When you throw a coin in the air to make a decision, you'd expect the outcome of the toss to be 50-50 whether you catch it or let it land on the ground. But, according to randomness expert Persi Diaconis, that's simply not true.
It's worth noting that Diaconis used to be a magician, so he knows more about weighted coins than most of us. As he explains in the video below, in tests, he's found that the normal old coins in your pocket can have a bias too, which is most evident when you spin a coin on a table top. Some coins demonstrate such severe "edge effect," as he calls it, that they can fall on one side 80 per cent of the time.
That same edge effect comes into play, at least a little, when a coin lands on the ground, as it bounces and then spins before settling on the floor (certainly, it has more effect here than while the coin is in the air). In contrast, it's incredibly difficult to time the catch of a tossed coin to cheat the other person — and even then, if all you want is a good, clean toss, there's no reason to even attempt it. All of which means that, if you're looking for a fair outcome, you should always catch it in mid-air. [Numberphile]