Recently, out of curiosity, I have been wondering what is the maximum possible core pop nations can get (outside of china & GDC). Now, the typical answers that I found online were completely lacking as most lacked even the basic attempts of min-maxing the numbers. So, without further ado, here are my results.
As a disclaimer, you're not going to get these in single player outside of a smaller version of first one, but it's entirely possible to get them in multiplayer if you involve about 8 players in certain countries. This would still involve a lot of luck as a result of the French Union is completely dependent on rng. Since this was done in singleplayer the dates and world situation will be off but add_core was not used. Some of the numbers will be inflated do to natural pop growth as these are not amounts taken on 1936.
France: 186m. Involves three countries but it's possible in single player to get some form of this. Portugal must take A Royal Wedding and unite with Brazil prior to a Carlist Spain completing Restore the Iberian Union. If you intervene and have Spain puppet Portugal prior to this they should accept, otherwise there is only a minuscule chance they will accept it. Once Spain has united with Portugal you can take Unite the Crowns to create the Kingdom of Franco-Spain. This version should have over 110m core pop and it would definitely be better to take Encourage Immigration but we're not being reasonable here. The way the French Union works is North Africa (8,7m pop - doesn't include Algiers as you core it immediately right before this) has a 25% chance of coring, West Africa (16,3m pop) has a 45% chance of coring, Central Africa (7m pop) has a 45% chance of coring, Syria (3,5m pop) has a 15% chance of coring, and Indochina (24,5m pop) has a 5% chance of coring, so on average you are looking at 14,4m in additional core pop on average, with a large resistance modifier applied on any that did not accept. In addition you cannot get rid of the full employment/worker shortage spirits. If you're stuck with only your starting lands it would only really make sense to take it if you are going Napoleonic, extremely lucky, or save scumming. Your chance of all of them accepting is around 0.03797%... But hey if they do +60m in core pop.
Franco-British Union: 219m - Starting with the above situation, a democratic UK can force change the government of France back to democratic and make France join the same faction. Then you just have to have them lose to Fascist or Non-aligned Germans. As soon as the Germans are beat you lose all French cores (which include spain etc) so this one is only temporary.
The Empire: 387m - Now this isn't your usual standard Imperial stuff but it's close. It's not worth the hassle to do the below from a normal game, but both South Africa and New Zealand can gain additional core pops. South Africa must choose to appease and demand the territories from the UK. Then a short war with a released Mozambique or Portugal will give them the territories needed to create Mutapa netting almost another 6 mil in core pop after the conference. The hardest part will likely be increasing their autonomy. New Zealand is a little easier, they have to go with Waitangi Tribunals and request Polynesian Islands from the UK. Then the remaining islands have to be given to them after wars with France, Japan and the US for an additional 1m in core pop. Fortunately, they do not need to become independent. All that would remain is to complete the Conference and form the EU.
Now, if you combine the above two, for at least a short while you can have the thickest western empire ever with an astonishing 512m core pop.
Which brings us back the title as a China with treaty ports has about 517m pop... so close...
As a disclaimer, you're not going to get these in single player outside of a smaller version of first one, but it's entirely possible to get them in multiplayer if you involve about 8 players in certain countries. This would still involve a lot of luck as a result of the French Union is completely dependent on rng. Since this was done in singleplayer the dates and world situation will be off but add_core was not used. Some of the numbers will be inflated do to natural pop growth as these are not amounts taken on 1936.
France: 186m. Involves three countries but it's possible in single player to get some form of this. Portugal must take A Royal Wedding and unite with Brazil prior to a Carlist Spain completing Restore the Iberian Union. If you intervene and have Spain puppet Portugal prior to this they should accept, otherwise there is only a minuscule chance they will accept it. Once Spain has united with Portugal you can take Unite the Crowns to create the Kingdom of Franco-Spain. This version should have over 110m core pop and it would definitely be better to take Encourage Immigration but we're not being reasonable here. The way the French Union works is North Africa (8,7m pop - doesn't include Algiers as you core it immediately right before this) has a 25% chance of coring, West Africa (16,3m pop) has a 45% chance of coring, Central Africa (7m pop) has a 45% chance of coring, Syria (3,5m pop) has a 15% chance of coring, and Indochina (24,5m pop) has a 5% chance of coring, so on average you are looking at 14,4m in additional core pop on average, with a large resistance modifier applied on any that did not accept. In addition you cannot get rid of the full employment/worker shortage spirits. If you're stuck with only your starting lands it would only really make sense to take it if you are going Napoleonic, extremely lucky, or save scumming. Your chance of all of them accepting is around 0.03797%... But hey if they do +60m in core pop.
Franco-British Union: 219m - Starting with the above situation, a democratic UK can force change the government of France back to democratic and make France join the same faction. Then you just have to have them lose to Fascist or Non-aligned Germans. As soon as the Germans are beat you lose all French cores (which include spain etc) so this one is only temporary.
The Empire: 387m - Now this isn't your usual standard Imperial stuff but it's close. It's not worth the hassle to do the below from a normal game, but both South Africa and New Zealand can gain additional core pops. South Africa must choose to appease and demand the territories from the UK. Then a short war with a released Mozambique or Portugal will give them the territories needed to create Mutapa netting almost another 6 mil in core pop after the conference. The hardest part will likely be increasing their autonomy. New Zealand is a little easier, they have to go with Waitangi Tribunals and request Polynesian Islands from the UK. Then the remaining islands have to be given to them after wars with France, Japan and the US for an additional 1m in core pop. Fortunately, they do not need to become independent. All that would remain is to complete the Conference and form the EU.
Now, if you combine the above two, for at least a short while you can have the thickest western empire ever with an astonishing 512m core pop.
Which brings us back the title as a China with treaty ports has about 517m pop... so close...
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