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I've been playing EU3: Divine Wind now for so long (I may be slightly addicted...) and with so many nations that I think I've come to appreciate most different aspects of the game.  Doing a world conquest - that is, owning every single province in the game - is probably impossible, given the infamy system.  It's not that I mind everyone having a Dishonourable Scum CB on me; if I'm strong, that's no problem.  It's the events that come with it.  They cause huge numbers of rebellions, and that will stop you; you'll just spend all your time firefighting.

That said, we can sure give it our best shot.  From my observations, the best starting nation (on 14th October 1399) to stand a chance of world conquest is Burgundy.  It is insanely powerful for a number of reasons (kind of odd because in real life, Burgundy just kind of faded away as a nation, but anyway...):
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[*]It starts with enormous manpower.
[*]It starts with enormous forcelimits.
[*]It has lots of missions to eat up its small neighbours and core their provinces, giving even more manpower and forcelimits.
[*]It starts out with access to the sea so it can colonize quickly.
[*]It starts out Westernized.
[*]It starts out with a bunch of rich European provinces so it can sustain a big army and lots of wars against strong powers.
[*]It starts out Catholic, which is great for colonization.
[*]It is surrounded only by a weak(ish) France that needs to annex its vassals, and an HRE that is virtually paralyzed by its internal rules.
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As something like a world conquest is so difficult with infamy, I'm coming up with a scientific plan to try and take as much territory with as little infamy as possible, from square one, with Burgundy.  For starters, we're not gonna want to be part of that HRE, so Burgundy will leave the HRE quite early on.  Forming the HRE with Burgundy is (I suspect) much more time-consuming and difficult than just eating through it province by province, over the course of the game, whilst you do other things.  Burgundy will stand alone as a nation for the entire game.

A few house rules: I will be using the ZZFZ version of EU3: Divine Wind for this game, with default game rules and the following settings:
[IMG]http://game-point.net/misc/eu3/burgundy/options.png[/IMG]

I know this pre-5.2 version makes it easier to siege and gain manpower, and halves the lengths of truces, but I reserve the right to use the version that makes it easiest to world conquest for the purposes of this game.  :)

So, rules/plans for this playthrough are roughly:
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[*]Play as Burgundy,
[*]Leave the HRE quite early on.
[*]Eat up as many nations as possible through missions.
[*]Get armies to the Americas ASAP and take out the natives, so we can core and colonize the Americas in 50 years' time.
[*]Try and get provinces next to hordes to gobble up lots of infamy-free horde territory.
[*]Try and stay above zero infamy at all times; always be working some infamy off.  If necessary just start a war of aggression to gain some territory.  Be insanely aggressive.  Everyone will hate us but we're not trying to be liked.
[*]At the same time, never go above the infamy limit if possible.  If by accident (new leader whose diplomacy is bad, dipping us below the limit) then get below the limit as quickly as possible.
[*]Try and use the Holy War CB as much as possible before 1650 to win low-infamy provinces.
[*]Always take every opportunity to gain territory; events that give cores, relevant CBs, etc.
[*]Make getting to Republican Dictatorship government a priority so we have the Imperialism CB to DoW on anyone for 50% infamy per province.
[*]The state religion will be Catholicism.  Obviously we start out as that, so it's the path of least resistance, but it's also best for colonization - 1 free colonist per year.  Try to convert all territories to Catholic.  Capturing Rome, Judea, and Mecca will help with the missionaries.
[*]Leave capital in Bourgogne; we will have a huge number of overseas territories, but our Eurasia empire should be so huge that moving the capital won't give any advantage.  We'll just want looooooots of ships to enforce all those tariffs.
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I will be posting updates on this Burgundy game from time to time so stay tuned for the first one.  Also, tell me if you can think of any more strategies for maximizing the extent of this world conquest and I may add them to the list.  :)