What is the most mathematical strategy for placing ships and for attacking ships in the board game battleship?

Question

I am looking for a mathematical answer not just "Don't place them next to each other"

Answer 1

This is really a "game theory" question. The best strategy for placing your ships must defeat the best strategy for finding them. You have to do two things: one, guess your opponent's finding strategy and two, pick the defensive strategy that hides best against it.

So first: what is the best search strategy? I think that the best search strategy is to eliminate the possible hiding places for ships in descending order from large to small. Then work your way down until you end up hitting every other square in a "checkerboard" pattern. (that is, a pattern including only squares of one color as they would be on a checkerboard)This method wastes the fewest number of shots, because if you sink the smaller ships along the way you then need a minimal number of shots to find and sink the big ones.

So, first you shoot to eliminate all the places the aircraft carrier and battleship can hide. You do this by laying down a diagonal pattern with 3 empty spaces between each shot. If you get a hit, fire your next "ranging shots" around the hit with one space between the shots (keeping the checkerboard pattern intact). Only shoot off the checkerboard if you are shooting between two hits.

After this pass you will have definitely sunk the aircraft carrier and battleship, and possibly one or more of the 3-space sub and cruiser and the 2-space destroyer. If you sunk the destroyer in the first pass then you are in great shape, because you only now need to eliminate the remaining 3-space regions to find the other ships. Second pass, eliminate the 3-space regions. This guarantees sinking the sub and cruiser. If the destroyer has not yet been hit, the only solution is to fill in the checkerboard.

If this is the best search strategy then the best ship placement strategy is the one that defeats it. Place your ships at random, and avoid placing two ships so that a "ranging shot" after a hit on one ship will not find the other ship. That is, don't place them with only one space between them. Note that you could therefore place ships with one end space overlapping, one ship would not be found from the other with a ranging shot.

Take special care with the placement of the destroyer. Your enemy must only find it by random chance, not by a ranging shot from a hit on another ship! Therefore place it so that no spot on the destroyer is one empty space away from any spot on another ship.

Mathematical caveat: if there is a search strategy that specifically defeats this placement strategy then we go to another layer of game theory complexity - but I do not think that there is any search strategy better than the one I described, even if the searcher knows that you are employing this defensive strategy. Any other strategy wastes shots.

Answer 2

This Site Might Help You.

RE:
What is the most mathematical strategy for placing ships and for attacking ships in the board game battleship?
I am looking for a mathematical answer not just "Don't place them next to each other"

Answer 3

Battleship Layout

Answer 4

Well, the general idea is that ships can't be placed diagonally, so placing your pegs diagonally is more likely to find a ship. I personally like to place pegs a knight's-move apart, ie place a peg, then move down 2 over 1 and place another peg, until I'm all the way across the board.

Answer 5

Mathematically I can't answer you because I believe it's a game of luck and skill. I have a way I set up where I almost always win. Line up a ship with 3 holes in a straight line, touching with the 2 hole sucker. It appears to your opponent as the carrier and will quite possibly confuse the hell out of them. Try it, it works well. Does not win EVERY game, but most. (Puts the mathematical odds of winning in your favor.)

Answer 6

Don't place your ships near the edge of the gameboard so your opponents chances of missing your ships aren't lessened. The game is a lottery. There really isn't a strategy.

Answer 7

you can find a free download of Battleship Game here: http://bit.ly/ZYulmW

Finally the full version is avaiable!
The game is drawn for the World War 2 and includes the most famous battles that happened during this time.
It's my favourite game.

Answer 8

i say every second square so that it looks like a checkers board

Answer 9

avoid patterns