Penney's game: Player A selects a sequence of heads and tails (of length 3 or larger), and shows this sequence to player B. Player B then selects another sequence of heads and tails of the same length. Subsequently, a fair coin is tossed until either player A's or player B's sequence appears as a consecutive subsequence of the coin toss outcomes. The player whose sequence appears first wins.
I understand that we could use law of total probability to calculate the exit probabilities as shown in the first answer here. I want to know whether we can (maybe intuitively) know the best reactive strategy without complicated calculation. Otherwise, we have to calculate all the exit probabilities to obtain the best strategy.