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.



Is there a fair coin?
This well-known paper seems to imply that the shape of the coin doesn't really matter:
<http://comptop.stanford.edu/u/preprints/heads.pdf>


From the lit review:



> 
> In light of all the variations, it is
>  natural to ask if inhomogeneity in the
>  mass distribution of the coin can
>  change the outcome. [Lindley, 1981]
>  followed by [Gelman & Nolan, 2002]
>  give informal arguments suggesting
>  that inhomogeneity doesn’t matter for
>  flipped coins caught in the hand.
>  Jaynes reports that 100 flips of a jar
>  lid showed no evidence of bias. We had
>  coins made with lead on one side and
>  balsa wood on the other. Again no bias
>  showed up.
> 
> 
> 


