communism, corruption,OCN

[kaskavel]

Communism, Emperor, 155 cities I think, huge. FP and SPH built. Completely won situation.
I am certain that the cities of Kazan and Allegheny had 80-82 uncorrupted shields and were thus building cavarly in one round. They have now dropped to 78. It seems that building more farms and conquering more cities changed something with the corruption and the OCN. I abandoned a dozen of cities to see what happens and one of the two cities, the closest to the capital, returned to 80 shields, but not the other. I am still somewhat confused with the issue in communism. I thought building more cities would not change existing corruption, but it seems I got that wrong. How does that stuff work exactly and what are the general guidelines to handle communism?

 

[tjs282]

As far as I understand it (and @justanick will no doubt correct me if I'm wrong! ), under a Communist gov, "Distance corruption" is set to be a flat rate (25% of the maximum possible distance, based on the map-size), instead of increasing with distance from the nearest Palace-type building (as for all the other gov-types), but "Rank corruption" continues to increase with each new town built/ conquered, and total Rank corruption is essentially averaged across all your towns. So, yes, for each new town added to your empire, every currently owned town will become a little more corrupt.

This means that under Communism, you do not want to build "farms", rather you want all your towns to be Metros (Hospitals built), roughly optimally placed (minimal overlap of BFCs), and Courthoused (except for your capital, obviously!).

The definitive analysis is here:

Everything About Corruption: C3C Edition - CivFanatics

This is a guide about how corruption works in Conquests. It's slightly different than how it used to work in PTW and vanilla Civ3. The information that follows was discovered by extensive testing and contributions by numerous members of the Civ3 community, including Aeson, DaviddesJ, Nor Me, and...

www.civfanatics.com

 

[tjs282]

Yes. Farming at CxCxC placement is not a useful tactic under Communism, but that setup is easy to adjust to the much more efficient CxxxC placement by removing the "in-between" towns.

You could of course just abandon those unwanted towns, but you get nothing back if you do that. Instead, building Workers (or Settlers, if Agricultural) out of the town, with net food harvest set to zero or negative (e.g. by using low-food tiles or Specialists), will give you the option to abandon the town while still preserving their populations. Those new Workers/Settlers can then be added to the towns you want to keep, to grow them to max. size much faster than would be obtained by 'natural' growth.

With Tundra, the best option would be to keep mainly/only towns on the edges of the Tundra (whether Coastal, or adjacent to Grassland), and then adjust tile improvements for maximum food from the fertile areas, to allow you to work the Tundra-Forests for shields.

So Tundra-towns near Grassland would be maximally irrigated + railed, and the best coastal Tundra towns to keep would be those which can work several adjacent food-bonus tiles (in these regions, that would usually be Deer, Fish, and/or Whales): build Harbours for food, and a cheap Culture-producing building to get the full BFC.

 

[kaskavel]

Oh, I removed the post before your answer. I didnt mean that kind of farms. Only cities sized at 2, exploiting hills/tundras.I guess those are still favorable at CxCxC as I cannot build metropolis in that land. Fertile lands will host metropolis of course, that is the point of communism anyway I guess.

 

[tjs282]

No, it's as I said: under Communism, those small useless towns drag your whole empire down.

Any potential Tundra town-sites that can't grow to at least 10-12 citizens, just leave them un-Settled, and obtain the tiles using Culture from the CxxxC "Tundra-border" towns, as I described above.

 

[justanick]

I am still somewhat confused with the issue in communism. I thought building more cities would not change existing corruption, but it seems I got that wrong.

Well it, is true. That is unless you choose communism. Outsite of communism the rank of a city is determined by the amount of cities closer to the capital with the city closest to the capital having rank 1. In communism rank is just the total amount of cities divided by 2 and rounded down.

How does that stuff work exactly and what are the general guidelines to handle communism?

You need courthouses as they halve distance corruption from 25% to 12.5%. Adding a police station will halve it again, but that is barely worth. That is unless the FP or the SPHQ is in the city as then the police station will reduce corruption to zero.

Since free unit support is a flat 6 for all city sizes you could be temped to max out the amount of cities. And in the short run that may work out alright. But in the long run both corruption and buildings maintenance will favour fewer but larger metropolises using roughly 17 tiles each.

