Last City State Not Falling
I have tried to take out the English in my game they had one City-State left and I had their health down to one or two more attacks to kill them, when my damage stop being counted. I'd end my turn they would regains some health and I would attack do damage then it would stop. How do you take take out Last City State? I was using all range attacks is that why?
Probably not. It is because you are not... funny....
I got Civ V yesterday and had the same problem. I dunno if you're still watching this thread, but it turns out you need to move a melee unit into their city to capture it.