Battleship

The rules it plays by

Milton Bradley rules. Ships sit flat on the grid, across or down, and they may lie against each other. Forbidding that would make the game easier to work out, since a sunk ship would clear its own border for you, but it is not how the box plays.

The one departure is that sinking a ship shows you where it was. Every version on a screen does this, and it matters here for more than appearances: it means you and the opponent are working from exactly the same facts. An opponent that knows something you cannot is not a harder opponent, it is a different game.

How the opponent thinks

Most versions of this hunt at random until they hit something and then switch to chasing it along. This one has no two modes. For every ship still afloat it walks every place that ship could still be, throws away the ones that some earlier shot has already ruled out, and lets each survivor vote for the squares it covers. Then it fires where the votes are highest.

Hunting and chasing both fall out of that on their own. On an empty board the middle of the grid is covered by more possible placements than a corner is, so it opens near the middle. After a hit, the placements running through that hit explain something the others do not, so they outrank everything else and it follows the ship along. One rule, two behaviours, and nothing to switch between.

There is one thing counting cannot work out for itself. While nothing is half found it only considers every other square, because the shortest ship afloat is two long and must therefore cross one square of any checkerboard. That skips half the board with no chance at all of stepping over a ship. It barely changes the average game and it takes a chunk out of the worst one.

Over two thousand games it needs 45 shots on average to clear the board, against about 95 for firing blindly, with the worst game taking 63. A person playing carefully lands somewhere in between. It is not the strongest Battleship engine ever written, and the honest reason is that it treats each ship independently rather than working out which whole fleets are still possible.

It cannot see your fleet. Everything it reads is the outcome of a shot, which you watched happen, and there is a test that holds it to that: forty different fleets that would have answered the same four shots identically all get the same next shot out of it. If it ever peeked at a square nobody had fired at, they would pull its aim in forty directions and the test would say so.