County of Essex
It had an interesting mechanic in which both a point score and an opportunity score (i.e., what sort of advantage each player had going into a round) were tracked. As I recall, the opportunity score didn't have much gameplay impact.
The game was a bit like Vinci... I think it involved playing various civilizations over time.
Does this ring any bells?
Might be Civilization or History of the World They are not eaxct matches, but dimly remmberd might be close.