The AI should be able to outcalculate the player in tactical battles.
It should be able to adjust its own formation and tactics depending on the players units' strength and formation. Before the armies make melee contact the AI should know what the outcome is, because it can just calculate it. Given on the foreseen outcome of the individual matchups it should plan flanking maneuvers and execute them in perfect synchronization with the frontal attack. It should frustrate the hell out of the player because you're never able to catch a skirmishing unit because the AI will always withdraw in the last possible millisecond. It should frustrate the player because it always calculates the higher ground, it always keeps a good formation, it's aware of the importance of the general, it knows the little details of the units better than the player and uses them to its advantage.
On the campaign map it's similar.
The AI should always be the richest and best developed because it knows exactly where the richest provinces and the best trade resources are. Timbuktu? We should've learned that by following an AI merchant. It would build huge trade empires and maintain them. It would use governors to best effect. It's agents wouldn't just linger around your cities achieving nothing, they'd start by sabotaging your entire building structure until they'd valoured up enough to be able to kill all your family and your best generals. It would always attack when you're weakest, with the best possible units available. Siege engines? It would only bring them deliberately to attack castles. In field battles you'd face powerful armies that outtech yours. The composition of the Armies should be balanced but favoring factions' specialties, like Horse Archer heavy armies. (Apropos HA, the most difficult thing for a player to beat should be a HA heavy army because here the AI can really shine in that it can control this bag of flies that 20 independently acting HA are.) The AI should keep with the time in so far as that it disbands old units and replaces them by new ones. It should be the first to field Gunpowder armies and it should show the player how to use a Pike and shot army by destroying the player.
Feel free to add some more shoulds
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