Related to this is how to flip a coin fairly when you think you've got a biased one.

A biased one is where Heads has some probability p <> 0.5 and Tails has probability 1 - p.

So if you throw it twice in a row, there are four possibilities, Pr(HH) = p^2 and Pr(TT) = (1 - p)^2 being unusable because you don't know what p is, but HT and TH are equiprobable regardless of what p is. So throw it twice and let HT count as Heads and TH counts as Tails.

This only works with someone who either understands probability or trusts you and believes that you understand probability. To anyone else, you could probably explain it till you were blue in the face and not get anywhere.

Of course it doesn't depend on p being other than 0.5, so it works for any coin.

And it doesn't depend on using coins, so it works for any arrangement where you have two probabilities summing to unity. For example, blindly taking a pen out of a drawer containing five blue and three black pens.