Friday, March 12, 2004

News Flash: Coin Toss is Not Random

Toss Out the Toss-Up: Bias in heads-or-tails: Science News Online, Feb. 28, 2004:

A new mathematical analysis suggests that coin tossing is inherently biased: A coin is more likely to land on the same face it started out on.

'I don't care how vigorously you throw it, you can't toss a coin fairly,' says Persi Diaconis, a statistician at Stanford University who performed the study with Susan Holmes of Stanford and Richard Montgomery of the University of California, Santa Cruz.

In 1986, mathematician Joseph Keller [link only has picture and e-mail address], now an emeritus professor at Stanford, proved that one fair way to toss a coin is to throw it so that it spins perfectly around a horizontal axis through the coin's center.

Such a perfect toss would require superhuman precision. Every other possible toss is biased, according to an analysis described on Feb. 14 in Seattle at the annual meeting of the American Association for the Advancement of Science.

The title of Dr. Diaconis' lecture: "The Search for Randomness"

So, how biased is a coin toss?
Their preliminary data suggest that a coin will land the same way it started about 51 percent of the time. It would take about 10,000 tosses before a casual observer would become aware of such a small bias, Diaconis says. "Maybe that's why society hasn't noticed this before," he says.
Sounds like grounds for an experiment!

By the way, Dr. Diaconis has an interesting 'hobby'--he catches so-called psychics cheating:
Diaconis' strong background in magic has proved useful in another area -- catching "psychics" cheating. If a person, even a well-trained scientist, has not had experience with human subjects and with cueing (subtle, body-language hints), then it is extremely difficult to spot what is wrong. Diaconis, however, is an expert at deception and has found cheating, or failure to perform, with every psychic he has been allowed to observe. Statistics is useful for spotting the errors and fallacies in the more 'scientific' parapsychology studies.
(This is from the mini-biography at the AAAS Annual meeting website.)