Wealth/Research vs City Improvements

[FloppyFishTully]

Hello lads and ladettes.

Lately I've been playing some of the older BTS games of the month, and I've started wondering about empire development.

Sometimes I think i build too many city improvements. They might pay off in the long term, specially in the earlier cities, but once the Alphabet and Currency come into play, I find a dilemma: building wealth/research, or further building stuff. If I'm running Organized Religion, the efficient thing is to build, but otherwise I couldn't say which pays off more.

Any thoughts?

EDIT: Also, about fractional beaker/gold output. How does it work?

For instance, let's say I have 4 cities with 7 commerce/turn, and 80% research. Each city would net 5.6 beakers. Are all the fractions (the 0.6 in this case) from each city eventually added up in the empire-wide output, or do they get lost/wasted?

 

[sinimusta]

No org rel doesn't mean the efficient way is to just build. It just makes it cheaper, but that doesn't justify highly developed science infra in a prod city for example.

My two points:
1) Think of the city role, do you want the city to be a cottage center, do you need to get a GP and the city fits for that or do you just need military to get more land? Cottage center and long term play justifies building extensive science multipliers.

2) Opportunity cost. Is there a good opportunity to still expand or go to war profitably? Would I rather get a shiny wonder/failgold or infra? Do you need to get to a tech real quick (in that case wealth builds shine)?

Wealth builds are great when the city isn't intended to be commerce oriented and you're not going to war. Or when infra just doesn't have time to pay back since game will be won with like after getting rifling.

 

[Seraiel]

What pays off is building the things that help reaching a certain type of victory = units (Dom- / Conquest) , buildings (Cultural victory) or everything that enhances but pays back before the finish date (Space) . Very often Wealth (or if possible Failgold) is the best choice though, even Forges (Space) before Sushi and Barracks (Dom- / Conquest) are debatable so need to be evaluated.

 

[Dewii]

Something I wrote to try to work this out for myself:

Someone on these boards – I forget who and can't find the post – suggested as an estimated figure that the utility of hammers or commerce is reduced to 97% on average for every turn they delay. This means that 97 commerce this turn is on average worth 100 commerce next turn.
Doing some basic maths (ie summing a series), and rounding to the nearest nice number, that means that an investment such as a library or a forge needs to pay off in 30 turns.
So Research is a better build for a city than:
A Library at less than 12 raw science per turn.
An Observatory at less than 20 raw science per turn.
A University at less than 27 raw science per turn.
(We ignore Culture, and any extra Great Person Points from additional specialist slots. I assume we're not running Organised Religion.)
Most cities will make more raw commerce in future turns. Assuming that a city's raw science increases by 1 beaker every 10 turns on average (this figure pulled from thin air), you should add 3 raw science per turn to the city's current output in order to take that into account.
Usually Wealth will be a better build than Research. Wealth allows you to shift the science slider upwards, and you will probably have better science multiplying buildings in your cities than you will have gold multiplying buildings. Assuming an average of just libraries in all your other cities, but no other science or gold multiplying buildings, you should be making the following amount of raw (pre-multiplier) science in a city before you add a building instead of just building Wealth (the estimated future growth is already allowed for):
Library: 12.
Observatory: 22.
University:31.

If you have the universities anyway, Oxford University pays off if the raw science is 8 per turn in that city if you have stone, or 16 per turn if you don't.

What about monasteries? If we ignore the fact that they go obsolete, they're as efficient as observatories: so they're a worthwhile build at 22 science per turn. (If they're worthwhile at all, you should build them before you build observatories or universities because they start paying back more quickly.)
But monasteries do go obsolete. However, because science now is worth more than science later, this doesn't hit them quite as hard as you might think.
If you think you'll research Scientific Method in 30 turns, a monastery is worth about 3/5 of what it would be if it didn't go obsolete. If you'll research Scientific Method in 60 turns it's worth about 5/6. In 90 turns, it's worth 14/15.
So that means a monastery is worth building for the science if your city is making:
30 turns: 39 raw science per turn.
60 turns: 28 raw science per turn.
90 turns: 24 raw science per turn.

If you're building the monastery in the Apostolic Palace religion, you'll get 2 hammers per turn from the monastery. That reduces the raw science per turn needed to make it worthwhile by 25. If you have the Spiral Minaret, and the monastery is in your state religion, that reduces the threshhold by 25 raw science per turn as well. If you have the University of Sankore, that reduces the threshhold by 22 raw science per turn. That means that monasteries in the Apostolic Palace religion will almost always be a worthwhile build, unless Scientific Method is imminent.

