The Uneven Odds of Flipping or Spinning a Coin

By Wesley Fenlon

Science takes some of the randomness out of a random coin toss.

What do we know about coins? They're legal tender, they usually depict dead men on one side, and they're the go-to tiebreakers for problems big and small. Thing is, coins aren't perfectly suited to that role. A study on coin tosses reveals that the "randomness" of a toss is actually weighted ever so slightly towards the side of the coin that's facing upwards when a flip begins. "For natural flips, the chance of coming up as started is about .51," the study concludes.

The paper, written by statistics and math professors from Stanford and UC Santa Cruz, also points out that a perfect coin toss can reproduce the same result 100 percent of the time. Of course, the perfect flip was performed by a machine, not a person. And the results that lean ever-so-slightly in favor of flipped-side-up don't take into account flipping a coin after catching it or letting it bounce around on a floor or table. In practical usage, the .51 bias is so slight that you'll never notice.

If, like me, you'd always heard that coins tend to land tails-up because the heads side is heavier, there's some science available for you, too. Spinning, rather than flipping, an old penny will land on heads something like 80 percent of the time. Lincoln's head is heavier than the Lincoln memorial on the reverse, which leaves tails facing up more often than not. Unless the penny has accrued enough dirt or oil to throw the weight off.

And let's be honest--how often do you come across an old, clean penny?