Any ideas for creating my own paper and pencil game?

Yes! You can create a battleship sort of thing on paper. It will work by each player draws two 10 x 10 grids, labelled along the sides with letters and numbers. On the left-hand grid the player secretly draws rectangles representing their fleet of ships: Each player's fleet consists of the following ships:

1 x Aircraft carrier - 5 squares

1 x Battleship - 4 squares

1 x Cruiser - 3 squares

2 x Destroyers - 2 squares each

2 x Submarines - 1 square each

During play the players take turns is making a shot at the opponent, by calling out the coordinates of a square (eg D5). The opponent responds with "hit" if it hits a ship or "miss" if it misses. If the player has hit the last remaining square of a ship the opponent must announce the name of the ship; eg "You sank my battleship".

During play each player should record their opponent's shots on the left-hand grid, and their shots on the right-hand grid as "X" for a hit and "O" for a miss