I would bet money that North Korea will not first-strike, and the US military will not fulfill a first-strike if directed.
My premises are that North Korea is a rational actor, and their overwhelming priority is preservation of their regime, and they know without a doubt they can't win a war against South Korea - let alone South Korea and its allies.
My premises are that North Korea is a rational actor, and their overwhelming priority is preservation of their regime, and they know without a doubt they can't win a war against South Korea - let alone South Korea and its allies.