Policemen are quite useful as they will be fully effective. That is unless you play at Sid and huge size and have max out the amount of cities beyond an amount that is still sane. In extreme it is possible for corruption to go to 70% which will mean that any other government will have a lower average corruption than communism. But that extreme case is hardly relevant for any normal situation.

No, it's as I said: under Communism, those small useless towns drag your whole empire down.

Any potential Tundra town-sites that can't grow to at least 10-12 citizens, just leave them un-Settled, and obtain the tiles using Culture from the CxxxC "Tundra-border" towns, as I described above.

This may indeed be favourable. Leave the wasteland to someone else. Or you could hope for global warming to make Tundra fertile.

A few towns in the wasteland may however do little damage. The free unit support may on balance still make them (barely) viable.

 

[kaskavel]

With Tundra, the best option would be to keep mainly/only towns on the edges of the Tundra (whether Coastal, or adjacent to Grassland), and then adjust tile improvements for maximum food from the fertile areas, to allow you to work the Tundra-Forests for shields.

So Tundra-towns near Grassland would be maximally irrigated + railed, and the best coastal Tundra towns to keep would be those which can work several adjacent food-bonus tiles (in these regions, that would usually be Deer, Fish, and/or Whales): build Harbours for food, and a cheap Culture-producing building to get the full BFC.

Yes, I got that right. It is favorable to build on the border of grassland/tundras and specificaly place the city in a tundra square to cheat one square. This allows maximum exploitation of tundra squares with minimum cities by getting irrigated grasslands from the south. This is a cute example from my game. Salamanca is inherited (and does have Sun Tsu) and cannot be abandoned. By building tundra-city (sic!) at this exact place, I exploit max tiles, while hurting Salamanca as little as possible. The funny thing is that Salamanca gets the northern tundra tiles in order to lessen the burden of tundra city and tundra city gets all the grass it can in order to support the remaining tundra squares. Salamanca ends up stable at pop 16 and tundra city ends up stable at size 15 exploiting exactly all available squares (7 tundras, 3 hills, 1 mountain). Only the tundra 9 of the cow cannot be supported but goes to Dalandzadgad which can afford it without trouble. (Tundra city should have been at size 16 in fact, but I assigned a barely visible sugared hill to Oil Springs, not sure why, seems like a mistake on principle-the bigger city should get as much as it can I think). Dalandzadgad and Nalayh are also built on a tundra square and have full irrigation. They both end up able to support all the tiles they can, ending up at population 16 and 20 respectively (no specialists). I think I got all that pretty perfect. But as we move to the north, I lose the ability to use those tricks. I have tens of pop-2 cities trying to exploit all the available squares there. Damn, someone will notice the factories and I will get into trouble...I think those "farms" are favorable and should be maintained. Closer to the Northen coast, we get some bigger cities of course.

 

[kaskavel]

No, it's as I said: under Communism, those small useless towns drag your whole empire down.

Any potential Tundra town-sites that can't grow to at least 10-12 citizens, just leave them un-Settled, and obtain the tiles using Culture from the CxxxC "Tundra-border" towns, as I described above.

Hmm...meaning that the damage from overall corruption (plus costs of setller/working the tiles/buildings etc) trumps the shields/commerce those cities offer? I have found the unit support to be irrelevant in all my games so far. I never get max troops in communism.

 

[kaskavel]

Also, let me add some further info that may matter. Some of those 2-pop cities are just city-tundra-tundra, but some are city-rivered hill-rivered hill. And many cases in between those two extremes. They have quite a different value of shields/commerce to offer.

 

[justanick]

Hmm...meaning that the damage from overall corruption (plus costs of setller/working the tiles/buildings etc) trumps the shields/commerce those cities offer?

It is corruption and the maintenance of buildings that matter in the long run. Those two have the potential to lower the net output of your empire.

Say you play at emperor, a standard size map and a noncommercial tribe like the mongols. You can chose between having 100 metros or 100 metros and 10 size 2 tundra towns. You have FP and SPHQ. Corruption is zero there and in the proper capital. For the remaining 97 Metros or 107 cities rank corruption will be 16.2338% or 17.8571%. That is assuming that with courthouse and police station Nopt is 154. So total corruption is 22.2484% or 24.1071%. Assume 3 tiles per tundra town and 17 per Metro. Assume those tiles average the same. Then after corruption you get 97*17*(100%-22.2484%)=1278.24 effective tiles or (97*17+10*3)*(100%-24.1071%)=1274.24 effective tiles. So in this case the net output of your empire is indeed slightly lowered by those 10 tundra towns. But the up 60 gtp saved by higher free unit support can outweigh the difference.

