Well put, Enchanter.
With this, even a much larger enemy can suddenly become a one-sided massacre in your favor; assuming things work out just right. And if you were close in strength starting out, your opponent will likely become easy pickings.
This is a similar principle to why one should keep your rivals from forming alliances: one enemy is easier to defeat than several.
Chinese scholar Wang Hsi, in his commentary on Sun Tzu's "Art of War," put it this way:
"If an enemy has alliances, the problem is grave and the enemy's position strong; if he has no alliances the problem is minor and the enemy's position weak."
This is a point Sun Tzu stresses, and for good reason! Ensuring your rival stays small is of cardinal importance, so split their cities whenever possible.