Culture Mechanics Disassembled

(Please note that all information given here is in regards to Vanilla Civ 1.61. It is probably unchanged in Warlords and the as yet unpublished Beyond the Sword expansion, but I have no way of being certain.)(Also note that the following information will generally refer to normal speed games, unless otherwise noted. For games played on the Epic, Marathon, or Quick settings, some numbers listed below may be scaled somewhat.)

There are several different values associated with culture in Civilization 4.
First of all, there is the ‘City Culture’. City culture actually affects only one thing: the city’s cultural level and thus cultural radius. The city’s cultural level and cultural radius start at ‘1’. When city culture reaches 10, the cultural level goes up to ‘2’. At 100, it goes up to ‘3’, at 500 it reaches ‘4’, at 5000, it reaches ‘5’, and finally at 50,000 city culture it jumps up to ‘6’, called “Legendary culture”. Get 3 cities of level 6 and you win a cultural victory. Also note that a city actually has a cultural value and cultural radius for every player in the game. However, unless a player has actually owned a city at some point, their culture for that city is zero. If they are not the current owner of the city, their city culture will have zero impact on the game. City culture never goes away unless the city is destroyed, or the civilization to whom the culture belongs is destroyed.

Of course you were probably already familiar with ‘City culture’. If not, you may need to actually go out and buy a copy of Civ 4 and play the game.

There is also a less accessible culture value, which I will call the ‘plot culture’. Every square/tile/plot/whatever in the game also has a cultural value for every single player. You can’t ever see the exact value, but it’s not totally invisible. On the city screen, the relative values of ‘plot culture’ for various players are shown in the city screen if you point the mouse at the ‘nationality’ bar. If you point the mouse cursor at a square near a city, the %nationality of the plot owner(but nobody else) is shown.
The main effect of plot culture is to determine whose civilization controls that particular plot of land. A civilization will own a plot, if at least one of its cities has that plot within its cultural radius, and if their plot culture is greater than any other civilization that has that plot within one of their cities’ radii. Note that they have to actually own the city. If they built some culture in a city, but later lost control of that city, that city won’t allow them to control any of the surrounding tiles. However, the culture that the city spilled onto the surrounding tiles might allow another of their cities to control those tiles. The exception to all this is plots containing cities. The city and the plot underneath will remain under the control of whoever founded or last conquered it, regardless of underlying culture. However, if the calculated cultural owner is different from the city owner (in other words, some other city, belonging to a different player has the plot within its cultural radius, and they have more culture on that plot), there is a chance of the city revolting and changing sides. We’ll go into revolts in more detail later. Finally, note that plot culture can never ever be gotten rid of, except in a couple of circumstances. Firstly, if you give away a city, you lose all plot cultire in the city square and surrounding 8 squares. Secondly, if you completely obliterate a civilization, their plot culture goes away. Still, if a civilization owns no cities in an area, their culture won’t have any effect except to alter the displayed nationality of squares in the region and to cause a small amount of unhappiness in cities who “long to join the motherland”.

You are probably wondering now where all these cultural values are coming from. The city culture is pretty easy, since the city screen clearly shows what all the sources of culture are. All the various temples, libraries, specialists, culture from the cultural slider, and culture from production are added up and then multiplied by the bonuses given by cathedrals, wonders, civics, and so on. This value, sometimes called CPT(Culture Per Turn), is added to the city’s culture each and every turn. If this gives the city enough culture to increase it’s cultural level and radius, these will also be increased.
The city’s CPT is also added to the plot culture of every plot within the city’s cultural radius, regardless of ownership or presence or absence of other cities. However, there’s an added factor based on the city’s cultural radius. If the distance between the plot and the city is less than the cultural radius, then 20 times the difference is added to the plot culture as well. Note that the square that the city is on counts as being 1 space away and that this 20 value is not scaled with regards to game mode. It is always 20 per turn, period.
To make sure that that’s clear, let me describe it another way. Think of the city’s potential cultural area as a series of rings. The first ring consists of the city and the 8 surrounding squares. The second ring contains the other 12 squares of the city’s production area, and so on. When the city’s cultural level is 1, only the first ring gets the points from the city’s CPT. When the city’s cultural level reaches 2, both first and second ring get the base CPT and the first ring also gets and additional 20 points a turn, even if the city isn’t generating any culture at that time. When the city reaches it’s third cultural expansion, The inner 9 squares get an extra 40 points, the next ring gets 20 points and so on. At the highest level of culture, the inner ring gets a whopping 100 extra points of plot culture per turn.
When you found a city, you also get some plot culture to allow you to control the surrounding area, specifically 2 points on the city square and 1 point in the surrounding 8 squares. This is why newly founded cities are so easy to culturally overwhelm. All you need is a few turns of an obelisk and you’ve got a majority of culture in your neighbor’s city.

