin to fall in a way you didn’t expect, even if that probability is very low. A small probability unlikely to happen is still a probability nonetheless. Try computing how a dice made up of a few particles will land. Good luck...