I have found the unit support to be irrelevant in all my games so far. I never get max troops in communism.

Yes, that seems reasonable for any large communist empire. And that is why fewer tundra towns are likely to benefit your communist empire. If communism had the unit support mechanic of a republic, then it might be different.

 

[kaskavel]

That is some impressive way of approaching and formalizing the issue. Certainly convincing but makes me wonder about some things.
Assuming those tundra tiles are more or less equal to other ones is quite generous. They beat most irrigated squares by "one" and irrigated grasslands by "two" but lose to most mined squares by "one" and to mountains and hills by "two". I think they are weaker on average, especially since in communism there is a tendency to irrigate less. Me, I never irrigate if the city has no new tile to exploit, I prefer the two+factory bonuses shields to one specialist (especially since I am usualy trapped with more money than can be reasonably spent). Also, those cities do not get full building bonuses, no one is going to build a factory or a university there. So the real handicap seems to be higher.
Still, such a city with more than three tiles and/or superior tiles (hills and river bonuses) may be favorable. Rivered mountains for example have double gains compared to tundras, there are many parameters here. I am tempted to investigate those corruption formulas and see if I can produce some general formula for things like that. (when a city is favorable to build or not) but it may be hard work. Similar dillemas may also be investigated in such a manner.
Very nice approach!

 

[justanick]

Assuming those tundra tiles are more or less equal to other ones is quite generous.

Yes, but in this context only commerce and shields matter. So this assumption is sensible enough.

I also assumed courthouse and police station even in the tundra towns. That of course is not sensible. I therefore underestimate how much those tundra towns lower the net output of your empire. Still, the effect of multiplier buildings such as libraries and factories is more important than that.

Still, such a city with more than three tiles and/or superior tiles (hills and river bonuses) may be favorable.

Yes. As a rough estimate any metro is worth is, a city can be worth it while a mere town is unlikely to break even in the scenario i painted. Of course having 100 metros on a standard size map is a lot. It can be done, but that may exceed the domination limit of 66% territory.

 

[kaskavel]

Yes, but in this context only commerce and shields matter. So this assumption is sensible enough

Yes, I know, that is what I mean by "they beat by one" in the text below. I am not counting food. "One" means one more commerce/shield. I think we get on average more than 3 shields/commerce across the map.

Assuming those tundra tiles are more or less equal to other ones is quite generous. They beat most irrigated squares by "one" and irrigated grasslands by "two" but lose to most mined squares by "one" and to mountains and hills by "two".

 

[kaskavel]

It ends up being a huge mess. Lots of farms that were useful before Lenin must now be abandoned. Metropolis are a little tighter than OCP and end up at average population of 14-15 or something which could have been higher. There are pairs of cities that should be replaced by a new metropolis in a third, different location. Borders between fertile lands and hills/tundras are not optimaly built in many places. Chaos. It looks like one should plan for communism from the ancient ages-build at OCP with in-between towns and constantly keep the idea of entering communism in mind for the whole game, without knowing if things will eventualy evolve into an empire-like civilization situation

 

[C0rTeZ48]

No, it's as I said: under Communism, those small useless towns drag your whole empire down.

Any potential Tundra town-sites that can't grow to at least 10-12 citizens, just leave them un-Settled, and obtain the tiles using Culture from the CxxxC "Tundra-border" towns, as I described above.

Policemen are quite useful as they will be fully effective. That is unless you play at Sid and huge size and have max out the amount of cities beyond an amount that is still sane. In extreme it is possible for corruption to go to 70% which will mean that any other government will have a lower average corruption than communism. But that extreme case is hardly relevant for any normal situation.

Hmm...meaning that the damage from overall corruption (plus costs of setller/working the tiles/buildings etc) trumps the shields/commerce those cities offer? I have found the unit support to be irrelevant in all my games so far. I never get max troops in communism.

