As usual, it’s humanity that messes things up. When flipped by a machine, coins come up heads a solid fifty percent of the time, and tails the other fifty percent. Put the fate of the coin in grubby human hands and the odds tip slightly in favor of the side that faces up just before the coin is flipped. The side that was face up at the beginning of the flip has a fifty-one percent chance of landing face-up at the end. Humans are not as precise as machines, and so the coin rotates around several axes instead of one. The extra rotation favors the side the original position, to a measurable degree. This is independent of the material that the coin is made out of. Scientists have tried the experiment using coins made out of balsa wood (and probably the labor of some very tired interns), and gotten the same results.
So we can totally rig coin tosses now?