Tuesday, September 14, 2010

We Will Recieve

Let's take a bet. Go grab a coin, and we'll flip it. Heads or tails?

Wait, wait, hold on. Before you flip it, which side is facing up?

I'll take that one.

According to a 2007 study by three researchers at Stanford and UC-Santa Cruz, Perci Diaconis, Susan Holmes and Richard Montgomery, a coin flip is not 50-50. The exact weighting depends on a couple things.

As noted, the first thing to look at is what side's facing up to start; the edge goes to the side facing up, which could land on that side anywhere from 51-60% of the time. Not exactly the advertised even odds at the high end.

But where along that 51-60% is the final number? It depends on a second factor, and unlike what Vince Lombardi liked to think, it's not the little bit of extra weight on the head side that made him pick heads all the time. Maybe the landing surface is a factor, but the study was done using grass as a surface, the same as used in some NFL stadiums, and similar to the FieldTurf used in others (which should make the implications here obvious).

It's how you flip it that counts. As the linked article explains:
Using a camera from the Stanford engineering department that snapped 1,000 frames per second, they determined that the laws of basic mechanics play a large role. Coins flipped from a thumb don't merely rotate around their axis, but they also spin like a Frisbee.

The degree of that Frisbee spin depends on the motion of the thumb.

The more Frisbee spin, the longer the side facing up stays facing up when the coin is in the air.

And the longer the side facing up stays facing up, the better chance it will land that way.

"Some people flip in a more biased way than others," Holmes said. "There's always bias to the side that's facing up, and the variance depends on the motion of the flipper."

Packers, I hope you're paying attention.

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