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by Paul Brown.
Original Post: Death of the Coin Toss
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In a result that is sure to change decision-making forever, Persi Diaconis has shown that flipping a coin isn't random. For those unfamiliar, Diaconis is the same mathematician who proved (with Dave Bayer) that seven shuffles will randomize a deck of cards.This is a great example of commonly held beliefs that are wrong, and it's good to remember to ask questions of yourself and others. Why is it done that way? Can that idea work? What are you trying to accomplish, and are you accomplishing it? Accepting the standard assumptions is a recipe for obtaining the standard results, and that's great if you're baking a cake but a lousy way to run a business or approach life's challenges.This is also an opportunity for a digression… When I was a graduate student, one of my cohorts claimed that a penny, when spun on edge, would rest heads up more often than tails up. (I am almost positive that this observation was originally due to Diaconis.) The statement was empirically verified through about an hour of spinning a variety of pennies on a table at Cafe Strada. It is also true that if you balance a penny on edge and then randomly perturb (i.e., hit from above) the table, the penny more frequently rests heads up.Once you look closely at a penny, you can see that there is more relief on one side than on the other, so that the center of mass is not positioned directly above the center of the edge when the penny is balanced on edge. Being naturally inquisitive graduate students with time on our hands, we proceeded to test other coins for spin-fairness, thump-fairness. I've since forgotten the results, but I do recall that we came up with some interesting attempts at a proof.While there are some famous examples of people who exploited non-random but assumedly random behavior for personal gain, I'm reasonably sure that no one has made money spinning pennies. Nonetheless, someone with the mindset to carefully think through "obvious" answers has the potential to make a difference.
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