A coin is biased such that the probability of throwing a H is p, where 0 < p < 1.
Two players, A and B, takes turns to throw the coin. The game ends when either the sequence HHH (then A wins) or HTH (then B wins) is thrown.
What must p be in order for the game to be fair?
(Because of the nature of the source, I expect that p = 1/2 isn’t the only answer).