How plausible in reality were the plots of Dr. Strangelove and Fail-Safe in regards to the bombers getting through?

Wiki makes it complicated:

The character is an amalgamation of RAND Corporation strategist Herman Kahn, mathematician and Manhattan Project principal John von Neumann, rocket scientist Wernher von Braun (a central figure in Nazi Germany’s rocket development program recruited to the US after the war), and Edward Teller, the “father of the hydrogen bomb”. It has been claimed that the character was based on Henry Kissinger, but Kubrick and Sellers denied this; Sellers said, “Strangelove was never modeled after Kissinger—that’s a popular misconception. It was always Wernher von Braun.” Furthermore, Henry Kissinger points out in his memoirs that at the time of the writing of Dr. Strangelove, he was a little-known academic.

More simply, the stereotype of a scientist (especially those involved in nuclear weapons and rocketry) for all mid-century Americans was the eccentric Central European epitomized by Albert Einstein, many of the Manhattan Project scientists, and, of course, rehabilitated Nazis captured after WWII.

That was The Navy. The definite article is definitely required:

Operation Sky Shield. There were multiple exercises. In these cases, the bombers did get through.
I hadn’t read before that the Brits were cheating; I thought it was the Vulcan was so good.

There are two different chains with two different components of the code, both of which update the president, who is the only one with both factors.

The British acted like an enemy would…an enemy is under no compulsion to act in a way that is convenient to you.

While the SR-71 was devilishly hard to intercept (I read that 4000+ missiles were unsuccessfully fired at them over the plane’s service), a lot of that was due to it being a sort of proto-stealth plane, as well as flying so high and so fast that by the time the air defense people realized what was going on, it was hard if not impossible to respond effectively.

But the whole idea of low-altitude bombers penetrating Soviet airspace was what SAC planned to do from the early 1960s on, once surface-to-air missiles’ effectiveness passed some threshold. They flew VERY low to avoid radar detection, and due to satellite reconnaissance, planned to follow routes to avoid most Soviet air defenses anyway, as well as take advantage of earlier ICBM/SLBM strikes to eliminate Soviet air defenses. (the bombers were expected to enter Soviet airspace hours after any ICBM/SLBM exchange)

I would assume that if the USAF bombers in either scenario had the element of surprise, they could get VERY far into the USSR before it was all figured out and the Soviets could react. However, I would assume that in the movie scenarios the USAF could tell the Soviets the targets AND the pre-planned routes that they were expected to take to those targets, which could let the Soviet pilots be waiting for them.

They had some other tools to enhance inbound survival, too. The Quail decoy drone, which looked on radar just like a B-52 bomber.

The AGM-28 Hound Dog nuclear cruise missile, which was intended to be launched against Soviet air defenses that might threaten the bomber in its ingress.

Similar tactics were planned for later standoff nuclear weapons, including the AGM-69 Short Range Attack Missile and the AGM-86 Air Launched Cruise Missile.

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Its not too dissimilar to an actual nuclear close shave in 1979 where a fault in a chip caused a false alarm (not finding any technical details on how exactly the chip went wrong). In the integrated circuit era, obviously, but seems analogous:

Still… they planned on flying at 500 feet. That’s slightly lower than the height of the Reunion Tower (the ball on top of the stick) in this shot of the Dallas skyline.