Well the 'lucky' tag give just some AI boost. Every competive player is still miles better than the AI so whats the problem with it?
AI got some bonus and uses some lines of very limited code and you got Trillions of brain cells, isn't THAT unfair?
For the cavalry (taken from FAQ, maybe not the most actual version):
This is western Tech 5 Cav.
Unit Techgroup/Techlevel/Type/Maneouver/Morale Off./Morale Def./Fire Off./Fire Def./Shock Off./Shock Def.
Hungarian Hussar latin 5 cavalry 2 3 2 0 0 2 1
Eastern got 2:
Mongol Steppe eastern 5 cavalry 2 2 2 2 2 2 1
Ottoman Spahi eastern 5 cavalry 2 2 2 2 1 2 1
For me the east cavalry with aditional fire is better than the western. The next step for better better cav start with tech level 14 which happens later in the game where cav start losing importance and even there i can't see much difference.