In general, heavy melee infantry (halberdier, pikeman, doppelsoldner) needs a buff. They get countered by almost every other unit type in the game, and anything they are strong against (melee cavalry, shock infantry) can just run away. Aside from the occasional pikemen in colonial age burning down some buildings, melee units are simply too weak after Colonial Age. To make them more viable, here are some ideas to improve melee infantry:
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Increase the speed of all melee infantry to at least 4.5. This is probably the weakest buff, but also affect the current counter system the least. If caught in a bad engagement, melee infantry can at least run away from cannons and skirmishers (except cassadors).
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Give all melee infantry a “sprint ability”, like caroleans. This is a temporary version of 1).
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Infantry Breastplate upgrade should give a greater HP buff (at least 20%). Most melee infantries do not have that much hitpoint to start with. The current increase of 10% is too small. For example, a halberdier will have its hitpoint increased from 200 to 220, which is barely a difference for most situations.
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Ranged Cavalry should have a (0.75) fractional damage multiplier against heavy infantry. This is sort of like how skirmishers have a fractional multiplier against melee cavalry. Ranged cavalry can still kite melee infantry, but it would not be as devastating as before.
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Remove (change) counter-infantry rifling. This technology effectively eliminates heavy infantry (even musketeers) from being viable in the mid to late game. And it is rather cheap for what it does. After all, it is not as if a skirmisher without counter-infantry rifling have too much trouble against heavy infantry anyways. Removing this technology could probably improve the viability of heavy infantry a lot. (Of course, there is the problem of the caroleans, but that is more of the Swedes being too strong.)
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Have a card/upgrade that changes the melee resistance of the slower heavy melee infantry (maybe not rodeleros) into ranged resistance. Unlike the Swedish card that changes the resistance of caroleans, this should not result in overpowered infantry. Melee infantry do not shoot back. so as long as their resistance are not too high, this should make a decent meatshield (and not die to skirmishers before fighting off the hussars charging my cannons).