Solution to COIN UNBIASING

Solution 1 - 1) Flip the coin twice.
2) If you get HT, guy #1 wins. If you get TH, guy #2 wins. These are equally probably, regardless of p.
3) If you get HH or TT, go to step 1)

Solution 2 - You hide the coin in one of your hands, and ask your rival to guess which hand has it.

Solution 3 - we know that heads is more likely. So both parties take turns flipping until they get tails. Whoever gets tails in fewer flips wins. If you both get tails on the first try, restart.

Solution 4 - A very practical solution: Why can't the girl just choose which bloke she likes better? :P