A 4x4 version of the Battleships game with one 3x3 and one 2x1 ships (placed horizontally only for simplicity) and 3 initial shots:

The simulation program has two grids, the one on the left is the grid in which the player plays, and the right one shows the expected value of shooting each cell highlighting the ones with highest value. 3x1 ship hits are shown in green, 2x1 hits are shown in gold and misses are shown in blue. All cells shot show the number of credits awarded to the player. The top left image shows the start of a game and advises the player to shoot any cells on columns 2 and 3 (1000000 games have already been played in a fast simulation). The top right image shows the state of the game after the player has shot a miss and a 3x1 hit. The right hand side grid advises to shoot cells on the same row as the hit. The player follows the advice and uncovers the 3x1 ship, getting the bonus. He then shoots a miss and next he hits the 2x1 ship, as shown in the bottom left image. He is then advised to shoot either of the cells next to the hit horizontally. He chooses to shoot the cell on the left of the 2x1 hit but misses. Thus, having shot 3 misses, the game ends and the player gets 455 credits.