Is there a fair coin? 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.
 A: I think a fairly good demonstration is Persi Diaconis' machine to toss a perfectly standard US quarter to a single predetermined side with something like 99% accuracy. I have heard it said that he could do it himself by hand years ago when he had practiced extensively. So the question may be more along the lines of "is there a fair coin tosser?" not "is there a fair coin to be tossed?" Your instructor may have been referring to a paper of his "Fair Dice." With J. Keller, Amer. Math. Mo., 96:337-339, 1989. (He has it freely available on his website). Just remember that a coin is really just a two sided die. 
A: Maybe you are thinking of "Dynamical Bias in the Coin Toss" by Diaconis, Holmes, and Montgomery?  They show that the same side you started with is slightly biased to come up when you flip an actual physical coin.
A: 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.

