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You get free settlers from Treasure fleets visiting Viceroy and Governor towns and Embassy building in a town you administer yourself (if you own the DLC), from Europe . If there are colonial goods (Tobbaco, Dye, Cocoa, Coffee) available to buy at one of those towns, the Treasure Fleet will buy and drop settlers/immigrants until their cargo capacity is full, then the fleet will head back to Europe.
You may also get a small numbers of free settlers daily from growth if a Hospital has been built in a town and the town's prosperity level at Prosperous. If a Poorhouse has been built in a town you administer, they'll attract some few settlers too. These are free settlers roaming from town to town, from towns with poor satisfaction to the higher ones.
To improve a towns prosperity level, you need to improve the satisfaction level. The satisfaction level is calculated from the availability of all commodities. So you need to sell goods to a town's market especially those goods that are in low supply. If a commodity completely run out, the satisfaction will drop.
If the satisfaction level drops below 50%, no free settlers will become workers even if there are job vacancies available. You need to improve the satisfaction level first. If it drops below 40% the workers will become free settlers and likely to leave the town. There'll be a shortage of workers and soldiers manning the town's defense. This is one of the purposes of military blockade of a port.
By selling goods that are in low supply, you're already making good profit because the price of that commodities would be high, in addition to improve a town's prosperity.
Oh, in case you didn't know, the Treasure fleets carry a lot of gold. If you capture them, not sink/destroy, you'll get whatever they carry. The amount of gold you loot scales with your rank. If a Treasure fleet hasn't docked at any port from Europe, you'll get a lot of gold with immigrants as sailors if you have space to carry them. Otherwise, you'll get a lot of gold and colonial goods for free, which you can sell back at Viceroy/Governor/Embassy towns. You can also sell a lot of those colonial goods at those towns, to trigger a Treasure Fleet to arrive from Europe. Check out Towns/World section at the Chronicle report info for the news of their arrivals
I'll tell more if you have a specific question to ask.
Does that mean towns would grow extremely slowly? I can't build every single town, can I? So selling goods and keeping satisfaction high does not make the towns grow? And so I'm mostly limited by the given demand per game?
More population means higher demand, right? So if I make, say, Corpus Christi grow to be the most populated town, it's gonna get demands higher than Turk Islands?
I mean, how much can I make all the towns grow altogether? How difficult it is to double the population of the map? How long? How much my sales impact that?
Is there a natural growth from birth?
If I make many automated routs, wouldn't that stop towns from having shortages and thus eliminate quests?
If population grows all around and monthly demand raises, would that make more NPC ships selling to towns?
I'm mostly interested in overall growth, not migration. But it's also an interesting question. If I neglect some far towns like Tampico, would NPC supplies be low enough to make the town slowly desert into other towns? Can towns wither completely? Would that affect NPC business\house price?
Yes, towns grow slowly without your intervention. Once in a while a random AI merchant build a new business in a town, but that's rare. The towns where I choose to build businesses in are amongst the most populous towns in the game.
Selling needed goods to towns will only prevent some towns from shrinking due to emigration caused by very low satisfaction, but can't help towns grow. If you play the pirate mode (A Pirate's Life) and you plunder trade convoys a lot and other pirates do the same, you'll see "Shortage of goods" happen eventually to nearby towns and the worst ones will start losing some inhabitants.
As you build new businesses, the town's population will grow and the rate of their consumption of goods will grow too. So, you'll need to build new businesses there or elsewhere to meet this growing demands. This will in turn increase the population even further. It's a cycle. I can't imagine a situation where all demands everywhere met. I think that's unreachable. I can only focus satisfying the needs of a few towns that I administer.
Yes, to that Corpus Christi-Turk Islands question.
Why do you want to grow all the towns in the game? You can if you want. I won't. It's just too much work. My games progress slowly while I'm just trying to meet the needs of towns I administer. Often I get overwhelmed trying to complete quests. These things can't be done by just automated trade. I like to micromanage things. So, my progress is much slower than most other players I guess.
Natural growth from birth? No. There's just this bonus growth if you've built Hospital or School (I forgot which one. Read the description. I usually build them as a pair.) and the town's Prosperous or above. The bonus you get from them takes into account how much population there is in the town. You need to build more once the town get bigger and bigger, otherwise the growth and satisfaction bonus shrink, for example to 4% or 3%, from max 5%. The growth from this bonus is small. The main source of new immigrants are from the Treasure Fleets. The priest may also offer you some source of immigrants in exchange for consumer goods, but this is not a cost-efficient source and the amount of new immigrants are not that big.
Only the towns that you administer won't get Tasks. Tasks aren't just spawned by lack of goods. In the towns where you have the license to build businesses, once in a while you'll get tasks to build new businesses. This depends on which of the 5 goods produced in the town has the biggest demand. The governors also offer tasks. If nearby town of an allied town lacks certain goods, you'll be asked to provide them. If the town is small you'll be asked to build a few new businesses there. Events may also trigger tasks. Towns stricken by Plague, there will be a task to provide Cloth and/or Clothing. Where there is fire, there will be a task to provide building materials.
