Ok here are my thoughts.
AI Problem.
"M'lord, the terrible sheaim are sieging our towns, their warriors pillage our countryside!!! - Warrioirs? Do you mean clubsmen from stone age? Meh...
Send my immortals to pwn them."
There's the problem. In the beginning AI builds warriors good, it fights animals and barbarians with them, but in the "middle" of the game there are warrioirs still and maybe a few religion-specific units. I think AI just can't find a way to upgrade (no gold) or dispose of them (they don't use "destroy" button i guess) so they occupy the combat units limit and AI can't build too many new good units.
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Unit tiers. I think the easiest desicion (not to tweak the AI and all) is to auto-upgrade some AI units if they're in their own towns and are in game for a long time (let's say, the 1st warrior if survived and if the needed tech is researched and he is in city will be auto-promoted to archer or swordsman. Also it'd be great if elven units will prefer the archery upgrade-tree, not melee (I'm sick of elven clubsmen everywhere every game).
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Unit XP. Also AI capital may give to units stationed in it some slow XP bonus, because this way we can engage something more difficult than just lvl 2-3 warrior in the capital when we attack it. At least I try to defend my cities with high-level units, what is not true for the AI.
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Heroes. AI heroes are too easy to die. THey are often easily killed by barbarians and even animals due to bad usage... I'd suggest to "teach" AI (if you can wary it's actions and it's not too hard) to preserve heroes, at least until they get level 5-7. Also they should be taught to level them right (as to get MARCH promotion for warrior heroes and skip some weird things like scourge, which isn't good at all due the warrior population now).
2) Unit type usefullness. I mean archers. Now the horseman are good to be quick and rule everything, and the melee units are not so quick but easier to obtain and still good. The problem in with archery units - they are not desired to be even n elven nations, because it's harder to get them than melee and they also require techs for bronze/iron thing.
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Different materials? First way to empower archery units, make them not tied to melee group and something preferable is to rid of "bronze" and "iron" bows (I don't like it). Maybe we should have "exceptional", "composite", and "enchanted" bows or something like this instead of bronze/iron/mithril, and these upgrades will be obtained through the archery tech-tree as you progress, and also require no resources, only special building in town, let's call it "master fletcher".
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Different tech-tree for materials? Another option is to separate melee tech tree from crafting materials. This way you'll develop +weapons and all unit types don't mess up with archery. But I don't like this option really, because it further expands the tech tree (unneeded) and also archery units are now something that don't require resources to build and melee are.
So I'd prefer just another bow-upgrades (If you think "exceptional", "composite" and "enchanted" are not good enough, try to think about names) without the melee techs.
3) Rock/paper/scissors? Melee, archers, mounted?
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Strategy over numbers. I think it's a nice idea to implement the "triangle" feature to the basic combat unit types.
I.e., archer beats pikeman, pikeman beats horseman, horseman beats archer.
Are you tired of your elite swordsmen dying under the rain of arrows? Send your fast cavalry to punish those bastards!
Well it is not necesarry to be implemented for the low tier units, but let's say archers will have bonus against melee (maybe a bit lower than shock promotion) and cavalry will have bonus against archers (due to the fast moving speed and maneurs). We can leave melee as they are, because I don't see the point why the warrior will beat knight, I think it's opposite.
Also you want to make it the way different - high lvl melee units have shields to cover from arrows and cavalry is more vulnerable to direct fire on short distance -.-. You decide which way is better.
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F34R MY KNIGHTS! It may be too hard to balance "strength" issues for mounted/melee/archers, so if you want to implement the morale some day, it'll be much easier - you will get morale pwnage if archers attack melee units or if knights rush into the archers' formation.
I put faith in you and hope my words can give you some nice ideas.