I think mathematically perfect strategy is not a problem for PvP Battleship. Certainly, there is a perfect strategy. But when you need to choose one square from N empty squares, mathematics is useless. And when you hit a ship, you don't need an advanced computation to search for rest of ship. Human reasoning is sufficient for that. I think, computer advantage is unlikely in the Battleship game.
EDIT: If anybody know about some mathematical analysis of Battleship game, post it here, please.