That’s a difficult question to answer as it depends on your definition of “Winning the War”. The USA has enough power to lay waste of North Korea but if they do, they will definitely get more enemies in this World, as Russia and China won’t tolerate it. So the USA will need to take care as they don’t want to start World War III.
Now, if North Korea takes the first aggressive move the USA would have a free game to strike back, and strike back hard. And yes, that could include the use of nukes on strategic locations in North Korea. But north Korea would never do such a thing as they know they would lose the conflict. Or if they do, they will use their nuclear arsenal as to bring a maximum destruction before going down. And North Korea can and would use those on South Korea, Japan and probably even Alaska and other parts of the USA that are within their reach. And as their goal would be to bring as much destruction as possible, North Korea would basically win the War as their objectives will be reached. Even if that means the death of each and every civilian in North Korea…
Now, you have to keep in mind that North Korea is controlled for over 60 years by it’s current regime. This means that everyone in North Korea doesn’t know better than to trust their government and that South Korea is occupied by cannibals who want to harvest North Koreans for organ trades and whatever more. And Japan and the USA are also considered extremely ruthless. Getting the north Korean people to surrender will be extremely complex as they will be scared and be thinking they’re fighting to protect their own lives and the lives of their loved ones. Their government has done a good job brainwashing a large portion of the population to make conquest even more complex.
Next to consider is the actual strength of North Korea. The Global Firepower website puts North Korea at the 25th location, making it stringer than Spain, Mexico or Ukraine. And as Russia (#2) and China (#3) might support North Korea against aggression from the USA, it would be hard to defeat them. Do keep in mind that the USA has already fought against North Korea at the beginning of the whole conflict and could not win back then!
Now, it is unlikely that North Korea would go on the offensive as that would give the USA, Japan, South Korea and other countries an opportunity to strike back. It would be political suicide. So North Korea takes a defensive role while working on nuclear missiles. Once they have some reliable weapons, they would have a weapon to deter any enemy attacks as they won’t hesitate to use them. And thus North Korea would be able to stay in control over the area they already control and the North Korean leaders are happy enough with the current Status Quo. They don’t want to expand as it just means more trouble. They prefer to stay in control over the citizens they have already.
So there can be no winner to this conflict if it comes to battle. North Korea is prepared to keep up their defenses at maximum strength and China would not accept any outside interference. Not even from the USA itself. If someone is to intervene in North Korea then that would be China itself.
It will continue to stay a stalemate for a long time. At least, as long as the current government stays in place. And yes, while the civilians in North Korea might continue to starve, this starvation also makes sure the population size continues to be small enough to control. For north Korea, the starvation is just another tool to keep the population under control…
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