Mathematically, what is the best strategy for Battleship?

Slap the crap out of your little sister every time she makes a good move! Just hope Mom's not around! :-)

[Only kiddin'...don't hit, especially girls!]

Old math is the best way to plan the operations of a battleship.

I've found the player that gets the small boat first is the most likely to win the game. Therefore luck is a big part of the game. An inefficient search "algorithm" only decreases your chances of finding the enemy boats faster.

I often go for a simple gambit. Start by hitting spots that can barely fit the largest ship, the carrier, or the second-largest ship, the battleship:

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---x----x-
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----------
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Continue searching in a pattern not unlike the following:

x----x----
-x----x---
--x----x--
---x----x-
----x----x
x----x----
-x----x---
--x----x--
---x----x-
----x----x

The pattern (20 turns) has a 100% chance to hit the aircraft carrier (5 squares size), 80% chance for the battleship (4 squares size), has a 60% chance of hitting the destroyer and for the submarine (3 each), and a 40% chance to hit the patrol boat (2 squares)

Once you've sunk the carrier, adjust the strategy as follows:

x---x---x-
-x---x---x
--x---x---
---x---x--
x---x---x-
-x---x---x
--x---x---
---x---x--
x---x---x-
-x---x---x

The pattern (26 turns) has a 100% chance to hit the aircraft carrier (5 squares size) and for the battleship (4 squares size), has a 75% chance of hitting the destroyer and for the submarine (3 each), and a 50% chance to hit the patrol boat (2 squares).

When playing against a human player, try to randomise which of the squares within the pattern you try to hit first. This prevents them from seeing your strategy early in the game.

Reduce the pattern as you hit the next biggest boat or, conversely, if you've hit the smallest boats first, find the spaces left behind on your map where the bigger boats could still fit without you having hit them already:

In this example, I've missed 6 times before hitting the carrier and once while trying to home in on the carrier's length:

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---o----o-
----o----o
o----o----
--xxxxxo--
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----------

Now I change my strategy to go for the battleship, taking care not to waste turns near where I've already hit:

o---o-----
-o---o----
--o---o---
---o----o-
o---o----o
o----o----
--xxxxxo--
---o---o--
--xxxo--o-
---------o

I've hit a submarine and continue searching for the battleship:

o---o----x
-o---o---x
--o---o--x
---o----ox
o---o----o
o----o----
--xxxxxo--
---o---o--
--xxxo--o-
-o---o---o

Finally, found the battleship. Now to find the destroyer, only hit into areas that are otherwise impossible for the destroyer to be or that would otherwise be more effective to look elsewhere. For example, in the second-to-last line where I've marked with I would be impossible for the destroyer to be. In the first 3 lines, Where I've marked with P are pointless because the area marked with A would find it anyway:

oPPAoPPAPx
-oPPAoPPAx
--oPPAoPPx
---o----ox
o---o----o
o----o----
--xxxxxo--
---o---o--
--xxxo-Io-
-o---o---o

Above, the first P will find the destroyer *if* it is in B1 to D1. However, the A will find it there *AND* will find it if it is in D1 to D3.

Continue as above when you've hit the destroyer and then apply the same strategy (only with smaller areas) to finding the patrol boat.

One variation on the above - I haven't exactly determined is better or worse - is to start with the pattern that gets the battleship right from the beginning. This probably has a 3 move deficit for finding the carrier but it makes for a better search pattern if you're looking for the patrol boat in the endgame.

Boat placement goes for a reverse of the above. But this also depends largely on what type of strategy the other player is going for and if you can predict what strategy the other player wants to try.

make an X starting from the middle. ull mostly likely hit a ship. it works for me. from then on u know what to do.

This is a modified binary search (for computer geeks like me). Do something like this.

1 - - - 4 - - - 6 -
- - - - - - - - - -
- - 1 - - - - - - -
- - - - - - - - - -
4 - - - 2 - - - 3 -
- - - - - - - - - 8
- - 5 - - - 3 - - -
- - - - - - - - - -
6 - - - 5 - - - 2 -
- 7 - - - 7 - - - 8

You will notice that there is a pattern. Eventually, you will shoot between the other numbers. If you manage to get the PT boat early on, then you only need to shoot every THIRD square instead of every other square. This will help alot. Naturally, when you get a hit, you need to sink that vessel. Then resume the pattern. If you sink the PT boat and the cruiser and sub, then you only need to search every 4 squares (or 5 if the battleship is also sunk).

The old fashion way would be to triangulate on to a position. Once you get a hit then triangulate from that hit.

do a checker board pattern until you kill the one tiny ship then you continue that diangonal pattern but at a spacing of two and then once you take down the ones which are three go three spaces on diagonal the on and on

Here is a discussion of the probability of a perfect battleship game. they claim using their strategy will increase your chances 11 billion fold when compared to random shooting:

http://bit.ly/bl0a6I