Okay, I have two things to discuss here, although both have to do with breaking others borders.
First of all, and this is a bit simpler, is it ever worth it to break a border of a continent whose bonus is less then the men you'd have to take to break the continent. And I'm referring to when you are not in the process of eliminating the player who holds the continent. For example, you are on Middle East and an opponent holds Africa. If they had 3 men on East Africa would it be worth it to attack it? What about 4 or more men? When is it beneficial to attack another's borders to prevent reinforcements? The assumption here is that if you are attacking a border with 4 men, you will often lose 4 men yourself in order to take your opponents 4 men. So, do you give up 4 men, to defeat 4 men and then prevent the bonus?
Secondly, I had this problem in another game of mine. What do you do in a 3 player game where all three players are relatively equal with equal numbers of men on each respective border? Do you use your fortifications to take out the border of one of your enemies? Do you try to take out both of your enemies borders? Or do you sit there and build your own borders in a situation where your opponent will have the same ability to break your own border with his reinforcements? For instance, in a game of mine, I used reinforcements to attack borders of both of my enemies, however all that resulted from it was the retaliation of both of them leaving me even weaker. The dice didn't help the situation but that is another discussion.
I don't know if this post made much sense, but if you understand any of it, I'd appreciate your opinions.