Originally posted by Aetherael
this seems like it would be a sound strategy, if used in tandem with the mirroring idea i just mentioned... perhaps imagine a checkerboard lattice on the board, and fill it in using spaces from one of each quadrant, and then filling in 4x4 checkers before doing the interior 2x2 spaces? and hope to get lucky with the smaller ships? would be great to see s ...[text shortened]... as each square is equally likely to contain a boat as any other square... what is optimal then?)
It seems like a sound strategy, but the question posed is "what's the optimal way to choose targets in order to find the enemy ships fastest?"
The optimal way would have to be:
b. find ALL ships
c. repeatable results using the same method
The solution fails if you can not find all ships, and leaving it to luck to find the small ships would negate the optimization of the process.
This is why I mentioned going to every other square. In this way, nothing is left to luck.
Battleship being 10X10 square, there are 10 columns and 10 rows (think of it as an Excel grid, columns being letters, rows being numbers.) Means 100 possible squares. 17 occupied with ships. Even if you sink the first 4 ships in your first 15 guesses, that still leaves you with 2 in a possible 85 squares (assuming that the placement of the other ships do no negate squares by blocking off one empty square)
Choosing any squares with the permutations of (A,odd) (B,even) (C,odd) (D,even) etc. or vice versa randomly will reduce your chances available choices to 50. Now you are looking for 8 or 9 hits in 50 (8 or 9, because skipping every other square will cut the hits in half). Much better chances.
Also, once you get one hit, continue with the same process of every other square around that hit, (unless the 4 largest ships are sunk already) because the best bet is that you hit one of the larger ships any way and you want to find out what direction it is pointing in, vertical or horizontal. Once that is determined, you can fill in the blanks.
So, the maximum guesses we need are 50 plus 3 (3 misses trying to find the direction of the Destroyer, 2 hit ship).
Since, in the beginning, unless you have prior knowledge or suspicions of how your opponent will place them, each square is equally as likely as containing a ship. Skipping every other space randomly, until ships are known, is the fastest way to garuntee that all ships are found and is easily repeated.
Now, whether or not you win, is a different question. Luck is a huge factor, especially if both opponents employ the same strategy.