One last source of culture is the great artist. When added as an artist superspecialist, he merely contributes to the city’s cultural (and science) production like any other specialist. However, when the artist is used to create a great work (often called a ‘culture bomb’), it gets interesting. Of course, the 4000 culture points are instantly added to the city’s culture. Guess how many of those 4000 points are added to the plot culture of the surrounding squares. The answer is zero. Of course, those familiar with culture bombing will be surprised by this, because they will remember using great works to take control of territory as well boost the city culture, so clearly something more complex is going on. Here’s what actually happens:
First, the city is brought out of revolt, if it is currently revolting. Then, the 4000 points (or whatever the value of the great artist happens to be) is broken up into 20 equal groups. The first group is added to the city’s culture. The city’s cultural level and radius are recalculated. Then, one turn worth of the city’s current cultural output is added to the surrounding squares, including the 20 point bonus for each ring below the outermost ring. Repeat this process for the other 19 groups of great work culture.
So, let’s walk through what this does. Suppose a great artist creates a great work in a city that has no culture. The first of the 200 point groups of culture is added. This brings the city’s culture level immediately up to 3. Now, although a turn worth of the city’s culture is now delivered, the city has no culture and is producing no culture. So, the only plot culture gained is from those 20 point bonuses. The city plot and 8 surrounding squares thus get 40 points of plot culture. The next ring gets only 20 points in each square. Now, we repeat. The next 200 points is added. City’s cultural level stays at 3. Same amount added to nearby squares. Third 200 points added. This brings the city’s cultural level to 4, where it will stay for the remainder of the cultural delivery as we’re only giving 4000 points and it needs 5000 for the next level. So, the innermost ring gets 60 culture each of 18 times, the next ring gets 40 culture 18 times, and the third ring gets 20 culture 18 times. Or, to sum it up, The first ring gets 1160 points of plot culture, the second ring gets 760, the third ring gets 360 and the fourth ring, although within the city’s cultural radius gets nothing. This may seem like a lot, but consider if you sat on the city for a mere 20 turns, you’d double it. Of course, if the city also had any cultural production, that amount would be delivered 20 times to every square in the first 3 rings, and 18 times to the fourth ring.
Note that when the city’s culture is delivered, it is the amount that the city produces at that instant, not that turn. This should raise some mental red flags as possibly abusive, because yes, you can set your culture slider to 100, assign everyone to artist specialist, deliver your culture bomb, then set them back before ending your turn. Knowing this, you can get a great deal of benefit at no cost, if you know the trick. Well, actually, there is some cost, because to use this trick to say add another 1000 to all your squares’ culture, you’d need first need to build the city up to where it can produce 50 CPT.
I don’t think that this would be a huge issue in most games. Normally a culture bomb would be used to gain minimal immediate control over a contested city. No time to build cultural buildings and not much cultural output anyway. However, if one’s goal is to culturally overwhelm the opponents and force their cities to change sides, it becomes an issue, because one might actually want to culture bomb in a huge city with many cultural buildings in order to speed the revolt of a powerful neighboring city. In such games, it might be desireable to impose some sort of a rule, such as needing to leave the artists and culture slider there for 1 turn, or not being allowed to crank up culture at all, prior to bombing. Perhaps even being required to minimize rather than maximize cultural output prior to bomb. Of course, you could just add it to the list of strange things you might need to do to win a culture war game, along with clearing out large garrisons with helicopters and such. But, do whatever you find fun. It’s not like I care how you play the game.

