Two players (A and B) are playing a game. Player A randomly chooses a sequence of three possible coin flips (eg HTH, TTH, etc) from the possible 8 and then player B replies with his own (non-random) choice. Then they flip a coin until one of the two sequences appears. What is the probability of player B winning?
We can immediately tell that certain sequences are advantageous to player B, for example if player A chooses HHH, then the sequence THH is an automatic win unless the first three tosses come out Heads. The same for TTT. Are all the others fair for both?