Does a "Fair" Coin Really Exist?
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Does a "Fair" Coin Really Exist? New mathematical analysis has shown that no matter how vigorously a coin is thrown into the air, it is more likely to land on the same face it started out on. Using high speed photography techniques, researchers at U. California and Stanford determined that only a superhuman ability to toss the coin so it spins perfectly about a horizontal axis through the coin's center would product a totally fair result. All other tosses are biased. In experiments, they were surprised to learn that what was believed to have happened by real-time observation often turned out to be quite different than what was revealed on the high-speed film. On many tosses, a coin that was thought to have rotated never rotated at all, but merely wobbled wildly about a horizontal plane. In fact, magicians and charlatans have exploited this effect as an illusion to fool their audiences (or victims). Even with the best series of tosses, the team calculated that the coin would land on its original face 51% of the time. Yet another study has determined that the "heads" side of most coins is slightly heavier than the tails side, producing a bias toward heads. Even so, 1,000 or more tosses is usually required to observe the phenomenon. |
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