08-24-2005, 01:19 PM
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#34 (permalink)
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Devoted
Donor
Location: New England
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coin flipping: Information From Answers.com
Quote:
Experimental and theoretical analysis of coin tossing has shown that the outcome is predictable, to some degree at least, if the initial conditions of the toss (position, velocity and angular momentum) are known. Coin tossing may be modeled as a problem in Lagrangian mechanics. The important aspects are the tumbling motion of the coin, the precession (wobbling) of its axis, and whether the coin bounces at the end of its trajectory.
The outcome of coin flipping has been studied by Persi Diaconis and his collaborators. They have demonstrated that a mechanical coin flipper which imparts the same initial conditions for every toss has a highly predictable outcome.
Morover, they have demonstrated both mathematically and experimentally that the underlying physics of coin tosses appears to have a slight bias for a caught coin to be caught the same way up as it was thrown, with a probability of around 0.51. They also state that stage magicians and gamblers, with practice, may be able to greatly increase this bias, whilst still making throws which are visually indistinguishable from normal throws.
Since the images on the two sides of actual coins are made of raised metal, the toss is likely to slightly favor one face or the other. This is particularly true if the coin is allowed to roll on one edge upon landing; coin spinning is much more likely to be biased than flipping, and conjurers trim the edges of coins so that when spun they usually land on a particular face.
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I can't find any links on magician's biased coin flipping, however.
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