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Resist in Age of Empires III is a value similar to melee and pierce armor. In contrast to previous games, a unit cannot have both melee and pierce defenses; units only have one resist value for the other. A value (for example, 0.30) translates as a percentage (30%) of enemy attack deducted due the unit's resistances.
Each value is displayed as a decimal number on the unit's statistics tab table near the relevant icon. The sword symbol indicates that the unit "resists" hand attacks, while the crossed muskets indicates "resists" against ranged attacks. The cannon symbol indicates "resists" against siege attacks, such as attacks from artillery or Flamethrowers.
As a rule of thumb, heavy infantry usually resists melee damage while light infantry and most cavalry resists ranged damage. Artillery and ships resist ranged damage, usually 50 or 75%. Building wagons are the only units to resist siege damage.