"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. All of this changes drastically if inhomogenious coins are spun on the table (they tend to land heavy side up). As explained above, some of this bias persists for coins flipped onto a table or floor."

You have to love Persi Diaconis. Having coins made up with lead on one side and balsa wood on the other.