Well, the Polaris warhead was hot garbage that probably would have had a 50-75% failure rate if actually fired, while the Minuteman had literally just come into service, was available in small numbers at best, and had a warhead, the W59, that was not terribly reliable either. Between the small number of missiles available, the likelihood of other failures prior to the warhead detonation, and the warhead issues with both, they're most likely not going to actually do that much damage. The bombers are basically irrelevant because even considering the fueling and arming time they won't get there until after the missiles have launched. Thus, the relevant weapon systems here are the Atlas and Titan I. Most likely at least a few Soviet missiles will get launched, especially since the U.S. lacks any way (at this point) of knowing precisely when the Soviets start arming and fueling their missiles.
I would tend to disagree. 50% failure mean the rubble bounces a little less and the B-52 airborne patrol locations were largely chosen to be within two-three hours of target (to the extent practical). Soviet missile launch procedures took roughly four hours and the missiles were insanely vulnerable throughout the process. Soviet missiles also had a fairly nasty habit of sort of blowing up if you looked crooked at them, and it would have been remarkable if the Soviets managed to get 25% reliability from their warheads (or got them to land in the correct state).
In order for the Cuban Crisis to go Hot there were a very limited number of triggers.
1. Soviets launch, whether is is an error, "lone gunman" or response to a U.S. conventional attack really doesn't matter.
2. Soviet Submarine uses a Special Weapons against the U.S. fleet (came all too close to happening).
3. The U.S. misreads a Soviet move and launches.*
4. The USSR misreads an American move and launches.***
5. U.S. simply decides "F*** these guys" and starts blasting, beginning with Cuba**
6. Soviets simply decide"F*** these guys" and starts blasting,***
* Unlikely. The U.S. had surprisingly good Intel on Soviet alert status, especially their air defense system. See comments made by General David Burchinal on the issue, The Soviets went to some lengths to keep those forces at a low readiness throughout the Crisis, even as the U.S. started to kick up its alert levels
** VERY Unlikely. Kennedy was pretty much bound and determined not to go down in history as a mass murder
*** Even more unlikely. Unlike Kennedy (or the rest of the Politburo) Khrushchev was fully briefed on just how badly the Soviets were outgunned.