There doesn't seem to be any pattern or logic to it. Sometimes I will have a city surrounded with 3 melee units and it doesn't happen, and other times I will have only a single (or even no) melee unit, not even adjacent to the city, and it will go under siege. Can someone offer a good explanation of this? Thanks
It’s mostly about your Zone of control. You have to remember that that your melee troops won’t exert ZoC across water/river tiles. If you’re standing next to a river with a warrior then that is enough to break it. You need all 6 tiles around the city to be placed under your ZoC. That means that you can siege with only two melee troops if the circumstances permit it, such as no river by either troop but they would have to be next to the city on opposing sides. There are circumstances where three may not be enough if rivers and coast/lake tiles are causing the the ZoC to be broken though.
Edit: I almost forgot, this still applies to cities on a coast or lake. Sometimes you will have to place a melee troop in the water to achieve the 6 tile ZoC.
The only thing I'd add to the above is to make sure you aren't using a ranged unit, because they don't exert ZoC unless you have the relevant (third tier) promotion.
A city is under siege if each of the 6 tiles surrounding it are either in an enemy ZOC or are impassible. It makes no difference if friendly units are in the tile.
A ranged unit or an embarked unit has a ZOC but this is only its own tile. Other military units including scouts ZOC includes the tile around them but the ZOC does not extend to water if a land unit and vice versa as well as does not extend across rivers. Even the Amphibious promotion does not help.
Please look at this post for visual examples - zoc
Note a city is not under siege unless the heart with a line through it is showing in the city name.
Also, any hostile unit is counted as to placing a city in siege. This includes units from your suzerain city states, another civ and its suzerain city states that are at war with the same civ as you and barbs, including those generated from cities in revolt.
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