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Another classic game, the object of which is to sink all your opponent's ships before they sink yours.
There are two playing areas (typically 10 by 10), and both players have five ships, each of which may be placed vertically or horizontally without overlapping. Each ship occupies a certain number of squares on their playing area:
To sink a ship, you must score a hit on each of the squares occupied by the ship. You and the other player take turns shooting at each other's ships. You could include more options, such as firing salvos and limited ammo.
You will have to deal with the problem of players needing to secretly place their ships on the board. Other than having players turn away from the screen at the required moments, you could place their ships randomly for them.
More information about Breakout can be found, for example, by searching AltaVista.
Games are distributed under the WebGames License