ORIGINAL: Mgellis
Let's try a well-known one...
What if the Soviets tried to run the blockade of Cuba in 1962? The American Navy fires on them, sinks a few of the ships, etc. Meanwhile, the one Foxtrot submarine that nearly fired nuclear-tipped torpedoes actually does fire them--would they be able to tell on sonar that ships are breaking up and other bad things are happening? That might be the reason for using their special weapons. Suffice that some American vessels go down, too.
Realistically, what happens now? Both sides fire all their ICBMs? Limited bomber strikes with conventional weapons against proxy states to indicate "a high level of displeasure" over what has happened--the U.S. bombs some Cuban bases and the U.S.S.R. bombs some Turkish ones? Kennedy gets on the phone to Khrushchev and, without either of them admitting they are both scared silly by what has happened, start to work out some kind of agreement? Something else? What do you think?
In all reality, the Soviet Union would be glowing for centuries. In November '62, the US nuclear arsenal vastly - VASTLY - outnumbered the Soviet. The Americans didn't realize it, though, apparently. Yes, the Soviets would get some shots off - especially in Europe - but the United States would have annihilated the Soviet Union (within 28 hours, if you believe the USAF estimation).

