Battleship

The numbers behind the guessing

Battleship has a reputation as a coin flip, and the reputation is wrong. Some years ago the statistician Nick Berry simulated millions of games of the classic version, a ten-by-ten grid with five ships covering seventeen cells, and measured how long each strategy took to sink everything. Pure random firing needed about 96 of the 100 possible shots. Hunt-and-target play, random search until a hit and then finishing the ship, dropped the average into the mid 60s. Adding a checkerboard search pattern trimmed a few more, and a full probability map finished typical games in the low-to-mid 40s. Same rules, same hidden fleet, half the shots. That whole gap is skill, and most of it is available to anyone willing to fire in a pattern instead of on hunches.

Hunt, then target

Strong play splits the game into two modes. Hunting is what you do with no information, and the goal is for every shot to interrogate as much of the grid as possible. Fire only on the squares of one colour of an imagined checkerboard: since even the smallest ship covers two cells, every ship must touch that colour somewhere, so the pattern cannot miss a fleet while skipping half the board. Targeting begins the instant you connect. Probe the hit's neighbours to find the ship's direction, then follow the line until the sink registers. Once the two-cell ship is gone, you can thin the hunt further, spacing shots so that every straight run of three cells contains one, because nothing small enough to hide between them is still afloat.

A worked finish: your checkerboard shot hits. You probe above, miss; you probe right, hit. The ship runs along the row, so you extend rightward until it sinks, and if the sink never registers you swing back and extend past the far side of the original hit, because first contact is rarely an end cell. Two isolated hits sitting on one line with a gap between them almost always mean a single ship spanning the gap: fill it in before hunting anywhere new.

Tips to sink the fleet faster

• Hunt on a checkerboard and skip the squares between; no ship can hide entirely in the gaps.
• The moment you score a hit, fire at its four neighbours to find which way the ship runs.
• Once two hits line up, keep firing along that line until the ship sinks, then extend one more in case it is longer.
• Track which ships you have already sunk so you know the largest that could still be out there.
• Point your search at the open middle; long ships fit there more often than jammed against an edge.
• If a line of hits refuses to sink, two ships may be touching; branch sideways from the extra hits.

Probability thinking and the computer

Advanced players think in probability density: at any moment some squares can host more of the remaining ships' possible placements than others, and the middle of large open regions is usually richest, since long ships fit there in more orientations than against an edge. You never need to compute this exactly; favour big empty areas while hunting and switch to relentless line-following the instant you connect. In this version both fleets are placed at random, which quietly strengthens the case for system over instinct: random placement has no habits to outguess, so an even, pattern-based search is provably the best you can do until a hit arrives. The computer, meanwhile, hunts your fleet exactly the way you hunt its, clustering follow-up shots around every hit it lands, and the match becomes a race between two search algorithms, one of which is you.

From pencil pads to pegboards

Battleship began as a pencil-and-paper pastime around the First World War, played on hand-drawn grids long before anyone sold a copy. Printed pad versions appeared between the wars under names like Salvo in the early 1930s, and the game took its familiar plastic form in 1967, when Milton Bradley added the peg grids and the little grey fleet. A decade later it led the way again: Electronic Battleship arrived in 1977 as one of the first mainstream board games with a computer inside, and a talking version followed in 1989. More than a century of packaging, and the loop underneath has never needed changing: call a square, hear the answer, update what you know, call again.