[C3C] cannon unit

They are situational, though I tend to find myself in those situations frequently, so once I learn mathematics, I invariably have a lot of my non-barracks cities building them whenever they have nothing overly important to concentrate on. My current game saw me forced to go conquesting into neighbouring Germany with nothing but archers and spearmen against swordsmen and emergent pikemen/medieval infantry to take their iron. I don't think it would have been feasible without a dozen catapults & trebuchets.

While the same shields could have been put towards more archers, my intuition tells me (perhaps wrongly) it would have been a less efficient investment in terms of production spent versus cities captured, mainly because the softening of city garrisons allows you to reuse attackers because they aren't dying en masse against technologically superior defenders (that they are also promoting at the same time, compounding the problem).

In the situation you describe -- going to get iron that you don't have -- using bombard units is essential.

Your intuition is correct, in general. Using bombard units (of whatever generation) to soften up the city garrisons makes sense, because all the units are reusable. The attackers don't die as often, the attackers can get promoted (to potentially generate military great leaders MGLs), and the bombard units are reusable. As you discover Metallurgy, the cats and trebs may be upgraded to cannons using the gold you get from conquering cities, getting the AI to pay you for peace, and from your strong economy.

Others here may disagree with me on the economics of upgrading existing units vs. (building new, disbanding old for the shields). I prefer to cash-rush a barracks in a conquered city (if the AI didn't build one already) and upgrade the units where they are, close to the front, rather than wait for new units to make their way all the way from my core.
 
As you discover Metallurgy, the cats and trebs may be upgraded to cannons using the gold you get from conquering cities, getting the AI to pay you for peace, and from your strong economy.
Upgrading with gold seems a no-brainer to me. You can often secure gpt deals with the AI in the region of 20–50gpt, or temporarily dial back science/luxury and rake in up to hundreds of gold every turn. You can't just increase your shield production in the same way.

From what I've read here, far better players than me do sometimes go the disband/rebuild route so I'd be really interested to hear the reason behind why it works.
Others here may disagree with me on the economics of upgrading existing units vs. (building new, disbanding old for the shields). I prefer to cash-rush a barracks in a conquered city (if the AI didn't build one already) and upgrade the units where they are, close to the front, rather than wait for new units to make their way all the way from my core.
I try to have barracks in at least a couple of cities with good production for the purpose of turning out new veteran units, plus a few more acting as upgrade stations such that all non-barracks cities should have an adjacent city where they can send garrison units for upgrades. It usually works out to around 1/4 of cities having them. Seems to strike a good balance between convenience and minimising upkeep.
 
I prefer to cash-rush a barracks in a conquered city (if the AI didn't build one already) and upgrade the units where they are, close to the front, rather than wait for new units to make their way all the way from my core.

This concern vanishes with railroads. With latency removed the reasoning is very different.

In the industrial age production approximatly fourfolds with railroads, hospitals, factories and power plants. Factories at 3 gtp add a lot to your maintenance bill. Those maintenance costs are one reason why 3 metropolises instead of 4 cities are better in the long run. In any case the relative scarcity of shields vs. commerce changes by a huge margin. Chances are you would need to build wealth to not reduce the science spending.

You can't just increase your shield production in the same way.

From what I've read here, far better players than me do sometimes go the disband/rebuild route so I'd be really interested to hear the reason behind why it works.

The essense seems to be that you can easily increase production to levels where there is plenty production and you have to decide what to do with it. This is obvious in the industrial age, but it can happen (long) before then. If you are playing strong, then you are likely to find yourself in a situation where building units just to disband those units(or preferably more obsolete units) somewhere else is your best bet. It is far more efficient than building wealth and cash rush. Also it is more efficient than building wealth and upgrade. Gold is just too valuable to waste it on upgrading.

There is one big advantage in upgrading: The timing. If you need to utilize a critical technological breakthrough such as military tradition, then upgrading is your best bet. In the short run regular production cannot keep up because production can only start after the tech. If you have say 20 cities and all of them have already stockpiled some shields you may have 20 cavalry within one turn of the tech. But the next batch will take some time. So boosting it with further 20 knights upgraded to cavalry seems like a good choice. Upgrading from 70 shields for knights to 80 shields for cavalry is unusually cheap. As 87.5% of the shields are not gained from upgrading this is a good bargain.

Upgrading catapults or trebuchets is a much lesser deal. Cheap artillery is a drain your financial budget. When you can build cavalry and cannons, building cavalry first and cannons second will save you some unit support. Cheap artillery is easily disbanded and rebuilt, pending on when the need for them rises and vanishes. Saving on unit support is usually a major motivation for disbanding. But you need some strong offensive units as a deterrent, so those are better not disbanded when it is not convenient.

I try to have barracks in at least a couple of cities with good production for the purpose of turning out new veteran units, plus a few more acting as upgrade stations such that all non-barracks cities should have an adjacent city where they can send garrison units for upgrades. It usually works out to around 1/4 of cities having them. Seems to strike a good balance between convenience and minimising upkeep.

Cheap barracks tend to make much more than 1/4 of the core cities. It is cheaper with Sun Tzu, but that wonder needs to be built first and conquered second.
 
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having a lot of units helps to disband one or two to get the barracks in the very first turn , while the civilians are still rebelling in the city . These might be artillery or other units , whatever suits at the moment .
 
@justanick: thanks for the explanation, that makes a lot more sense now. It also gives me something to think about, since I am a fairly heavy cash-rusher in general. I almost never have cities producing Wealth, but from a combination of gold from trades and a tidy profit margin from the tax slider, I tend to have a lot of cash that I like to put to work before the AI can demand it in tribute.
 
@justanick Thanks as well. Most of my upgrading happens in the Middle Ages, not the Industrial Age. By the time I get the production boost you write about, I have a decent military of cavalry cannon, and muskets. City garrisons (on the coasts) are still pikes. Crusaders come along to guard the cannons.

I realize that I have been not grown my cities to size 12 as fast as the better players recommend. Many of the maps I have been playing (especially continents) have only 3 or 4 luxuries, and I tend to grow my cities slower to keep them happy. I virtually never add workers to my core cities, since I always have roads to build or irrigation to spread. If I did grow my cities strong in the Middle Ages, and run the lux slider at 20%, I would probably see the production boost that you talk about before the railroad/hospital/factory boost in the Industrial age.
 
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