Should You Catch a Tossed Coin?

January 21, 2016 | Elizabeth Knowles

A hand flipping a coin into the air
Photo credit: Nicu Buculei/Flickr (CC BY-SA 2.0)

Or is it more random to let it fall?

Pretty much everyone, at one time or another, has flipped a coin to make a decision. Whether it was to pick what movie to watch with your family, or to make a life-changing choice, you probably assumed that there was a 50 percent chance that it would come up heads and a 50 percent chance that it would come up tails.

Have you ever actually thought about how fair a coin is? Well Persi Draconius, an American mathematician, former magician, and current randomness expert and professor at Stanford University, has. In fact, he made two whole Numberphile videos about it.

He explains that, if we had all the necessary information (how fast a coin was revolving and how fast it was moving vertically) we could calculate which way it would land. It’s basic physics after all!

He also explains that a typical coin flip isn’t completely random. There is a 51 percent chance that a coin will land the way it started. So, if you’re hoping for heads to come up, start with heads on top when you flip your coin. That tiny difference won’t change much, but you will up your chances ever so slightly. It can’t hurt to try, right?

In a second video, he looks at whether a coin is more random if you catch it or if you let it hit a surface like a table. You might think that adding a human component — a hand — will interfere with the randomness, but that isn’t actually true. A coin that lands on a table tends to spin before it falls. If it is weighted a certain way, that will interfere with the randomness.

“A given coin has it’s own biased when spun on the edge. But that bias fluctuates from coin to coin,” he says. Coins with un-serrated edges tend to be most biased.

However, regardless of how a coin is weighted, the odds won’t be affected so long as it is caught in the air and you neglect air resistance. To test this, Draconius created a coin where one side was made of balsa wood and the other side was made of lead. He flipped it many times and confirmed that the weighting of the coin didn’t affect the proportion of heads and tails as long as it was caught in the air and not given the chance to spin on a surface.

You might want to avoid trusting a coin to make a life-changing decision for you, but if you’re just looking for a quick and easy way to end a debate, go ahead and flip that coin — but don’t forget to catch it!

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