The Not So Random Coin Toss
Mathematicians Say Slight but Real Bias Toward Heads

From All Things Considered on National Public Radio
February 24, 2004

Feb. 24, 2004 -- Flipping a coin may not be the fairest way to settle disputes. About a decade ago, statistician Persi Diaconis started to wonder if the outcome of a coin flip really is just a matter of chance. He had Harvard University engineers build him a mechanical coin flipper. Diaconis, now at Stanford University, found that if a coin is launched exactly the same way, it lands exactly the same way.

Statistician Persi Diaconis' mechanical coin flipper.
Credit: Susan Holmes

The randomness in a coin toss, it appears, is introduced by sloppy humans. Each human-generated flip has a different height and speed, and is caught at a different angle, giving different outcomes.

Persi Diaconis' mechanical coin flipper, designed by Harvard University engineers.
Diaconis says that if a coin is flipped exactly the same way, the coin lands the same way.
Credit: Susan Holmes

But using high speed cameras and equations, Diaconis and colleagues have now found that even though humans are largely unpredictable coin flippers, there's still a bias built in: If a coin starts out heads, it ends up heads when caught more often than it does tails. NPR's David Kestenbaum reports.

*Note: In football's inaugural kickoff coin toss, the coin is not caught but allowed to bounce on the ground. That introduces an extra complication, one mathematicians have yet to sort out.