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Sir Garnet

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Unless appointed to Council, or given their own land, do they matter?

The Manual says that State Martial, State Learning and State Diplomacy that affect technology are the sum of those ministers' stats. The ruler's stats are boosted by the relevant minister's stat in that area.

What about the wife? Or for a female ruler, the husband?
 

Me_

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I know that they can influence maximum demense size. Probably by giving a bonus to stewardship.
 

InnocentIII

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+1 to thinking half her stats get added to the ruler's.

I like that if she's on the counsel, ALL her stats count when you look at research (each of the three tabs adds to a total of all counselor stats, plus ruler?). I know research doesn't matter much in a 20-year game, but over time, having a spouse with maxxed-out stats in all categories will help even more if you have her on the counsel. A bonus to picking well-rounded characters, not just one-stat wonders.