You have a coin that may be biased. If P is the probability of your coin flip being Heads, you don't know what P is...

Question

You have a coin that may be biased. In other words, if P is the probability of your coin flip being Heads, you don't know what P is, (and therefore you don't know whether it is 1/2)

You and your friend want to toss for who goes first in a game. Can you use your coin to generate a fair coin flip (How)?

Answer 1

If the probability of coin flipping head = P
The probability of coin flipping tail = 1 - P
Now
The probability of flipping heads & then tails = Probability of flipping tails & then heads = P(1 - P)
Which means to make a fair coin toss we now need 2 flips
Player 1 wins if the sequence is HT
Player 2 wins if the sequence is TH
Any other sequence (HH, TT) implies the toss has to be repeated.