I am not certain that Putin would not use nuclear weapons given the chance. But I think his wealthy allies and high level leaders would put a kibosh on that. Putin may be willing to accept the consequences but I doubt many of those that keep him in power would be willing to make that sacrifice. For that reason, I think there is little chance and should he even try, I suspect he would rapidly be eliminated in an 'accident'.
It's difficult to know how seriously to take this. Putin is the king of crappy posturing. Making constant threats to get the allies to act more slowly responding to him.
He also knows that we know that:
Much of Russia's nuclear arsenal is inoperable due to neglect
He gets to light up ONE nuke, and then Russia is forever over. I wouldn't be surprised if the rest of the world has a post-nuclear breakup plan for the country.
So, I'm confident that Putin won't actually nuke anyone, as even he isn't that stupid. Moving moldy Soviet equipment around makes great posturing and makes us fear him a little bit.
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