Losing with Heads or Tails

Flipping a coin may not be the fairest way to make a choice.

Heads, you win. Tails, you lose.

It turns out that coin tosses may be less fair than you might think. A new mathematical analysis even suggests a way to increase your chances of winning.

People use coin tosses all the time to make decisions and break ties. You’ve probably done it yourself to decide who gets the last piece of pizza or which team gets the ball first. Heads or tails? It’s anybody’s guess, but each side is supposed to have an equal chance of winning.

That’s not always true, say mathematicians from Stanford University and the University of California, Santa Cruz. For a coin toss to be truly random, they say, you have to flip the coin into the air so that it spins in just the right way.

Most of the time, though, the coin doesn’t spin perfectly. It might tip and wobble in the air. Sometimes it doesn’t even flip over.

In experiments, the researchers found that it’s practically impossible to tell from watching a tossed coin whether it has flipped over. A tossed coin is typically in the air for just half a second, and a wobble can fool the eyes, no matter how carefully you watch.

To see how wobbling affects the outcome, the researchers videotaped actual coin tosses and measured the angle of the coin in the air. They found that a coin has a 51 percent chance of landing on the side it started from. So, if heads is up to start with, there’s a slightly bigger chance that a coin will land heads rather than tails.

When it comes down to it, the odds aren’t very different from 50-50. In fact, it would take about 10,000 tosses for you to really notice the difference.

Still, when you’re gunning for that last piece of candy, it can’t hurt to have a leg up, no matter how small.—E. Sohn

Going Deeper:

Klarreich, Erica. 2004. Toss out the toss-up: Bias in head-or-tails. Science News 165(Feb. 28):131-132. Available at http://www.sciencenews.org/articles/20040228/fob2.asp .

Peterson, Ivars. 2003. Flipping a coin. Science News for Kids (April). Available at http://www.sciencenewsforkids.org/pages/puzzlezone/muse/muse0403.asp .


This is a very cool article. My friends and I always break a tie or make a

decision by flipping a coin.—Natasha, 13

More Stories from Science News for Students on Math