"If population grows all around and monthly demand raises, would that make more NPC ships selling to towns?"
I don't know. It's hard to keep track of what trade convoy belongs to what town and how many trade convoys a town has sent out. There's no such information in the game, sadly. My guess is no. I feel like the towns rely on my involvement more and more as the game progresses and towns get bigger.
"I'm mostly interested in overall growth, not migration. But it's also an interesting question. If I neglect some far towns like Tampico, would NPC supplies be low enough to make the town slowly desert into other towns? Can towns wither completely? Would that affect NPC business\house price?"
If you ignore other towns, you'll see they'll be lacking goods. Famine happens. Eventually, some AI trade convoy will visit there after a long while. In my observation, no, unless it's because of pirates become so rampant. Those town will just become very small, like less than 1000 pop. I never care about random "merchant" (AI) -owned house or businesses. They're expensive to buy. I'd rather build what I need myself. Unless, there's a lack of new building space. I've never reached that point so far.
Mostly, I ask because I have 2 major questions about the towns growth and about how much my actions affect them. I also tend to micro-manage too much. I find myself gathering all the cheap goods from town to town and leaving them portions of my goods, keeping a bit for later in case I meet a town with 0 given good. It's not very profitable, I understand that. But I get this feeling like I need to take care of as many towns as possible instead of simply dropping all the goods at the nearest shortage. =)
So, do I get this right: if I fast forward 1000 years, towns will not grow? So my choice at the beginning of a free play of how large towns would be decides once and forever? I mean, look... I come to a poor town and it may buy 4 dyes and 8 rum (10 days demand). I assume the town would have to be 10 times bigger to demand 40 dyes and 80 rum, roughly. If I cannot make ALL towns grow at least 2-3 times bigger, I will face a time when I produce too much and have nowhere to sell it.
It's hard enough to find shortages. NPCs provide too well. So of course I want all towns to grow eventually. Especially since it's the only reason to trade with them. If they don't benefit from my visiting care, the best option is to sell more to 1 town and leave the other ones for later, generating shortages. Dirty trick... But that's optimal profit. If towns grow from my provision, it changes everything and allows me to invest into the future. But if they don't, I'm forced to use that trick. To not get overwhelmed with micro-management. Obviously it's easier to sell all at once place and not tickle the slider 2-3 steps per position every time I dock.
Also, what does high prosperity give? Any bonuses?
And... when towns are struck by sickness, does that kill population?
If there's no natural growth, does that make treasure fleet the only source of population for the map?
Like I mentioned previously, hospital or school gives a small percentage bonus growth while the city is at Prosperous level or above (satisfaction 75% or 80%). You'll see the info at the city info screen. There's a population icon with green plus sign. Another building is park, if you own the DLC. I forgot what bonus it offers.
I think wealthy residence and poor residence yield different rent income. I don't know how much the difference. If you administer a town, you'll also collect tax. I also don't know how it's calculated. I don't care much about my income. My wealth is accumulated primarily from plundering Treasure Fleets and then from completing tasks. These income scale with your rank, so I try to rank up as fast as possible. With higher rank, you're also given more time to complete the tasks. Money is not a problem for me with these income sources I generate from.
I don't think plague decreases population. Bad events hurt a town's satisfaction and affect certain goods production or consumption. Check out this list of events with their effects on this wiki:
https://portroyale3.fandom.com/wiki/Events
I mentioned the sources of new settlers to grow the population in my previous post. To summarize: immigrants from Europe come with Treasure Fleet, immigrants arrival arranged by the missionary exchanged with some consumer goods, population growth bonus from hospital or school. A building that comes with DLC, Poorhouse, attracts settlers that are not yet absorbed by a town after some time, wandering from town to town.
I suggest start by building construction material production first. You'll need this to construct more businesses. You can't rely on just buying from towns. What they produce is too little. Buy from them only to start building your own construction material production.
Next I suggest building businesses producing raw materials. You'll find that it's easy to find demand for these goods. For example, build Cotton farm and sell it to the towns that produce Textiles. Later, you should build your own Textile production and supply them with your own Cotton production.
Build colonial goods production building bit by bit as you build other businesses. These goods are to be exchanged for immigrants to supply your businesses with workers. Sell these goods in bulk at a town that's about to be visited by a Treasure Fleet. You can also sell these goods to trigger the arrival of a Treasure Fleet. When enough of these goods available at a town's market, a Treasure Fleet will pick them up.
I learned a lot from these guides when I was new to this game:
https://steamcommunity.com/sharedfiles/filedetails/?id=173134866
This guide explains different trade route strategies:
https://steamcommunity.com/sharedfiles/filedetails/?id=188838043
If I didn't explain it well about things related to Treasure Fleets, then read this guide:
https://steamcommunity.com/sharedfiles/filedetails/?id=121468251
Thank you! That was a lot of help. I'll try to apply it all in practice =D
No problem. Just play the way you enjoy. It's important that you know how things work in this game. This game isn't informing players well enough, although the two campaigns are basically tutorial followed by free play and they do provide some info about the mechanics. Find out about the rest in the guides and the wiki.