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This design adapts the real-time, city-building video game from Ubisoft for play on the tabletop, but I am not familiar with that video game — or pretty much any video game — so I'll comment only on the board game.
Your goal in Anno 1800 is to have more points than others, and you score points primarily by satisfying the needs of people on your island and completing public objectives. For each person on your island — which starts with four green farmers, three blue workers, and two red artisans — you have a card in hand that at top shows their needs and at bottom shows what they'll grant you should you satisfy those needs. The guy in the image below, for example, wants sausage and schnapps, and in return he'll lure a new artisan to my island. Don't ask for details — just accept it.
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You start with nine cards in hand to match your nine starting people, but if you look at that image, you'll see that I have eleven cards in hand, despite a decent stack of played population cards being on the table in front of me. Each new person you add to your island comes with an associated card, which is both blessing and bane because you can score points and get stuff by satisfying that person, but you can also find yourself in need of a fur coat, rum, or a gramophone for some entitled doofus that's now burdening your hand and it can be a pain in the butt to chase down such things.
In general, players take dozens of tiny turns over the course of play, with most actions consisting of you placing people on the appropriately colored buildings on your island to get stuff — e.g., wood, coal, steel, pigs, the aforementioned rum, etc. — that you then immediately convert into a new production building or a satisfied person. If you don't have the ability to create something needed, which can easily happen in games with three or four players since only two of each production building are available, you can use trade tokens to acquire the good from someone else, with them receiving 1 gold in return. Supply bricks? Get 1 gold. Supply a light bulb? Get 1 gold. Supply a steam carriage or advanced weaponry? Get 1 gold! I'm not a dedicated student of economics, but even I understand that system is out of whack.
You have a limited amount of space on your island, so you can either replace existing buildings with new ones — possibly removing your ability to easily get sails or coal — or expand your island by visiting other places in the "old world", i.e. other parts of Europe. The more "old world" locations you want to add, the more exploration tokens you need, which means you need warships, which means you need larger shipyards, which means you need to get engineers or investors on your island, which means you need to "upgrade" existing residents or attract new people, each of whom will come with their own card.
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Endstate of a two-player game
As you can see, you need to chain together many tiny turns in order to get things done. Most of the time, what your opponent does while you're trying to line up those ducks is irrelevant, especially in a two-player game since you can always acquire whatever building you want, assuming that you have the proper items to input for it.
The challenge often comes from you trying to keep in mind all the steps of whatever you're trying to do: Do you have people of the proper color? (A teal investor won't get their hands dirty building you a level-2 shipyard, for example, as someone might mistake them for a mere engineer.) Do you have the buildings that supply the input? Do you have the buildings that supply the input for the building needed for the secondary input? Do you have trade tokens to acquire what you can't make? Do you have gold on hand to lure (read "force") people to go work somewhere else before they can rest?
Aside from meeting the needs of your people — one-time needs, mind you, because once that guy gets his sausage and schnapps, he'll never tug on your sleeve again — you should have an eye on the public objectives. Maybe you're trying to have more people on your island than everyone else has on theirs? Maybe you'll receive bonus points for buildings that produce gramophones, steam carriages, and penny farthings?
How am I doing so far? Daniel Day Lewis laughs at my self-assessment ability
In some cases, though, the public objectives seem like gravy on top of whatever else you're doing. If none of your people require a penny farthing, for example, then the 6 points you'd receive for jumping through the hoops to get that building into play on your island are probably not worth the effort. What's more, once you have that building in play, the schmoes competing against you can now acquire penny farthings for the low, low price of three trade tokens and in return you'll get all of — wait for it — 1 gold, which amounts to one-third of 1 point at game's end.
This question of what an action is worth arises repeatedly during Anno 1800, and even after 4.5 games on a review copy from Thames & Kosmos, the North American publisher of this game, I'm still not sure how to assess what I'm doing. Grabbing the soap-production building will help me play these three people, sure, but soap is only one of their needs, so I need to also get these other buildings or trade for these goods, with me needing more trade tokens so that I don't have to hold a festival and reset my board too often — this being a "wasted" action — but to get more trade tokens, I need ships, which means I must take actions to build those.
In the end, the game is a rich, entangled web of teensy decisions, and those teensy decisions sometimes seem to weigh heavily on what's possible. If someone else can produce light bulbs, then it probably makes more sense to use theirs twice than go through the effort of producing your own — but if no one has them, would it make more sense to spend one action to swap those people for others who might have more attainable demands, or should you plot a course toward becoming a light bulb baron, a course that will take a half-dozen actions and in the end result in, say, 8 points and a bonus action that feels like an afterthought? Hmm, that second choice doesn't seem ideal, but I need to do something, right? Right?!
In this video, I go through the nine actions in more detail, give many examples of the tech trees present in the dozens of building tiles, and expound upon my conflicted feelings about the game:
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