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Beeline for and build science districts / buildings. You'll also need population growth to get the best benefit out of a campus. Great Scientists aren't all that useful, though some of them can be very valuable - if you're prioritising science though, you should be winning them anyway.
Spam cities early, aim for at least five and they don't need to be too close together, so feel free to space them out to get the best yields of jungles, mountains and resources - don't worry too much about culture and civics as they are less important for science than you might expect. When you do focus on civics, concentrate on city states and trade routes.
Boosting science techs is valuable, but don't boost sciences at the expense of working directly towards your objective. Concentrating on boosts doesn't always help, though some of the early game ones are useful.
If you nail your opening gambit, you can be in the modern era and producing infantry and tanks as early as 1200AD.
Population? Less important the lower the difficulty
How many cities? (and how close together?)
As many as possible allways. Further apart to max 6 tiles apart the higher the difficulty.
what districts in what order?
At low difficulty you want science district first, higher difficulty often industrial If you can get away with it. Allthough the reason for saying that is you want to be growing powerfull cities fast on high difficulty so prioritising growth and production is up there, allthough it deponds on civ and map size / how crowded / whats happened around e.g. If I'm gorgo i'm more likely put an acropolis early so that I can get fuedalism quick for growth amongst other benefits. If its a map with lots of space And i'm set on a science victory and its on deity ill settle more weak citys with campuses early because with my many other cities I can field a usable military to defend them. Allthough early war and taking cities is more efficient than settling if you can.
Its important to stay in touch science wise early on higher difficultys however it really doesnt matter if you dont have campuses straight away You can explode later if you have lots of land and strong cities. For example if its a crowded map on diety as gorgo and I have a 5 mountain spot that may be the only one I build for a while. An accropolis would probs also be built to get the early civic on the same plane as political philosophy to double campus adjecency bonus.
What civics should be rushed? (should culture be prioritised over other things?)
The previous example sais yes. Generally culture is more important initially it provides substantial bonuses straight away (faster unit production (military builder settler directly) note plus one production in all cities is often better than 30% for builders for a while/) and gives the first policy that accelerates the growth and stength of your empire namely feudalism. Science Provides some bonuses for tiles and archers but nothing that makes your cities directly stronger for a while.
(This ties in with what district what order. Next on diety you'll be weighing up do i need crossbowman do i need industrial zones whats gunna get me stonger faster. Archers with two promotions can beat crossbowman so if you've got some of them production often wins)
Really you want to grow in production and growth as fast as possible culture allows this more initially, When your stong and have lots of land then you can go crazy with science, of course on easy difficult you just expand and build campuses you don't need anything else.
What's more important teching boosted techs or beelining the science tech regardless? A mix for if your purely just worrying about science, beeline for techs that directly boost your science techs then do intermediate techs that are boosted. Again if your on easy just beeline because you don't need to worry about everything else
How important are great scientists? Issac Newton and Einstein are very important, I will often pass(which there allways is on diety) if there is great competition so I can get these ones. They directly buff the science output of buildings for the rest of the game.
How important are tile improvements and builders compared to other things like districts.
one mine provides more output than a workshop makimising growth and tile use comes first , districts come second If on diety.
Should I ever use builders to chop down woods early on or should I save them all for space race parts at the end etc. Definetly I consider it exponential benefit, for example its turn 70, You have a 5 charge builder and a campus that is going to take 26 turns to build, you scrap that and build a industrial zone surrounded by 3 mines, You build it with 3 chops, get another builder with your next chop then chop some jungle and have a more populous city with a campus and an industrial zone in like 6 turns and transfer to other problems with a city who wil produce more for the rest of the game allowing for even more growth in turn and snowball.
If your australlia less chopping of course, I will often leave 1 forest hill as its a good tile and apeal allows for good neighbourhoods. Lumber mill hill beats mine however it takes 100ish turns to do so if you chop wich can almost put out an insta workshop with +2 production and some other stuff. So I am an advocate for the chop.
In summary if on easy just grow and plonck down campuses as fast as possible and belign direct science improvements. If not your primary aim should allways be getting as many stong cities as possible as fast as possible early game (Do war its faster and without it you can't outpace the cheating AI.) Then explode in science once the eras advance and borders start to form.
Just tried giving more focus to expanding at the start and improving cities as well as culture early on and managed to get a science victory before 1900s so yeah culture and lots of builders early on and lots of cities is definately the way to go for science victory.
Gorgo very strong for this science victory as well since they get extra wildcard, unique culture district and gain nice chunks of culture killing units. That's the civ I did it with.
I'd say priority in districts looks to be:
Science>Culture>Entertainment / industry
building priority I did was roughly Settler (If you can see room for a nice expansion) > Worker(If improvements are needed)> City center buildings (waterwheels, monument, sewers if you need the housing etc.) > Science buildings > Culture buildings > Everything Else
Keeping expansions not too close seemed to be important too, seemed to make a big impact on overall city development rate.
Religion didn't seem as useful as I thought it'd be for science victory. Culture>>Religion since earlier you get fuedalism and enlightenment the earlier your cities and science can start going off. Next time I'm not going to bother with religion, only really did it a little because the extra wildcard slot meant I could very easily race pantheon and then prophet with the +2 prophet card.
You also want enough faith and religion to hold off your oppoents, if nothing else inquisitors who can clear your citys. You want enough other citys to make a defense army. You need enough culture to progress there as well. You may have to build up defensive tourism if the computer gets rolling, but it rarely does.
Sci on normal difficulty ... the computer struggles to get over 100-150/turn for a long, long time. You should double this as fast as you can and then keep increasing it... 200-300/turn.
The 2 things that control the win are how good you are at production and how fast you can move up the sci tree. Everything else you do is just enough to defend yourself against any other issues that the game throws at you.
specifics...
3 sci citys. The rest depends on map size, I play huge maps and go all empire at it, often have 15 total...
population is thin in an empire, but my 3 sci citys have ~20 by the time it matters.
district order... those 3 need encampment (1), industrial and harbor (any order depends on map). Campus if you can get a 4th, but the other citys will handle this part. These 3 are all about production. If only building 3, you need sci also.. youll have to decide what to do.
you need culture to get great certain wonders, great scis, great engs, ... there are too many to list that help, and you may not get them all.
Great sci are very important. There is one that gives a huge sci bomb per mountain tile, X4 will get you 3-4 techs completed. Be sure to set a distant tech like rocketry or the actual mars launch end one first, so it will select them in a sensible order to burn the points. Others give tech boosts that push you on the way.
Tiles are huge, again, lumber mills, mines, production, and enough food to grow people to man the tiles...
Saving woods is nice if you can. If not, you don't have to have it. If you plan it, you can have the woods tiles out far to pick up later and the inner tiles accessible early game. This isnt easy for all maps, though. You do what you can with the terrain you have.