There's a popular battleship clone called Fleet Battle with a large active player base.
There's a few different strategies and shot patterns that top players use but none of them shoots directly in the middle to start the game.
That game does have slightly different rules with a different board size, different ship shapes, and it allows you to place ships adjacent to each other.
I'm not sure how much that would make a different in the approach but it would be interesting to see how those aspects change the analysis and compare them to what we observe in real human players.
There's a few different strategies and shot patterns that top players use but none of them shoots directly in the middle to start the game.
That game does have slightly different rules with a different board size, different ship shapes, and it allows you to place ships adjacent to each other.
I'm not sure how much that would make a different in the approach but it would be interesting to see how those aspects change the analysis and compare them to what we observe in real human players.