After keeping my eyes out for this game for months, I finally found it at Target a few days ago. Since then it has quickly become one of our favorite ultra-fast games. A perfect way to spend an extra 10 minutes before leaving to catch the bus or before bed.
Having a pretty good intuitive grasp of probability, I was pretty confident that I had the relative strengths of each ship figured out by about our fourth or fifth play. But the scientist in me wasn't content with intuition. And so, lacking the probabilistic rigor to find exact probabilities, I wrote a quick program to compute approximations.
What follows is (an approximation of) the probability of success for each combination of ships. "Battleship to Carrier" implies the probability of a Battleship successfully sinking an Air Craft Carrier in one turn. This may be considered a spoiler to some, so if you don't want to have the game ruined by knowing exactly which ship to use in which situation, don't read on. However, if you've played the game much at all, there shouldn't be anything too surprising.
The program used to generate these takes all of the ships' special abilities into account (i.e. the "Admiral" rules) except for the Carrier's ability to roll first and then decide which of the two front ships to attack. This means that the Carrier, until an opponent has only a single ship left, is a better attacker than the numbers below indicate.
Also, again note that these are approximations. The numbers below are from only a single run (10,000 attacks for each combination). While the numbers show a slight difference in probabilities, for example, between "Battleship to Destroyer" and "Battleship to Submarine", these probabilities are actually identical. In other words, round liberally.
And with all of those caveats out of the way, here are the numbers:
Battleship to Battleship: 40.33%
Battleship to Destroyer: 66.97%
Battleship to Submarine: 67.82%
Battleship to PatrolBoat: 87.09%
Battleship to Carrier: 87.08%
Destroyer to Battleship: 58.92%
Destroyer to Destroyer: 76.36%
Destroyer to Submarine: 76.67%
Destroyer to PatrolBoat: 88.78%
Destroyer to Carrier: 88.87%
Submarine to Battleship: 43.08%
Submarine to Destroyer: 42.02%
Submarine to Submarine: 42.55%
Submarine to PatrolBoat: 42.7%
Submarine to Carrier: 42.27%
PatrolBoat to Battleship: 17.39%
PatrolBoat to Destroyer: 52.96%
PatrolBoat to Submarine: 54.11%
PatrolBoat to PatrolBoat: 83.79%
PatrolBoat to Carrier: 84.09%
Carrier to Battleship: 16.42%
Carrier to Destroyer: 44.91%
Carrier to Submarine: 44.99%
Carrier to PatrolBoat: 75.11%
Carrier to Carrier: 75.63%
If you're interested in the program used to generate these (written in Haskell), feel free to send me a GeekMail.