In my opinion there is a very high likelihood of a war with North Korea. So far the war of words has been heating up and has come very close to a breakdown. But, although the North Koreans have officially stated that Pres. Trump’s comments amount to a declaration of war, the US has certainly not taken such a step. If there were to be an actual war there is no doubt that the US could destroy North Korea, but the damage inflicted on South Korea particularly would be great with possible high loss of life.
The key issue is that the US has control of the air, and can therefore attack North Korean missile sites and heavy artillery near the border with S. Korea almost with impunity. It seems in character for Pres. Trump not to take these overt threats by Kim Jung Un to attack Guam and the US mainland and to attack US planes flying outside Korean air space without some visceral response. It is clear that China and Russia are very concerned about the US posture and the UN Secty. General has openly declared that N. Korea has acted contrary to the regulations of the UN that forbids one member country threatening another member country.
However, when Iran has threatened to destroy Israel many times and has even specifically described how they will use nuclear tipped warheads to do so, the UN has essentially ignored this blatant and continuous threat by one member country against another. This is another example of the UN double standard applied to Israel.
To come back to the US and N. Korea, it will only take one deliberate mistake by either side to initiate hostilities, such as the Tonkin Gulf incident that was used by Pres. Lyndon Johnson as an excuse to start armed hostilities with N. Vietnam, and we all know how that turned out. Nevertheless, the Vietnam syndrome has largely been overcome in the US Defense Department since the positive outcomes in Iraq and Libya. The belief is high that whatever happens, the US would clearly win any conflict with N. Korea and destroy that disgusting regime, that puts the development of ICBMs and nuclear warheads before the welfare of its own people. However, how China would react to any US move to reunite the Korean peninsula remains to be seen.