Say you play at emperor, a standard size map and a noncommercial tribe like the mongols. You can chose between having 100 metros or 100 metros and 10 size 2 tundra towns. You have FP and SPHQ. Corruption is zero there and in the proper capital. For the remaining 97 Metros or 107 cities rank corruption will be 16.2338% or 17.8571%. That is assuming that with courthouse and police station Nopt is 154. So total corruption is 22.2484% or 24.1071%. Assume 3 tiles per tundra town and 17 per Metro. Assume those tiles average the same. Then after corruption you get 97*17*(100%-22.2484%)=1278.24 effective tiles or (97*17+10*3)*(100%-24.1071%)=1274.24 effective tiles. So in this case the net output of your empire is indeed slightly lowered by those 10 tundra towns. But the up 60 gtp saved by higher free unit support can outweigh the difference.

Abandoning 9 of my most outer undeveloped towns in my large 117 city Communism empire on a 40% Pangaea Standard Deity game only down to 108 (OCN was at 108 exactly) lowered corruption only from 29.8% to 28.7%, and waste from 25.77% to 24.3% (calculated these average by adding up all corruption and waste using CivAssist II). I had about 68% of all area under control. A roughly +1% corruption for every roughly extra 10% cities build over the OCN seems like a great deal. Seems nothing like ''extra small towns dragging my empire down'' under Communism, or my corruption increasing to ridiculous levels. I was still gaining plenty of net bonus uncorrupted shields and commerce.

 

[justanick]

OCN was at 108 exactly

You most likely mean Nopt. OCN is a property of map size only. Nopt on standard size, Deity, VP+SPHQ is 108 without courthouses, 113 with courthouses and 118 with courthouses and police stations. In the later case corruption for 108 cities is 29.1314% and for 116 or 117 cities 30.8263%. So in you example the drop in corruption is slightly smaller than in my example.

Thread 'Everything about Corruption: C3C edition'

Jan 25, 2004

This is a guide about how corruption works in Conquests. It's slightly different than how it used to work in PTW and vanilla Civ3.

The information that follows was discovered by extensive testing and contributions by numerous members of the Civ3 community, including Aeson, DaviddesJ, Nor Me, and Qitai. We also recently got some inside information (a look at some of the actual corruption code), which helped find the last few missing pieces of the corruption puzzle.

DEFINITIONS

Corruption in Civilization 3 is commerce from city tiles that cannot be used by the empire...

• alexman
• Replies: 120
• Forum: Civ3 Strategy Articles

• 

Abandoning 9 of my most outer undeveloped towns in my large 117 city Communism empire on a 40% Pangaea Standard Deity game only down to 108 (OCN was at 108 exactly) lowered corruption only from 29.8% to 28.7%, and waste from 25.77% to 24.3% (calculated these average by adding up all corruption and waste using CivAssist II).

Well, that means that rounding issues are a major concern. If prior to corruption and multipler buildings there are 24 shields, then a rounding of 0.5 equals 2.0833 percentage points.

A roughly +1% corruption for every roughly extra 10% cities build over the OCN seems like a great deal.

Statistically speaking it is not. But 1.6949 percentange points difference may not be sufficient reason for any major change in strategy.

If we apply you measured difference of 29.8% to 28.7% to my example, then it is 97*17*(100%-28.7%)=1175.737 effective tiles or (97*17+10*3)*(100%-29.8%)=1278.658 effective tiles. Rounding clearly matters at such insignificant scales.

 

[C0rTeZ48]

You most likely mean Nopt. OCN is a property of map size only. Nopt on standard size, Deity, VP+SPHQ is 108 without courthouses, 113 with courthouses and 118 with courthouses and police stations. In the later case corruption for 108 cities is 29.1314% and for 116 or 117 cities 30.8263%. So in you example the drop in corruption is slightly smaller than in my example.

Well I simply used Lbhhh's ''OCN'' Excel sheet based on Alexman's equations. When I filled those in, I got the 108 number. Perhaps a bit confusing, since Alexman's page does indeed put OCN and Nopt as two different variables in the equation, but also states ''optimal city number (Nopt)'' and ''optimal city number, Nopt'', thereby making it seem like the two are interchangeable.

