From Deseret News archives:

Impossible to get a 'fair' coin toss

Published: Thursday, Oct. 14, 2004 12:00 a.m. MDT
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Question: What is it about flipping a coin that makes this a 50-50 proposition for getting either heads or tails? And isn't this why the coin toss has become a central symbol of a fair chance in games or sports events?

Answer: Surprise! A coin toss isn't "fair" at all. It took some deep digging by Stanford statistician — and former magician — Persi Diaconis, but after working with other mathematicians (including his wife) and technicians who constructed a mechanical-coin-tosser, Diaconis uncovered that a coin will come up heads 51% of the time if the heads start out on top, and vice versa.

So, if there's such a strong bias, why hadn't anybody ever discovered this before? Because you'd have to flip coins about 10,000 times — and record the data VERY carefully — to achieve statistical significance and become relatively certain of the finding.

Magician Diaconis is himself capable of flipping coins and getting them to come up either heads or tails 10 out of 10 times. Here he is careful to make the coin appear to turn over many times, but it really doesn't. The fact is, says Diaconis, that even when the coin is flipped with the intent of unloosing a "fair" toss, this is not humanly possible. Bias is going to creep in, and out the window inevitably will go 50-50.

Question: Would you say a bird flies more with its wings or its feathers? Isn't there a clue to be found in the ancient Greek myth of Icarus, who flew too close to the sun and plunged to his death in the sea?

Answer: You might think a bird flaps its wings backward on the downstroke, pushing on the air to gain forward thrust, says Jearl Walker in "The Flying Circus of Physics, with Answers." But slow motion movies show the wings moving forward as well as downward on the downstroke. Recall that flying Icarus fell when the heat of the sun melted the wax that held feathers to his arms. The myth got it right, in that a bird's feathers twist in the air and act a little like propellers. So feathers are indeed critical right along with wings, that act as airfoils. "Perhaps a plucked bird could soar, but it could not propel itself."

Question: We humans are such social beings that it is an enormous benefit at times to know what's on each other's minds. So how do we do this?

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