With the release of its new action film Battleship this weekend, Universal Studios hopes to make millions of dollars, and sales of the classic board game are expected to rise as well. The gameplay is straightforward, as readers will recall: Each player places five ships—an aircraft carrier, Battleship, cruiser, submarine, and destroyer—on a ten-by-ten grid of squares and tries to “sink” his opponent’s ships by calling out the yards where he thinks his opponent’s ships are hiding. Most players treat the game as a game of chance, randomly selecting squares and hoping for a “hit.” Is there, however, a better approach? Is there a way to improve your fleet’s chances of winning a nostalgic game of Battleship this weekend if a friend challenges you to one?
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Yes, there is. Nick Berry, a Seattle-based technology consultant and president of DataGenetics, a data-mining firm, has meticulously laid out several strategies to increase your chances of sinking your opponent’s ships before she sinks yours. Berry developed computer algorithms to test his systems in hundreds of millions of simulations to calculate their success rates.
Berry began by evaluating the Hunt/Target strategy that most players intuitively employ. The computer goes into Hunt mode, which means it fires at random until it hits a ship. When it gets a hit, it focuses its fire on the squares around it. When the ship is sunk, the computer switches back to Hunt mode until it finds a new target. In Berry’s simulations, sinking an opponent’s Battleship took an average of 66 moves. It’s a reasonable approach, but it still involves a lot of guesswork.
Berry devised a strategy that combines Hunt mode with the concept of mathematical parity to improve on the Hunt/Target method. Consider the following scenario: Consider a board with white and blue squares that were color-coded like a checkerboard. Even the smallest ship, the destroyer, would have to rest on both a white and a blue square because it covers two squares. If you only fire at blue squares, you’ll hit every ship at least once. When you’re in Hunt mode, this method effectively reduces the number of targets on the board by half. (When you register a hit, Target mode is activated, and both blue and white squares are active until the ship is sunk.) This strategy sinks your opponent’s fleet in 65 moves on average, slightly better than regular Hunt/Target mode.
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Berry’s most efficient Battleship method employs a probability density function, which accounts for the various ways the ships can fit across the board. Berry’s algorithm considers all of the five ships’ possible configurations and calculates the likelihood that any given square is occupied by a ship. The ships could be anywhere at the start of the game—the probabilities for each square aren’t that different. However, as the game progresses, you remove more and more squares from the board, reducing the number of possible configurations—a five-square aircraft carrier can’t hide in a four-square stretch of sea, for example. Although a human player will not be able to calculate the probabilities for each square as precisely as Berry’s model, she will remember the underlying strategy. You can greatly improve your hit rate by considering the length of each ship that remains on the board and aiming for the board’s area with the highest probability of containing those ships. Berry’s computer reduced the average number of moves per game to 44 when he used this method.
Battleship is, after all, a game of chance. When I spoke with Berry, he pointed out that no strategy will guarantee a win for man or machine every time. My small sample of three games using Hunt/Target, Hunt/Target with parity, and an attempt at using probability density yielded games lasting 38, 41, and 55 moves, respectively, as a testament to the game’s random nature (and undoubtedly some human error). I came out on top two out of three times.
Berry, who worked for Microsoft’s Casual Game division (which now produces the Xbox) for ten (10) years, enjoys deconstructing classic board games.