I don't know where in the equation you got it from that anti-corruption buildings like courthouses and police stations increase Nopt. It's also not in Lbhhh's Excel sheet. Anti-corruption flag decreases distance corruption, not rank corruption by what I can see.

Well, that means that rounding issues are a major concern. If prior to corruption and multipler buildings there are 24 shields, then a rounding of 0.5 equals 2.0833 percentage points.

Using corruption and waste percentages from CivAssist II is far more accurate than calculating uncorrupted shields and commerce from cities. Those are misleading, since for example, an 11th shield in a 90% waste city would add up to two shields, not 1.1. One may get the impression waste in that city is 1 - (2 / 11) = about 82%. Sure enough, 90% corruption/waste won't be a problem under Communism, so my example is hyperbolic, but it still underlines the problem with calculating corruption and waste from city shields and commerce..

But sure, if we're perhaps only taking a few cities rounding issues would be somewhat of a concern. But since we're talking about more than 100 cities, those rounding issues would outbalance against each other (principle of large numbers). At these numbers margin of error is about 5% (which would mean an expected value of about 1.05% to 0.95%).

But if you want me to be more exact, I can calculate total uncorrupted shields and commerce for you, before and after abandoning of these cities. And do keep in mind these were all the furthest, smallest towns I deleted.

Statistically speaking it is not. But 1.6949 percentange points difference may not be sufficient reason for any major change in strategy.

If we apply you measured difference of 29.8% to 28.7% to my example, then it is 97*17*(100%-28.7%)=1175.737 effective tiles or (97*17+10*3)*(100%-29.8%)=1278.658 effective tiles. Rounding clearly matters at such insignificant scales.

Well you're only assuming 3 tiles for those towns, and 17 tiles for all other cities. In my game about 25 cities were metropolises averaging about size 15-16, about 70 or so about size 12 (full city size), and the remaining in between about 3 and 9-ish (the towns I deleted were about 3-5 size). I only entered Communism recently and still had to build hospitals in many of these cities (I mean, I already won the game, but I should if the game still went on for many more turns). I wouldn't have let those towns only grow to size 6 or so, but as large as possible, which would be to at least size 10, likely even beyond 12. And still, my total uncorrupted shields and commerce did drop after abandoning those cities.

What I actually should end up calculating is what the percentages would be if all cities were of equal size, or at the very least, more developed as they were now. Since it is what then will end up being as eventually. Maybe you misunderstood, but I wasn't per se arguing for a ICS/CxC spread. Maybe it might still actually be useful under Communism? I should at least know what they would end up producing as uncorrupted shields, commerce, and even extra food.

In any case, I expected to get a far larger decrease in total corruption and waste percentage, like maybe about 0.5% or 1% per city. But 0.1% is very low, and still very much worth adding additional cities imo. And I can calculate the number of uncorrupted shields and commerce before and after for you if you want me to.

I don't know where you got the 1.6949% from though, when the expected values of corruption would be in between about 0.95% and 1.05%, and waste (many marketplaces were still being build in cities, which would have led to even lower waste due to WLTKDs).

And I probably understand what you mean by ''statistically speaking it is not'', but let me ask you this: if the average corruption in your empire grow from 2 to 3%, would you say that's a 50% increase, or a 1% increase? Yes, statistically speaking it's a 50% increase, but taking that for as it is would be very misleading, since global corruption would still only raise from 2% to 3%. Therefore, me saying 28.7% to 29.8% to it being a 1% increase, rather than a (29.8 - 28.7) / 28.7 x 100 = 3,83% increase, is far less misleading and more meaningful to players.

 

[justanick]

Well I simply used Lbhhh's ''OCN'' Excel sheet based on Alexman's equations. When I filled those in, I got the 108 number. Perhaps a bit confusing, since Alexman's page does indeed put OCN and Nopt as two different variables in the equation, but also states ''optimal city number (Nopt)'' and ''optimal city number, Nopt'', thereby making it seem like the two are interchangeable.

I don't know where in the equation you got it from that anti-corruption buildings like courthouses and police stations increase Nopt. It's also not in Lbhhh's Excel sheet. Anti-corruption flag decreases distance corruption, not rank corruption by what I can see.

"Ni" is the number of anti-corruption buildings. The formula of alexman is clear on that. Outside of communism courthouses and police stations have a mid sized impact on rank corruption. In communism the effect is somewhat miniscule.

