Toss Out the Toss-Up: Bias in heads-or-tails

If you want to decide which football team takes the ball first or who gets the larger piece of cake, the fairest thing is to toss a coin, right? Not necessarily.

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, 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 f