Free advice (which this thread is slowly becoming anyway):
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Until you have no room left to expand into, don’t get more than about 2 or 20% of your cities above level 6 or so. Remember too that a size 6 city produces less trade, all other things being equal, than 3 size 2 cities (size 6 city has 7 squares producing trade, whereas 3 size 2s have 3 each for 9). Expand, expand, expand.
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If you have a city size 6 with bad production but it’s getting lots of food (on a flood plain, for example), have it pump out your workers. Then you can have the other cities that don’t recoup as easy building other stuff. If you’re on a flood plain you’re probably also getting to level 12 without an aqueduct, so try to base your settler migration from there.
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Don’t think you need a colosseum? Don’t think you need a cathedral? The Oracle expires sometimes at the worst moment, and those 2 or 3 citizens made content from unhappy can be the difference between city disorder and none. It’s also culture, and cultural conversions are a happy thing.
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If you can afford it, put your luxury rate at 0. Early in the game this might not be possible if you don’t have any natural luxuries, but if you find yourself with a lot of happy cities, try lowering your luxury rate. You’ll either get more money, more sci production, or both.
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Last turn to a scitech discovery, set your science as low as you can to still get that discovery in one turn. You get more money. In this case there is such thing as a free lunch:)
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Have a city be building something massive before you get that scitech discovery that lets you build Sun Tzu’s, or whatever. Then, when you get the tech (feudalism, in this case), instead of having the discoveries continue down whatever path you or the computer have set, say you want to change it. Go from there to the city menu (F1 unless you’ve changed it), right click on the city building your massive thing (I go for palaces), and change it to the wonder. You can get 3 techs in one turn doing this (Atomic Theory, build Theory of Evolution same turn, then get your two desired techs. I usually go for Sanitation and Replaceable parts).
Another thing I’ve learned from Civ3 is that slavery of another country’s people is completely ethical; those foreign workers never get paid, so in one sense I’d rather have three German workers, or whatever, than one American (I play as America for the scout and worker speed). There’s no civil unrest from capturing workers, the workers don’t only last a certain amount of time, they never try to escape…they’re soulless drones. I’ve also learned that humans as scientists are disturbingly slow; you can get railroad in 600 AD and I had my spaceship launched many years before Columbus’ little boating trip. Also, ivory exists as deposits in the ground; you don’t need to kill anything to get it. Oil doesn’t need to be drilled, iron doesn’t need to be mined … you just build a road to it and it’s magically transported to wherever it needs to go. Uranium deposits are completely harmless to your populace, and there is no sort of penalty for transporting warheads via railroad; no chance of spills or whatnot.
I enjoy Civ3 more than Civ2; the AI in both games lacks something, but I have enough fun without worrying about AI.