Armies can either be supplied from a supply wagon or forage for food. If it is stationed in an allied (owned) province, it consumes locally available food in the first place (this may lead to a famine in an economically weak region). If its on the move in an enemy territory, then it depends on the situation at hand.
When your troops fail to capture or seize anything, they will starve and begin to desert. If a city was captured, the army will feed on it and options Ravage, Sack and Take captives become available (their gameplay impact differs, but in general they are intended to maximize the damage, gold loot and captured labor respectively). After the player activates any of these options, the captured city returns under the rule of its previous owner you are not forced to hold captured territories and can simply devastate enemy infrastructure and drive his people away as captives.
If your troops capture a village, they block food flow into an adjacent enemy city and famine starts ( ... more.
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