Using corruption and waste percentages from CivAssist II is far more accurate than calculating uncorrupted shields and commerce from cities.

If the goal is to be accurate, then yes. If the goal is to understand the mechnics behind corruption, then no.

But sure, if we're perhaps only taking a few cities rounding issues would be somewhat of a concern. But since we're talking about more than 100 cities, those rounding issues would outbalance against each other (principle of large numbers).

One might think so, but your concrete example is (anecdotal) evidence against that idea. The theoretical difference is 1.6949 percentage points, the measured one is only 1.1 percentage points. Since both cases are very close to each other, rounding has a relatively large impact. So while rounding is small compared to your total output, the (net) difference in rounding is not small compared to the difference in output.

Well you're only assuming 3 tiles for those towns, and 17 tiles for all other cities.

Such an assumption is necessary. Abandon this assumption and the conclusion is different. Any meaningfully sized city is meant to increase the output of your empire.

In the example of Nopt=118 two additional city increase corruption by 0.4237 percentage points. At 236 cities corruption is 55.8263%, at 238 cities it is 56.25%. At 10 tiles per city that is 234*10*(100%-55.8226)=1033.67 effective tiles vs. 236*10*(100%-56.25)=1032.5 tiles. So there is a negative net contribution.

At 176 cities corruption is 43.5381%, at 178 cities it is 43.9619%. At 10 tiles per city that is 176*10*(100%-55.8226)=993.73 effective tiles vs. 178*10*(100%-56.25)=997.48 tiles. So there is a positive net contribution. In practice you are likely to run out of territory before you get to 176 proper cities. So the whole point of this discussion is rather mute for you.

I don't know where you got the 1.6949% from though,

Abandoning 9 out of 117 cities is equal to abandoning 8 out of 116. Nopt=118. (8/2)/(2*Nopt)=0.016949.

when the expected values of corruption would be in between about 0.95% and 1.05%, and waste (many marketplaces were still being build in cities, which would have led to even lower waste due to WLTKDs).

The impact of WLTKD in communism is very small when you already have courthouses and police stations.

And I probably understand what you mean by ''statistically speaking it is not'', but let me ask you this: if the average corruption in your empire grow from 2 to 3%, would you say that's a 50% increase, or a 1% increase? Yes, statistically speaking it's a 50% increase, but taking that for as it is would be very misleading, since global corruption would still only raise from 2% to 3%. Therefore, me saying 28.7% to 29.8% to it being a 1% increase, rather than a (29.8 - 28.7) / 28.7 x 100 = 3,83% increase, is far less misleading and more meaningful to players.

That however is not what i did. What i refer to is the case when rounding does have no relevant net effect. You seem to refer to the difference of percent vs. percentage points.

 

[C0rTeZ48]

"Ni" is the number of anti-corruption buildings. The formula of alexman is clear on that. Outside of communism courthouses and police stations have a mid sized impact on rank corruption. In communism the effect is somewhat miniscule.

Ah I see. Very silly of me, but I glossed over it since the 'Ni' value isn't explicitly laid out in rank corruption among the other variables. Handy to know that it actually misses from Lbhhh's OCN Excel file.

You most likely mean Nopt. OCN is a property of map size only. Nopt on standard size, Deity, VP+SPHQ is 108 without courthouses, 113 with courthouses and 118 with courthouses and police stations. In the later case corruption for 108 cities is 29.1314% and for 116 or 117 cities 30.8263%. So in you example the drop in corruption is slightly smaller than in my example.

I'm doing some calculations of your previous comment, and I'm getting slightly different answers. Assuming Nopt of 118 (in my game it was actually 109, more info down below), and total of 108 cities, I get:
Rank corruption average across empire: (108 / (118 * 2)) / 2 = 22.88%.
Distance corruption: 12,5% (Standard map size, assuming all cities roaded, and about 25 of 117 cities have both courthouse and police station): 12,5 *(0,5^1.213675) = 7.585%. The 1.213675 is a result of 1 + (25/117).
Adding these together, we get about 30.47%, not 29.1314% as you calculated. Or did you only take the Palace, FP and SPHQ also into account? That would lower these values a tiny bit more.

