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Personally I never take exploration ideas, I consider them to be utter rubbish. Expansion + map stealing is the way to go as any colonial nation.
PS: I take Exploration 2nd, only temporary until reached the Moluccas.
An optimal Portugal run easily conquers the entire world. But before I outline how, I want to address some misconceptions you have:
1) Colonial nations are not about tariff income. They're about trade. Tariffs are nearly useless, and I ignore them completely. What I love are the trade power and bonus merchants colonial nations provide. A good Portugese empire will make thousands per month in profit from trade alone--literally thousands. Gold fleets are a nice secondary source.
2) The Americas and "Africa and Beyond" aren't an either-or choice. A good Portugeese player grabs every scrap of the New World, sub-Saharan Africa, India, southeast Asia, Indonesia, and Australia--and that's just for starters.
As for how, before you unlock your first idea group, you start wrecking Castile with the help of Aragon and/or France. You don't want to share your initial collection node (Seville) with anyone, and you don't want them to compete with you for good colonies. So you take Granada before they do. You take one province each of Galicia and Leon to fight reconquest wars. You grab their islands and their entire coastline. Etc. It takes multiple wars, but you start as soon as possible and you wipe them out.
For ideas, you take Exploration first (which has been buffed recently and is much better now) and use explorers to open your horizons. Exploration also boosts colonial range. Combine that with strategically placed colonies, and you can get anywhere you want. You follow Exploration with Expansion and then the Big Three (Admin, Diplo, Influence). Religion is also helpful.
While you're building your colonial empire, you annihilate both France and England so that you have no colonial competition to speak of. You also take over the Low Countries (no Netherlands) and move your trade collection point to the English Channel, by far the best trade node in the game.
At that point, world conquest is a matter of just mopping up. You'll have total control of the Americas, most of Africa, the richest parts of Asia, and most of western Europe. Nothing can withstand you then.
Also, I strongly recommend that you play other nations than Portugal. You're not learning much about the game by sticking with one nation that has a very atypical start. And you're not learning important lessons even from Portugal. Statements like "Colonial Nations are not worth it" are wildly wrong.
Your CNs will colonize alongside you, but each one takes 5 provinces to set up. Much much faster to get there with 2-3 colonists than with just the one from Exploration.
Keep in mind you're also racing against other Europeans who may crowd you out (and if they're Catholic, nab the Tordesillas bonus before you do, which is really just an annoyance but still.)
In the short term maybe, but not enough to really hinder you from keeping on par.
Plus, Exploration gives you +50% colonial range anyway. That's a bigger bonus than you'll get from Diplo techs 9 or 11.
This is horrifyingly wrong. Colonial nations give you control of trade power in their nodes, and they also fill those nodes with productive provinces that actually generate trade value. Then they give you merchants you can use to push all that trade value back home to Europe and make absolute stacks of cash. Those four provinces you have in the Caribbean are generating a trifling amount of tax and production money, and giving you control over a paltry amount of trade- at least, until England or Spain comes along and forms an actual CN that dominates the node and pushes trade to them.
As a side benefit, sufficiently large CNs will sometimes ship their armies over to help you fight your European wars.
Because your colonial nations will be both greater in number and vastly larger, richer, and stronger if you colonize. You'll also gain access to far more of the world more quickly.
Maybe tariffs could instead be a modifier to the amount of trade power a CN gives to its parent nation. E.G. at 100% tariffs or whatever, all the CN's trade power goes to you and they get a correspondingly high liberty desire. So if you wring them for extra money you'll actually get something meaningful, as opposed to driving them to rebellion for 3.6 extra ducats a month.
Also, do u just colonise 5 provinces for the CN to form and subsidise them? Or is it often better to continue colonising a few more provinces for them to boost their income so they can be more self-sufficient?
Honestly, there's such a short window for that that I don't think it even matters much
Unless there's a really compelling reason to focus on a region I've already got a CN in (like making sure they get a provinces that was buffed by a Seven Cities event or helping them outgrow a rival CN), I usually do five and move on.
One exception is the Caribbean. The AI is terrible at settling non-contiguous islands (those that don't have a direct land or strait connection), so I'll give them a hand there sometimes.
Im not a noob and tried most of the things you mentioned, Which lead to my conclusion that "Colonial Nations are not worth it".
1) Colonial nations are not about tariff income. They're about trade.
A Colonial Nation gives you half of there trade power, this means if they have 100% trade power you will get 50%. That is the maximum trade power you can get from a Colonial Nation. In my latest save (1680) I have only 4 provinces in fully colonized Caribbean (half british, half dutch) and I have 63% trade power. So where are the benefits of the Colonial Nation, its not tariffs, but it isn't trade either. Please tell me where are the benefits, show me numbers.
2) The Americas and "Africa and Beyond" aren't an either-or choice.
But it is. If you go to the Americas 'Exploration Ideas' is a must, just for the claims. Its not a bad idea group, but for "Africa and Beyond" there are better like Influence (for Vasalls) or Espionage (less AE).
For ideas, you take Exploration first
No, you dont. Portugal gets 3 Navigators (1 from the start, 2 and 3 from missions) which makes the first Exploration Idea useless for Portugal. The second idea gives you a colonist and plus 50% colonial range with the third Exploration Idea (+80 at this stage).
If you go Expansion first and push to Diplo Tech 7, you will get your first Colonist 400pp earlier (first Idea) and Dip 7 gives you flat +115 Colonial range ( thats not much more, but often just the one sea tile you are missing).
Going Admin first, has its downsides of course. It means, that have to expand mostly via Vassals at the start. Dont push it take Ideas when you can, its mostly about the early Colonist.
the English Channel, by far the best trade node in the game.
I dont know about that, but I can say that Sevilla is probably the easiest node in the game. In 1680 (latest save) I am making 663 ducats per month in Sevilla on trade alone and with 95% trade power it is effectively an end node. I am not sure how long it takes to get 600+ ducats per month in the English Channel.
/cu steelm
P.S. I would have put screen shots in here, but I couldnt find out how :(