In the biological sciences, at least, 'random' means unpredictable. As you say, it may be that there are no 'truly random' events - after all, the evolution of the Schrodinger equation is deterministic, and the appearance of randomness could be due to the 'Lottery Effect' (self-locating uncertainty).Ah, that's a fun physics question, and we might guess right off there can also be the uncommon instances where the coin could land on it's edge and perhaps bounce and then balance on it's edge, as you might guess, or....even rarer starting conditions where the outcome would sometimes be unpredictable even with our best measurement!
Because of quantum uncertainty, there are some instances of just-so starting conditions where the landing of the coin where the quantum uncertainty in measurement of initial starting conditions would prevent you from being able to be sure of a certain outcome due to the Heisenberg Uncertainty Principle which prevents precise measurement of every aspect of position and velocity to perfect exactness.
And that's not all. It may be even more fraught with uncertainty than we'd guess even with that, in the view of a more speculative possibility in QM of some true randomness which might affect a near-the-edge-between-2-outcomes situations.
I doubt the Uncertainty Principle is relevant to measuring macroscopic objects such as coins as it is practically impossible to measure the position and momentum of the whole of a macroscale object within the relevant timescale; and quantum effects are also unlikely to be relevant given such a tiny Compton wavelength.
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