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.