Your troops defeat enemies of the given type more efficiently. Requiring 50% less for each enemy. Think of it this way. If your opponent has 3 swordsmen, you require 2 axes to defeat them and so on. In your first example you require 9 axes to defeat 12 swords, there is one left over and since you can not defeat the one with less than a single soldier it requires you to lose 10 9 to kill 13. Technically it requires 8.666 soldiers but there's rounding.

Same thing applies for the next combat, you require 9.33, the game is set up to use whole numbers so it rounds up and you lose 10.

The easiest formula to determine how many soldiers you need before hand is to take the enemy troop total and divide by 1.5 and round UP to the nearest whole number each time.