Coin Flipping Sequences
Two players are playing a coin-flipping game. They each choose a sequence of 3 results (for example, THH or HTH). Then they begin flipping one coin at a time and recording the outcomes in order. The first player to have his or her sequence appear in order in the results is the winner.
If Player 1 picks a sequence at random and announces their sequence first, what is the minimum probability that Player 2 will win if Player 2 chooses their sequence optimally?