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I've set the target to beat the game before the first council in 1825 on hardest difficultiy (nigh-on impossible) by conquering the capitals of all Great Powers before then. And I've finally succeeded.

I did it on the random map »Cowcre« with the Green power, by far the best map there is resource-wise.

These are the elements of strategy that were essential:

• Build the capital on a tile adjacent to 4 forests, so that you can produce 2 lumber per turn from start.
• Declare war on Haxaco on turn 1 and use your starting army (2 Inf, 1 Art) to conquer all their provinces except the capital, destroy as much of their arrmy in the process as possible (so that you don't have to face it when you finally assault the capital). I managed to destroy 2 Inf, 1 heavy cavallery.
• At start, build a trade ship (Indiaman). Buy only cloth (2 per turn), lumber (1 per turn), and steel (2 per turn), and use your furniture factory, clothing factory, and metalworks to produce furniture, clothing and hardware. Sell 3 of those resources per turn, for a full usage of your merchant fleet. Scale up once you managed to build a ship of the line and captured additional trade ships from Haxaco. Never buy iron, coal, timber or wool – it's not worth it.
• If you fail to sell or buy the resources that you want, reload. Rely on buying 4 steel per turn once you can afford it.
• Beginning from the start, each turn, upgrade furniture factory until it is at capacity 4, such that towns produce lumber as soon as possible. Upgrade to capacity 8 as soon as the first towns produce lumber.
• Build a second engineer on turn 1. Connect the towns in the forest-rich provinces (by port unless they are close to your capital). They will eventually produce lumber and furniture. Together with the provinces of Haxaco, you have 5 such provinces.
• After that, build mines and connect the towns of all provinces that have iron+coal mines, starting with the one that has 2 iron + 2 coal. They will eventually produce steel and hardware (4 of them only with square set timbering). Together with the provinces of Haxaco, you have 5 such provinces. Make sure your metalworks is at capacity 4 once the city is connected and at capacity 8 once the first steel resource is produced.
• Don't forget to upgrade your transportation network in order to collect the materials that your towns produce, including coal and iron for your steel mill.
• In the meantime, get Cotton Gin, upgrade the cotton fields in your 2 coal + 2 iron province, and in the province east of the Haxaco capital, such that you have 4 wool/cotton per province in total. They will produce clothing if clothiing factory is at capacity 8.
• Don't bother connecting resources except those accessible by ports or railway stations that also connect towns. Towns are much more important.
• Don't bother building a textile mill. Build and expand a steel mill up to capacity 8 to match the number of resources that you can transport. Cease production of furniture once your towns produce enough, and switch your metalworks to arms instead of hardware once you get enough furniture for export from your towns. You never need to export more than 4–5 manufactured goods per turn.
• In 1820–22, start producing ships-of-the-line and send them to the enemy capitals (2 per country). Make a short visit to the Haxaco capital to capture 1–2 traders. In 1823, switch to frigates, because they are somewhat faster and will help you reach the capitals before the council meets the first time in 1825.
• In 1823–24, build your army and capture those capitals once your ships reach them.

I'm now looking for a new challenge. Perhaps the same task with a different map?