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Soldiers are Citizens that you have tasked to become part of the military. To designate a citizen as a soldier, you must first have a Barracks built. Then you must choose a citizen, right click on him and select 'Convert to Soldier'. Your citizen is now a soldier. To equip weapons and armor, choose a soldier, then right click on her and select 'equip to citizens name' and choose what weapons and armor to equip.
Soldiers have three tasks that can be given, Guard, Patrol, and Supervise.
Soldiers tasked to Guard will stay around the area where they are, which tends to end up being between the Food and the Personal Rooms. When any Towny (but not hero) is attacked, Guards will rush to assist.
Soldiers tasked to Patrol will move between points you set on the map by right clicking, selecting patrol, and choosing a particular Soldier. This is useful for keeping a static boundary between cleared dungeon and unexplored dungeon, as monsters tend to wander in from the dark. Patrolling Soldiers will not assist Townies when they are attacked.
Soldiers tasked to Supervise will follow around a Civilian and "assist" him or her by providing "encouragement", making the Civilian work faster. Supervising Soldiers will attack any monsters that the Civilian they're helping encounters, but they won't go out of their way to help when a Towny is attacked.