Regarding House chains, why don't we try something like this?
Dukes can have unlimited number of Counts swear fealty to them, Counts can have unlimited number of Barons swear fealty to them, Barons can have unlimited number of Knights swear fealty to them.
That way, only Counts can swear to Dukes, Barons to Counts, and Knights to Barons.
Regarding the prioritised units, I reckon that each player should be able to prioritise a specific unit once per term. Maybe 2 for dukes, 2 for a prince, and 3 for a king?
Bookmarks