Penney's Game

Two players play the following game. Player 1 chooses a triplet of coin flip outcomes (e.g. $HHT$) and announces it. Then Player 2 chooses a different triplet. They keep flipping a fair coin until one of the two triplets appears as a consecutive subsequence. The player whose triplet appears first wins.

Both players are perfectly rational and want to maximize their probability of winning.

Would you rather go first (as Player 1) or second (as Player 2)? If you go second and play optimally, what is your guaranteed minimum probability of winning?