Uh, you have to declare at the start if the actor thinks starting a nuclear war is rational or not, none of this "Assume they thinks its a good idea, but also think that it's a bad idea".
But the theory is somewhat sound -- you need more nuclear weapons than they can defend against. Which is a question less of quantity and more whether you can delivery payloads in faster, quieter, and therefore less interceptible ways.
Quantity is a brute-force override when you don't know how good their defenses are. Or you want enough to hit everyone in the world regardless of their defenses because you're nuts. Or you'll make someone a lot of money by ordering more, rather than better, nukes.
Honestly, the US buying more nukes is more an indicator that any previous technology gap is closing. The US is less confident in its own defensive capability relative to opponents' offensive capacity. So it feels it needs to up its offensive capacity to prevent its defenses from being tested. However, since the US is not confident of the QUALITY of its nuclear weapons program, it must make up for that with quantity.
Having more targets than the enemy has missiles is Usually a recipe for success
Where did I wrote anything like that?
Nuclear deterrence is built on the idea that if I don't get to live, nobody gets to live.
The leaders of the nuclear powers decided it would be better for all humanity to die than for a nuclear power to be striked.
To clarify, not just the two fighting parties too. No country works alone. Everyone has skin in the game, so there's large incentives to encourage your allies to back off or even sabotage or turn on them should you believe they are going to risk it. Everyone and everyone is playing the game, not just the superpowers.
No. The end goal is to live. If the end goal would be to end civilisation you would just shoot, and shoot now. Easy. All the complications is because you want to live.
'Dying is easy, young man. Living is harder' to quote from Hamilton the musical. :)
How does that logic goes? Is it some simplistic tale we tell children or an actual strategic calculation?
> so you can start the chain reaction that ends all human civilization
You know that the goal is not to end all human civilization?
> it seems like the best move would be to have far fewer nukes than everybody thinks you do.
It sounds like you haven't heard of the nuclear sponge and the shell game. Let's say you want to hit your adversary. And because you are not suicidal you want to do it in such a way that they can't hit you back in retaliation. "Simple!" You just aim a warhead at each of their rockets. Now how many warheads do you need to do that? About the same number as many rockets they have. One for each. Or maybe 2 if you are accounting for malfunctions. Or maybe 4 if you want to saturate their defenses.
And because you can put multiple warheads on a single rocket this favours the attacker. Because the defender needs even more rockets to "soak up" the warheads of the attacker. And the defender needs even more than that so they can ensure a retaliation, which in turn stops the attacker from even trying in the first place.
So that is why you need many missiles. This concept is the nuclear sponge.
And of course this is super weapons race-y. Because if you need more missiles than your enemy, and your enemy need more missiles than you... there is a problem with that.
So what you can do is that you build more missile launchers than you have missiles for. And you play a shell game. You have X launchers but only 40% of them are ever armed with a missile at any single time. And to prevent your enemy figuring out which ones are filled you play complicated distractions. For example you make sure the empty launchers are guarded just as much as the full ones. And you periodically go with a big truck to swap missiles around. Or maybe to swap nothing with nothing? Or to bring missiles to maintenance? Nobody knows, and nobody is supposed to know. If you do it well enough your enemy won't be confident in their knowledge on which launchers are filled so they have to hit all of them if they want to be the one who first throws a punch.