As of right now, how worried should you be about war with North Korea? The odds are against it, but the odds are objectively worse than they have any moral right to be. We don't have troops amassing anywhere, but that isn't how it would happen. Trump would just lose his temper, and order missiles launched, or an air strike, and he'd do it on a whim. And he'd announce it over Twitter.
Why are tensions escalating? Last summer, I wrote a series called "Political science & craziness," about what would happen if someone as crazy as Trump became president. The links are at the bottom of this post. Part of the benefit, yes, benefit, is that a crazy person can threaten to do things that no sane person can do, and cause other people to back down. Give me what I want, or I'll do something bugfuck crazy that will kill us both! The goal is to appear crazy, but be sane because truly-crazy people will eventually do the bugfuck crazy thing, and that would be bad. Scholarly reference: Thomas Schelling's The Strategy of Conflict.
Trump does enough bugfuck crazy stuff that his threats to carry out potentially self-destructive acts should have more weight than those of other actors. That, as I noted last summer, should allow him some extra bargaining leverage. Yet, tensions with North Korea are escalating because that's not happening. North Korea is, if anything, ratcheting up their provocations, with missile tests, rhetoric about Guam, and development of ICBMs with nuclear capability. Trump is sounding like a North Korean propagandist with that "fire and fury" schtick, and Kim Jong Un is going full steam ahead.
It isn't necessarily that Trump's threats have no credibility. It is that Kim Jong Un has a lot more than just Trump on his mind. Trump is probably too stupid to understand this, thinking exclusively about the world from a Trump-o-centric perspective, but Kim Jong Un has a bigger world view.
Kim Jong Un, of course, wants one thing: to remain in power. His weapons are a deterrent. It is highly unlikely that he will carry out a first strike because he doesn't want to be wiped off the map in an act of retaliation. He wants his weapons to be as powerful as possible to deter a first strike against him. The stronger his weapons, the better the deterrent.
Suppose Kim Jong Un gives up his nukes and/or missiles. He becomes vulnerable. Suppose he slows the development of his weapons. He becomes comparatively vulnerable, particularly as our missile defense system develops.
And he has to look beyond Trump. Trump's term ends in 2020. Even if he somehow manages to win re-election, which would be difficult given that he is, by far, the most unpopular president at this stage ever, and he won't have Comey helping him, that's only another four years. Besides that... [cough, cough]... Trump is old and doesn't have a healthy lifestyle.
What, aren't you used to me saying shit like that?
Kim Jong Un has, what we call in economics, a longer time horizon. He is playing against adversaries other that Trump who will succeed him. Even if he were to accept some sort of detente with Trump on the premise that Trump is uniquely threatening, requiring him to give up several years of weapons development, that would cost him in the long term against subsequent adversaries, not just because he backed down, which weakens one's bargaining position (see Schelling), but because of the lost time and development.
Kim Jong Un sees Trump as, hopefully, just a bump in the road. He is looking towards future leaders who can be deterred conventionally. He won't strike first because his goal is just to remain in power. This may be a mistake, though, because it is a view dependent on the notion that Trump is intelligent and rational, which just isn't the case. Trump is stupid and crazy. If Trump gets it in his little Trump-head that Kim Jong Un is actually going to attack Guam, then he may strike first, and all of this goes to hell. Mattis and the other non-bugfuckers are assuredly telling Trump not to do so. Whether he listens is another matter.
Then again, we don't actually have a lot of solid information on North Korea, and Kim Jong Un is pretty young. Maybe he really is as crazy as his father and grandfather pretended to be. If so, we're all bugfucked.
Links to "Political science & craziness"