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i just had to make that decision myself.
in the end i went with religious.
the big thing about humanism (in my opinion) is the reduced seperatism (even better if combined with offensive).
i allows rapid expansion without increasing autonomy.
that is of course not an issue if u play tall.
Flip to protestant as your preferred nation ASAP and the religious center will take care of the majority of your conversions when christian missionary strength is pretty low
Late game conversions are super easy as a western christian since you get so many buff to missionary strengths its ridiculous.
In all honesty you can skip both nowadays as Prussia
But i would say Innovative is a definite pick for the policy with offensive and for the tech cost reduction which was buffed to 10%
Ich hatte folgende Ideen -> Offensiv, Handel, Qualität, Wirtschaft, Defensiv, Innovativ, Quantität, Diplomatisch
Ich würde humanistisch empfehlen. Religiös würde sich nur lohnen, wenn du in nicht-christliche Länder expandieren würdest.
Do you want to roflstomp Russia and Ottomans pre 1600? Pick Religious.
Are you taking it slower and mostly expanding in central europe? Pick Humanist.
Or actually if you stay in central europe you might not even need Humanist.
Humanist is also a rare idea group which has no useless ideas: benevolence is super important ever since it began to affect aggressive expansion reduction; tolerance pretty much guarantees that you never get below 100% unity and cultural ties are not great but still useful. At the same time, religious idea group is teeming with useless ideas: stability cost, missionary maintenance, and culture conversion are dead weight; prestige is mediocre at best.
The only thing that the religious ideas have really going for it is still Deus vult. But it's pretty unreliable if you are Catholic because even when the reformation starts, you can't be sure that you can use it against your neighbors. It can truly shine when used with "small religions": Orthodox, Shinto, Sikh and so on. Having one of those religions (or converting to it early) is, in my opinion, the only situation when religious ideas become really attractive. On top of everything else, the net gain from deus vult is halved if you take influence ideas (and it is a pretty good idea group).
What do religious ideas have to do with roflstomping anyone?
Easiest cb there is in the game...? Show Superiority gives you such insane easy warscore its crazy. Winning 4 battles gives you ticking warscore, 8-14 give you the maximum 40.
Against Ottomans you would only have to win battles for example and siege down one or 2 forts in Balkan + Constantinople to get up to 70-90 warscore (more twards 90 when you wait for the ticking) with ease instead of having to siege down whole freaking Anatolia to get the warscore higher. With normal Conquest cb you get barely any warscore from battles unless you are entirely destroying the enemy army or even stackwiping, therefore you need to siege down way more forts.
That being said, the net gain from deus vult is never ever being "halved" if influence were picked - since you apparently forgot the 75% AE it gives too and the fact that it can make conquests faster.
I wont argue which one of the 2 ideas is overall better (thats not the the topic), i just answered the question that was asked.
Nevertheless, here is why I think that show superiority wargoal is irrelevant to how easy the war goes. Basically you can get up to 25% from ticking warscore and up to 40% from winning battles. Warscore from battles is unaffected by the war goal (that is to say you'll need to get the same amount of victories taking into account the size of armies to get the same warscore from battles regardles of what CB you use and what wargoal you have). "8-14 give you the maximum 40", - that sounds about what I would expect to get in a war of that time period (mid 16th century taking into account army sizes) with a conquest CB. Have you actually tried reloading and fighting the same war with both CBs? The only part of the warscore to which wargoal is important is ticking warscore. In that respect "take province" is a little better because it's easier to occupy some enemy province on your border and hold it for the duration of war than to have enough warscore from battles.
Again, I don't think I have heard the idea that a wargoal affects the warscore calculation (except for the ticking warscore) before so I can't dismiss it completely. But I'll need to see some proof or at least this idea being mentioned somewhere else for me to change my opinion on this matter.
75% AE is mostly canceled out by the increased AE reduction from benevolence if you take humanist instead of religious.
You said Influence canceled half of the cbs net gain, NOT humanist...
You cant just say "Influence halves the net gain" and then say Humanist also reduces the AE... That would be 2 for 1 then.
...Thats pretty basic stuff.
https://steamcommunity.com/sharedfiles/filedetails/?id=1860061901
On normal conquest you get low warscore on normal battles, just as here: 1-2 max.
https://steamcommunity.com/sharedfiles/filedetails/?id=1860061840
On "Show Superiority" you get 3-4 on normal battles. Religious League would be another example for Show Superiority.
The larger the war the more you benefit from this cb.
https://steamcommunity.com/sharedfiles/filedetails/?id=1860071852
On the next war i now used the Religious cb and i get now triple the warscore from normal battles.
https://steamcommunity.com/sharedfiles/filedetails/?id=1860072278
...and even tons for killing ♥♥♥♥♥♥ secondary war participants.
On top of that you have a weird rule that if the enemy stack is of a certain size (depending on their total army or forcelimit, i am not sure) you also get the +3 warscore. Against such a big Ottos its probably 3k.
And there ya go, after barely 2 years and only sieging down Balkan (and some of Crimea) i got about 70 warscore.
...with only 12 battles (and 3 of those were actually naval ones)
https://steamcommunity.com/sharedfiles/filedetails/?id=1860095843
Meanwhile only barely 50 warscore after 3 years in a reconquest cb even tho owning whole Anatolia and all the forts down to Egypt - due to them having such a huge territory and being allied to a huge Morroco and Timurids... (also note on how i dont even have 10 warscore from battles with the same amount of battles won)
Hope that clarifies how and why the Religious cb makes wars significantly easier and faster.