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Exploration will help to initially start setting up that gloabal trade empire you're after. It'll also allow you to grow your fleet, both directly through the idea within it that increases fleet force limit, as well as indirectly through the creation of colonial nations. As others have said, this is the only sure idea group you should be taking (unless you want to play a very unorthodox Portuguese game).
Humanist or Religious ideas can be good for ensuring the loyalty of your territories. Each idea group has a few different benefits, so decide on which one suits you best at the time (although if you want to take large swathes of territory at a time, Humanist is the direction you should be headed). Remember that most Old World provinces you colonise and conquer will need to be either converted or tolerated in order to not cause unrest for you!
A military idea of some sort to help your troops hold their own against others. Specifically look out for nations who have taken Defensive/Offensive/Quality ideas, as these offer reasonably significant combat bonuses. Investing in one of these sometime early on (2nd or 3rd idea group) will help to keep you at the cutting edge of military campaigning (unless of course you plan on keeping out of serious wars - although seeing you want to take down England, you'll at least need to do some fighting). My personal favourite here is Offensive for all the various "offensive" benefits it offers, but any of the aforementioned three would serve well.
Consider taking Diplomatic ideas at some point, it's great for playing the Royal Marriage game and trying to get your relatives on the thrones of other monarchies (possibly ending in a Personal Union under you!). Influence ideas is also a wonderful idea set, but if you're not looking to wage too many wars across Europe, it will be of much more limited use to you.
Does your country have glaring weaknesses via national ideas? (yes) Fill in those weaknesses with idea groups.
How likely is it that you will be expanding into land with other religions (Religious or Humanist)
Will you be expanding so much that you will be crunched for monarch points? (Admin & Influence)
Does your military suck in some way? (Quality (better troops), Quantity (more manpower), Offensive (better generals / quicker wars), Defensive (Good for turtiling (fort defense / cost, cheaper troops, misc bonuses)
Are you going to be taking large peace deals or dealing with AE often? (Diplomacy (lowers warscore cost, makes AE tick away faster) and/or Influence (greatly lowered AE gain) or Humanist (AE ticks away faster))
Does your navy either:
A) Guarantee your very survival?
B) The only way for you to expand?
If either one, you may want to consider Maritime or Naval. Both groups are on the weak side, but if it is game over if your navy is not superior, its worth considering.
Are you going to have money problems? (Trade or Economic)
Portugal has a few glaring issues, but they may or may not be a big deal depending on what type of game your going to play.
First off. Your probably going to expand into North Africa. Are you doing this expansion personally or by Vassal? I always do this by vassal. I always take the north 3-5 provinces of Morocco and release Fez as a subject and feed all of the Muslim & increased core cost land to Fez. When Fez starts to get to large, I will Annex and release another small North Africa vassal. Tlemcen has one on their coast that only has 2 or 3 cores (cant remember name). If you choose to core this land personally, that is a strong case for taking Religious or Humanist idea groups. I prefer to stuff my problems in a vassal and take other idea groups.
Portugal has a completely generic army. Not a single military national idea or tradition of any type. You should do something about this. Especially if your plan is to conquer the Iberian Peninsula. This is where you will start to feel a pinch on what idea groups to take. A go to idea plan for countries like this is Innovative, Quality, Offensive. This opens up some extremely OP policies once those idea groups are finished. When are you taking Innovative though? If this method appeals to you. I would suggest you start like this: Exploration, Innovative, Offensive, something here (Expansion?), something here (Influence?), Quality. Other options besides going this far are just not worrying about the OP policies and make your army equal or slightly better than whoever your planning on conquering and use Diplomacy to give you the edge. Use someone else's OP troops. France makes a great ally! Use his OP troops instead. You can still go Offensive or Quality, but it frees you up from taking Innovative. Again, it all depends on the direction you want your game to go.
Colonization is a race. Castile has some advantages over you. They get a colonist as part of their national ideas, and they get slightly more Global Settler increase mid game. You are far better prepared to gain monetarily from colonies however due to national ideas and you do have better range towards South America & Caribbean. Portugal has a few advantages:
1) You have better range towards the New World.
2) You start with an explorer.
3) You will automatically get a free province in India. (Gao)
4) 25% Colonial Range national idea
TL:DR Figure out how you are going to play a certain country. Pick idea groups to fill in weaknesses first and then compliment strengths second. (I don't mean just military weaknesses, if you have the strongest military ideas in the game, but don't have the economy to afford an army, thats a weakness. If you can afford that army, but are constantly spending all of your manpower killing rebels, thats a weakness.)
When everything is explored in the new world & most of the old world you could try ditching exploration ideas (if you want to situationally pick up another idea group, religious is good) and going expansion ideas instead (circa 1600 or sooner) to get claims on india while the opportunity is still ripe and you're in south west africa moving towards the golden horn & Mutapa's gold.
Now castile is probably not going to be your friend forwever so you need some way to neutralize them when they turn on you, or perhaps when you want to turn on them. Either pick diplomatic ideas or military ones while allying strong countries, preferably ones that have them as rival and will be happy to beat them. I prefer to ally france and ditch england because france should be able to beat castile and its just by its border. I would then try to conquer the genoese trade node because it seems to be the easiest one to get as portugal. Dont take any provinces that border your allies if you can help it.
Portugal is the most easy and piceful gameplay, Colonization and Trade that what you should pick for Portugal. If you want more adrenaline + colonization then Castile or France
1 - Exploration
2 - Expansion - Since Expansion is expansion for Exploration
3 - Economic / Admionistrative / Innovative / Trade
After this 5 - Since in 3rd will be good if you take them all. Also maybe something for Navy to build a mass trade ships.
Stay away from war and be ok.