Abandoning 9 out of 117 cities is equal to abandoning 8 out of 116. Nopt=118. (8/2)/(2*Nopt)=0.016949.

I think you're making some two mistakes here:
1) First, you're assuming I had courthouses and police stations build in all my cities. In my game I'd say only about 25 of all 117 cities had both a courthouse AND a police station. None of the towns I deleted had one, so those are irrelevant in the equation. And pretty sure all other cities didn't had one yet. The total added value of courthouses and police stations to Nopt would therefore be: 25 / 117 * 0.5 = 0.10684. Putting this value into the large Nopt equation we get 109.28. I guess this has to be rounded down to 109.

2) Second, even if all my cities hadn't reach Nopt yet (which was the equation you used), then you don't have to divide by another 2. If I solved your equation, I get: 110 / (2 * 118) = 0.4661%, or in meaningful expression 46.61% corruption. So deleting 8 cities from full Nopt (118) to 110 would lower corruption from 50%, down to 46.61%. That's a -3.3898% difference, which is exactly double of -1.6949%, what your answer was.

Now let's try to calculate the actual in-game lowering percentage of first deleting cities over Nopt from 117 down to 109: (2 * 117 - 109) / (2 * 109) = 0.5734, or 57.34%. So the 117th city will have 57.34% corruption, rather than 50%, which is actually a fair bit higher than I expected. However, we still have to divide this by 2 to get average rank corruption across our empire: 28.67% (is actually even a little bit higher as we also deleted the 109th city). However, if we then also add distance corruption, we get 36.25%, which is also far higher than I expected (and is the case).

So I'm assuming I'm making a mistake at this last part?

The impact of WLTKD in communism is very small when you already have courthouses and police stations.

The page states: ''For waste calculations only, when the city is in a WLTKD celebration, add OCN/4 to Nopt.'' Exactly where does this part get added in the equation? Is it when everything is already calculated? If it merely divides OCN by 4, doesn't this actually significantly lower Nopt? Because for Standard maps f.e., you now have a mere 5, rather than a full 20. Is it therefore perhaps more of a multiplicative added to OCN?

 

[justanick]

I'm doing some calculations of your previous comment, and I'm getting slightly different answers. Assuming Nopt of 118 (in my game it was actually 109, more info down below), and total of 108 cities, I get:
Rank corruption average across empire: (108 / (118 * 2)) / 2 = 22.88%.

That i get as well. It is no average, though.

Distance corruption: 12,5% (Standard map size, assuming all cities roaded, and about 25 of 117 cities have both courthouse and police station): 12,5 *(0,5^1.213675) = 7.585%. The 1.213675 is a result of 1 + (25/117).
Adding these together, we get about 30.47%, not 29.1314% as you calculated. Or did you only take the Palace, FP and SPHQ also into account? That would lower these values a tiny bit more.

I ignored the 3 capital cities as they have zero corruption. The way you calculated distance corruption is wrong. Both rank corruption and distance corruption are calculated separately for each city. In communism this leads to same results if everything relevant is the same. In case of courthouse and police station it is 0.25*0.5^2=0.0625=6.25%.

I think you're making some two mistakes here:
1) First, you're assuming I had courthouses and police stations build in all my cities.

That "mistake" is on purpose to stay true to the original example. Inhomogeneities as you describe were unknown to me and complicate calculations beyond reason. Police stations barely pay off in communism, but they do in the long run. So that is a semi-sensible assumption.

[...] I guess this has to be rounded down to 109.

Nopt is not rounded. It being an integer in the examples above is just luck resulting mostly of OCN=20. Outside of communism such luck is less likely.

2) Second, even if all my cities hadn't reach Nopt yet (which was the equation you used), then you don't have to divide by another 2.

Rank in communism is amount of cities divided by 2 and rounded down.

The page states: ''For waste calculations only, when the city is in a WLTKD celebration, add OCN/4 to Nopt.'' Exactly where does this part get added in the equation?

Think of it as increasing Ni by 1. So WLTKD is essentially just a third anti-corruption building.

There may be one difference. WLTKD may not lower the upper threshold for corruption. At least i have seen no evidence for it to do that. So there is that caveat why alexman did not describe it as as a third anti-corruption building. Such an inconvenience.