Should You Catch a Tossed Coin?

Chris Higgins
YouTube / Numberphile
YouTube / Numberphile / YouTube / Numberphile

Here's the question: During a coin toss, is it more fair to catch the coin in mid-air, or to let it hit the ground? Meaning, will one of these methods result in any change to whether the coin comes up heads or tails? I was quite surprised to learn that apparently it does matter, even if it's just a little. (And I immediately thought of the Super Bowl, where the coin hits the ground and everybody stands around staring at it.)

In this video, randomness/coin-flipping expert Persi Diaconis talks us through the reality of biased coins and why they are biased. Then he gets to the meat of the question. I was genuinely surprised by his answer. Incidentally, Diaconis is also a former magician, but he's not talking about doing crazy hand-catching tricks; he assumes a typical human just catching a coin without trickery versus letting it hit the ground.

Somewhat related, here's a long examination of the recent Super Bowl coin tosses, and what was up with that 14-toss-winning streak by the NFC champions. Warning: lots of math in this one.