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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. Corrupted commerce is indicated graphically in the city screen by stacks of red coins. There are numerous factors that influence corruption, all of which are addressed in this article.
Waste is the loss of production as opposed to commerce, and is governed by almost the same rules as corruption. Everything in this article that applies to corruption, also applies to waste, unless otherwise mentioned.
CORRUPTION BASICS
The total corruption in each city is equal to the sum of two independent components: distance corruption, and rank corruption.
For non-communal government types, distance corruption depends on the distance of each city from its closest palace. Rank corruption in a city depends on how many other cities are closer than that city to the palace.
For communal government types, distance corruption does not actually depend on distance. Each city is considered to be the same distance from the Palace. Rank corruption depends on the total number of cities in the empire.
You can reduce corruption in your cities by building appropriate city improvements and Wonders, changing to a more efficient government, choosing a Commercial civilization, and connecting your cities to the trade network of your empire. In addition, you can reduce waste by bringing your cities into a WLTKD celebration.
You can determine the total number of ‘red’ commerce in a city by multiplying its total corruption by the number of raw commerce produced by citizens working the land, rounded to the closest integer.
DISTANCE CORRUPTION
For all non-communal government types, the distance corruption component is proportional to the distance of a given city from its closest Palace. For communal governments, the distance to the closest Palace is considered to be the same for all cities on a given map. The “closest palace” to a city can be the Palace, the Forbidden Palace, or any other Wonder with the “reduces corruption” ability.
For corruption purposes, distance is always an integer number, and is given by:
In the special case of communal governments, the distance for all cities is taken as:
where MaxD = (MapW+MapH)/4, MapW is the width of the map, and MapH is the height of the map, as given in the editor.
The distance, d, is used to get the adjusted distance, da, as follows:
For waste calculations only, when the city is in a WLTKD celebration, divide da by 2.
So each anti-corruption building, which is a city improvement with the “reduces corruption” ability in the editor (Courthouse and Police Station), divides distance corruption by 2.
Finally, the exact value of the distance corruption component is given by:
RANK CORRUPTION
The rank corruption component depends on the rank (R) and optimal city number (Nopt) of each city.
In a non-communal type of government all cities of an empire are ranked in order of distance to the capital, starting at zero for the capital itself. If several cities have the same distance to the capital, they are ranked in order of founding, and if they also have the same date of founding, they are ranked by their order in the database. In a communal form of government, all cities have the same rank, which is half the total number of cities in the empire, rounded down.
Each city also has its own optimal city number, Nopt, given by:
For waste calculations only, when the city is in a WLTKD celebration, add OCN/4 to Nopt.
The rank corruption for a city is then given by:
MAXIMUM CORRUPTION
The sum of the distance and rank components of corruption can be greater than 100%. The game sets an upper limit for the total corruption in a city to be equal to 90% minus 10% for each city improvement and minus 70% for each Wonder in the city with the “reduces corruption” ability:
POLICEMAN SPECIALISTS
By assigning one of your citizens to be a policeman, you can cause one corrupted commerce and one wasted shield to become uncorrupted. This reduction in corruption comes before applying the maximum corruption limit described in the previous section, so the city may not show any reduction if was already taking advantage of that limit.
SUMMARY
To summarize the above, distance corruption depends on the distance of the city from the closest palace (or a constant number for communal governments), multiplied by a factor that depends on the government type, and another factor if the city is not connected to your capital by road, harbor, or airport. Each corruption-reducing building in the city halves distance corruption.
Rank corruption depends on the ratio of the city rank to the adjusted optimal city number. The city rank is equal to the number of cities closer to the capital (or half the total number of cities for Communism). The rate of increase of this corruption with rank doubles after rank exceeds the optimal city number. The optimal city number of the map gets modified by the difficulty level, the commercial trait, the current government, and the number of improvements and Wonders with the “reduces corruption” ability.
Courthouses and Police Stations decrease distance corruption and increase the optimal number of cities. They also each decrease the maximum corruption limit.
The Forbidden Palace acts as a second Palace for distance corruption calculations, but not for rank calculations. The Forbidden Palace itself will have low corruption, but if there are many cities closer to the Palace than the Forbidden Palace, the cities around the Forbidden Palace will have high rank corruption. However, even though it doesn’t provide a new set of city ranks, the Forbidden Palace reduces rank corruption throughout the empire by increasing the optimal number of cities.
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. Corrupted commerce is indicated graphically in the city screen by stacks of red coins. There are numerous factors that influence corruption, all of which are addressed in this article.
Waste is the loss of production as opposed to commerce, and is governed by almost the same rules as corruption. Everything in this article that applies to corruption, also applies to waste, unless otherwise mentioned.
CORRUPTION BASICS
The total corruption in each city is equal to the sum of two independent components: distance corruption, and rank corruption.
For non-communal government types, distance corruption depends on the distance of each city from its closest palace. Rank corruption in a city depends on how many other cities are closer than that city to the palace.