As we're on the subject, when is the University of Sankore worth building? Suppose we've got 30 turns to Scientific Method. Also, we've got Stone, but are not Industrial and are not running Organised Religion. Every city with a monastery in your state religion also has a library. Then you need to get ((550*(5/9)/(30*(3/5)))*(5/4)= appr. 22 science per turn out of it to make it worthwhile. That means it's worth building if you've got 8 monasteries in your state religion with libraries. I'm not counting temples because temples are only worth building if you're Spiritual or are going for a cultural victory. (If you have temples anyway, you only need 5 to make the University of Sankore worth building.)

 

[FloppyFishTully]

A lot of stuff to chew on, excellent

@sinimusta

Fair enough. With 'efficient' I meant that the multiplier from the civic meant more hammers/turn, therefore building city improvements = greater production. Whether going for buildings is effective or appropriate varies according to each game.

@Seraiel

Cheers. I've noticed I'm not bad at playing, but somehow don't really play to win.

EDIT: .. or I'm just bad at playing

@Dewii

Those are a lot of numbers

I suppose that, in addition to all the factors you've mentioned, turns remaining is also a variable to consider. A city might not fill the criteria for a building paying off in x turns, but the longer time before the game ends, the more the building will be worth (assuming you don't lose it to some other civ).

Regarding the University of Sankore, it's certainly better for larger civs. If you founded one or more religions, your religious infrastructure might be already developed before building the wonder. Plus, temples are not bad as sources of happiness... I think. They come earlier than Colosseums, cost the same and provide a little culture (not to mention you can have multiple temples/city, though not all would benefit from Sankore).

Still, you'd probably build Sankore more than 30 turns before Scientific Method (not sure by how much).

 

[DrCron]

How about courthouses? Do you guys have the numbers for when is it useful to build them?

I'm currently playing a non-organized leader, so I normally wouldn't, but I'm trying archipelago maps and the maintenance accumulates quickly (and communism takes a while to come). Which numbers would you normally consider here?

 

[elmurcis]

How about courthouses? Do you guys have the numbers for when is it useful to build them?

I'm currently playing a non-organized leader, so I normally wouldn't, but I'm trying archipelago maps and the maintenance accumulates quickly (and communism takes a while to come). Which numbers would you normally consider here?

Any city above 20/turn And most cities above 15 gold/turn.
And its nothing unusal to see even 40 gold/turn (big Ai capital on island other side of map with 3-4 cities already on that island). 4 cities island can cost >100 gold/turn after revolt here 5 cities island close to 150, 6 cities... damm, just vassal and gift back /Just me, playing with no-tech trading (muuuch longer game guarantee, harder to bribe, easier to avoid "knife in back") and with Bug version that has no overflow gold from whip (feel more fair, failgold from wonders already is good enough for me /

 

[Powerfaker]

When it comes to wealth/research versus (multiplier) buildings, one needs to compair hammer output versus science or gold output in a city.

Building wealth (never research as mentioned earlier) means 1h equals 1g equals 1 to 1,25b (assuming slider up and lib's in core cities; and note that wealth/research do not get any bonus).
Most multiplier buildings yield 1b/g for every 4 b/g produced.
So for every hammer produced in a city you need to produce at least 5 beakers or 5 gold to make the multiplier building equally or more productive compaired to wealth building.
Core science/gold cities will definitely reach the point where multiplier buildings become more efficient. So you may just want to build them a little bit later than you do right now.
Ironically multiplier buildings become slightly more favourable when you plan to switch the role of the city away from economic (to unit producer or....). The multiplier building keeps providing some b/g while the wealth is all gone.

This is all long term mathematical bla bla of course.

(I still have to find my way with icons by the way, so excuse me for using just words)

 

[Seraiel]

How about courthouses? Do you guys have the numbers for when is it useful to build them?

I'm currently playing a non-organized leader, so I normally wouldn't, but I'm trying archipelago maps and the maintenance accumulates quickly (and communism takes a while to come). Which numbers would you normally consider here?

I've gone over to only build just enough Courthouses to unlock the FP or right before Corporations.

 

[Dewii]

How about courthouses? Do you guys have the numbers for when is it useful to build them?

Using the 30 turn payback rule of thumb I suggested earlier, a courthouse is worth building if maintenance in the city is above 8 gold per turn. That's a very handwavy and circumstance dependent rule of thumb though.

It also doesn't take into account espionage points. Knowing what the AIs are researching and how long it will take them to research it is useful in more ways than just the obvious.

 

[FloppyFishTully]

Also, regarding Courthouses, you also have to take into account inflation. When you reduce any expense, you reduce the inflation cost.

So, while the city management screen might tell you a Courthouse would save you, for instance, 3 gold, the actual savings would be higher.