FLIPPING COINS WITH A BETTER THAN 50/50 PROBABILITY OF WINNING. Kids, flipping a fair coin is often used as an example of a random process, with a 50% probability of the coin coming up heads. This article, based on David Adler’s book SNAP JUDGMENT, reports on a paper by three Stanford mathematicians which concludes that if a coin is heads up before it is flipped, the probability of a coin coming up heads after it is flipped by an ordinary person is at least 51%–not 50%. The paper is really about the physics of coin flipping. When an “ordinary person” flips a coin, the coin tumbles, but it also spins —Adler compares the spin to a pizza being twirled. The spin is what causes the deviations from 50/50. The paper has photos of a coin-tossing machine which, after adjustments, will flip a coin so that it will always come up heads if it starts out heads up. I used the phrase “flipped by an ordinary person” in the earlier sentence because there are magicians who can make a coin come up the same way it started every time, just as the coin-flipping machine does. And the magician’s flip will look like the flip of an “ordinary person.” The article points out that if the initial position of the coin is random, then the coin is equally likely to come up heads or tails and points out: “We have friends who preface a coin toss by vigorously shaking the coin between their cupped hands.” two kinds of expertise contributed to the paper. Adler tells us that one of the authors of the article was a professional magician before becoming a mathematician.

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