For communal government types, distance corruption does not actually depend on distance. Each city is considered to be the same distance from the Palace. Rank corruption depends on the total number of cities in the empire.
You can reduce corruption in your cities by building appropriate city improvements and Wonders, changing to a more efficient government, choosing a Commercial civilization, and connecting your cities to the trade network of your empire. In addition, you can reduce waste by bringing your cities into a WLTKD celebration.
You can determine the total number of ‘red’ commerce in a city by multiplying its total corruption by the number of raw commerce produced by citizens working the land, rounded to the closest integer.
DISTANCE CORRUPTION
For all non-communal government types, the distance corruption component is proportional to the distance of a given city from its closest Palace. For communal governments, the distance to the closest Palace is considered to be the same for all cities on a given map. The “closest palace” to a city can be the Palace, the Forbidden Palace, or any other Wonder with the “reduces corruption” ability.
For corruption purposes, distance is always an integer number, and is given by:
Code:
d = max(x,y) + min(x,y)/2
where
max(x,y) denotes the maximum between x and y,
min(x,y) denotes the minimum between x and y,
x is the distance in the NW/SE direction,
y is the distance in the NE/SW direction,
and the integer division is rounded down.
Code:
d = (MaxD) / 4
The distance, d, is used to get the adjusted distance, da, as follows:
Code:
da = 0.5^Ni * min(Gd * t * d, MaxD)
where
Ni is the number of anti-corruption buildings,
t = 1 if the city is on the trade network
5/4 otherwise
Gd = 3/2 for Rampant corruption (Despotism)
3/4 for Minimal corruption (Democracy)
1 otherwise
So each anti-corruption building, which is a city improvement with the “reduces corruption” ability in the editor (Courthouse and Police Station), divides distance corruption by 2.
Finally, the exact value of the distance corruption component is given by:
Code:
Cd = da /MaxD
The rank corruption component depends on the rank (R) and optimal city number (Nopt) of each city.
In a non-communal type of government all cities of an empire are ranked in order of distance to the capital, starting at zero for the capital itself. If several cities have the same distance to the capital, they are ranked in order of founding, and if they also have the same date of founding, they are ranked by their order in the database. In a communal form of government, all cities have the same rank, which is half the total number of cities in the empire, rounded down.
Each city also has its own optimal city number, Nopt, given by:
Code:
Nopt = max(OCN * (L/100 * (1 + c + Gr + Gp*Nwe) + 0.25*Ni), 1)
where
OCN is the optimal number of cities for the map size,
as found in the editor
L is the percentage of optimal cities for the current
difficulty level, as given in the editor
Nwe is the number of active Wonders in the empire with
the “reduces corruption” ability
(Forbidden Palace, SPHQ)
c = 0.25 for a commercial civilization,
0 otherwise
Gr = 0.1 for minimal or nuisance corruption
2 for communal corruption
0 otherwise
Gp = 3/8 non-communal corruption
3 for communal corruption
The rank corruption for a city is then given by:
Code:
Cr = R / (2 * Nopt), if R < Nopt
(2 * R – Nopt) / (2 * Nopt) otherwise
The sum of the distance and rank components of corruption can be greater than 100%. The game sets an upper limit for the total corruption in a city to be equal to 90% minus 10% for each city improvement and minus 70% for each Wonder in the city with the “reduces corruption” ability:
Code:
Cmax = max(0.9 – (0.1 * Ni + 0.7 * Nwc), 0)
By assigning one of your citizens to be a policeman, you can cause one corrupted commerce and one wasted shield to become uncorrupted. This reduction in corruption comes before applying the maximum corruption limit described in the previous section, so the city may not show any reduction if was already taking advantage of that limit.
SUMMARY
To summarize the above, distance corruption depends on the distance of the city from the closest palace (or a constant number for communal governments), multiplied by a factor that depends on the government type, and another factor if the city is not connected to your capital by road, harbor, or airport. Each corruption-reducing building in the city halves distance corruption.
Rank corruption depends on the ratio of the city rank to the adjusted optimal city number. The city rank is equal to the number of cities closer to the capital (or half the total number of cities for Communism). The rate of increase of this corruption with rank doubles after rank exceeds the optimal city number. The optimal city number of the map gets modified by the difficulty level, the commercial trait, the current government, and the number of improvements and Wonders with the “reduces corruption” ability.
Courthouses and Police Stations decrease distance corruption and increase the optimal number of cities. They also each decrease the maximum corruption limit.
The Forbidden Palace acts as a second Palace for distance corruption calculations, but not for rank calculations. The Forbidden Palace itself will have low corruption, but if there are many cities closer to the Palace than the Forbidden Palace, the cities around the Forbidden Palace will have high rank corruption. However, even though it doesn’t provide a new set of city ranks, the Forbidden Palace reduces rank corruption throughout the empire by increasing the optimal number of cities.
thanks Alexman, It all seems so easy now 
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