I attended a course on stochastic processes a few years ago. During the course the lecturer mentioned that there is a mathematical proof (with some assumptions, naturally) of non-existence of a fair coin. Now I can't recall the details and can't locate the paper.

Is there such a proof?

I vaguely remember that the idea was to prove that given that coin's sides are distinguishable (by the structure, not color) one can't make the coin fully balanced.