Is Spinning a Penny a Fair Way to Make a Random and Unbiased Decision?

Forget what you know about statistical probability. If Persi Diaconis and researchers at Stanford University are right, spinning a standard-issue penny (the one with the Lincoln Memorial, clean and shiny) will come up tails side up roughly 80 percent of the time -- not 50-50, give or take a percent either way, as we’ve all come to expect. The reason: The side with Lincoln’s head is a tad heavier than the other side, causing the coin’s center of mass to be slightly skewed. And so, the spinning coin tends to fall toward the heavier side more often, leading to significantly more “tails.”

Heads I win, tails you lose:

• Diaconis warns that an older penny with built-up dirt and oils could sway the heads-or-tails outcome, one way or another.
• A magician in his spare time, Diaconis also discovered that it requires either five or seven shuffles, depending on the criteria, to get a deck of cards into a mathematically random order.
• Diaconis, a professor of mathematics and statistics, is author of “Magical Mathematics: The Mathematical Ideas That Animate Great Magic Tricks.”