What is the probability that $HH$ occurs before $TH$ in an infinte sequence of coin flips? This is one of the questions of a set of exam review questions that don't have solutions to them. I can't get my head around this but it seems so simple.

By flipping a fair coin repeatedly and independently, we obtain a sequence of
  H's and T's. We stop flipping the coin as soon as the sequence contains either HH or TH.
  Two players play a game, in which Player 1 wins if the last two symbols in the sequence
  are HH. Otherwise, the last two symbols in the sequence are TH, in which case Player 2
  wins.
A = "Player 1 wins"
  and
  B = "Player 2 wins."
Determine Pr(A) and Pr(B)


Hint:  Note, the only way player 1 wins is if the sequence starts "HH".  Once a "T" appears, the second player is guaranteed a win eventually.
