Battleship is the game everyone played as a kid and few have played as an adult — a shame, because there's a genuine probability puzzle hiding underneath the kids'-game packaging.
The single biggest discovery for intermediate players is parity. Battleship ships are all 2+ squares long, which means at least one of every two squares on the board must be empty. If you only target squares matching one parity, you cover the whole board in half the shots and still hit every ship.
Modern reimaginings include Captain Sonar (real-time team variant) which is genuinely excellent — but the original remains the universal 20-minute, two-player pickup game.
