How many submarines do I need to take down an aircraft carrier?
Check out the Axis &amp; Allies Combat Simulator/Calculator. You can choose which variant of the game you're playing (Original, Revised Edition, etc.), how many simulations to run, and a number of other options. (There's even a iPhone and Android versions!) The combat simulator then tells you the average IPC loss for both sides and the average winning percentage.

Presuming you play with the Revised Edition (a/k/a, the 2nd Edition), here are the odds. (Note that each simulation has a link to the combat simulator with the attacking and defending units already entered. The link sets the simulation runs parameter to 1,000, but the results I present here were computed using 5,000 runs.)


1 sub: 49.8% chance of winning, average IPC loss: 4 for attacker, 8 for defender
2 subs: 85.4% chance of winning, average IPC loss: 4 for attacker, 14 for defender
3 subs: 97.9% chance of winning, average IPC loss: 2 for attacker, 16 for defender


What about super subs (which attack at a 3 instead of a 2)? If so, here are how the odds unfold:


1 supersub: 67.1% chance of winning, average IPC loss: 3 for attacker, 11 for defender
2 supersubs: 95.0% chance of winning, average IPC loss: 2 for attacker, 15 for defender
3 supersubs: 99.6% chance of winning, average IPC loss: 1 for attacker, 16 for defender


Also, because a sub has the benefit of "first attack," there will never be a scenario where both the sub and carrier are destroyed. In this type of battle you know that one side (and only one side) will be standing at the end.