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Armor classes are semi-hidden unit attributes in Age of Empires and Age of Empires II, and visible attributes in Age of Empires IV. They are necessary to make attack bonuses work correctly. Basically, the bonus damage is calculated the same way as the base damage is calculated (simply by subtraction of attack and armor), but in order to calculate bonus damage in the first place, the attacking unit logically has to have an attack bonus against its target. This is where the armor classes come into play. Simply speaking, bonus damage is a flat additive value to the base damage and if a unit has more than one armor class, the bonus damages of the attacking unit stack. However, these work differenty in different games. To read about the working in a particular game, follow the adequate link from below.