Anyway, let’s move on to the topic of revolts. A revolt in a city can occur if the owner of the city and the person who would own the underlying square if there were no city are different. In other words, a city might revolt if a neighboring city belonging to a different civilization has it within its cultural radius and that civilization’s plot culture under the city is greater than the city’s owner and that of all other civilizations with a city in range. You don’t have to have a majority, you just have to have more of your nationality than the other guy. If a revolt can occur, there is a flat 10% chance each turn of making a revolt check.
During a revolt check, a random number between 0 and the city’s revolt power is compared with the garrison strength. If the number is greater than the garrison strength, the city revolts. Barbarian cities always fail this check, so will always revolt. If a city revolts there are several effects. All units in the city lose half their current hit points, the city’s cultural radius becomes 0 and it produces nothing for a certain number of turns. Also, there is a possibility that the city may change sides (called a flip). A barbarian city will always flip, period. A non barbarian city won’t flip if this is the first revolt (there is always one warning revolt). It also won’t flip if the option “no city flipping” is on (this by default is off). It won’t flip back to someone who has previously owned it, regardless of reason for ownership change, unless the game option “city flipping after conquest” is enabled (this is by default off). If a city flips, all units belonging to enemies of the new owner are destroyed. If the units aren’t at war with the new owner, they simply get expelled unless the new owner has open borders with the units’ owner.
So, how is revolt power calculated? The base revolt power starts at 1 and then two factors are added. The first is 2x the city’s highest ever population. The second is the number of directly adjacent squares that the revolting people’s civilization controls times the current game era. Current game era is considered to be the average era of the remaining players, rounded down, with ancient being considered ‘1’, medieval ‘2’, and so on. So, in the final era (6), if the side the city wants to revolt for controls all 8 squares around the city, this could be as high as 48.
The base revolt power is then multiplied by several factors. The first is the ratio of the two sides’ plot culture for the city square. The formula for this multiplier is 1 + ((revoltCulture – cityOwnerCulture) / (revoltCulture)). This would be a number between 1 and 2, being near 2 if the revolt’s plot culture is much higher than the owner, and being near 1 if the two are almost equal. If the revolt’s plot culture is twice that of the city owner (i.e., 67% revolting nationality, 33% owner nationality), the value would be about 1.5. Sorry for the ugly math, but I can’t find a way to explain it more simply at the moment.
Fortunatly, the other multipliers are a bit simpler. If the revolting civilization’s state religion is present, the value is doubled. If the city owner’s state religion is present, the value is halved. If both are present, these two multipliers cancel each other out. If somebody doesn’t have a state religion, they don’t get a multiplier.
The city’s garrison strength is also simple. Start at 1 and add the cultural garrison strength of all units in the city, regardless of ownership. Double this if the owner and revolting civilization are at war. The only catch is that cultural garrison strength can’t be found in game, so here is a list of unit values:
warrior, quecha: 3
archer, skirmisher, axe, spear, phalanx, chariot, immortal, catapult: 4
swordsman, jaguar, praetorian, horsearcher, keshik, war elephant: 5
mace, samurai, pike, longbow, crossbow, chokonu, knight, camelarcher, conquistador: 6
musketman, musketeer, grenadier, cannon: 7
rifle, redcoat, calvalry, cossack: 8
machine gun: 9
infantry, SAM infantry, gunship, artillery: 10
marine, SEAL, tank, panzer: 12
mech infantry, modern armor: 16
Note that ships, planes, workers, great people, and other non-military or non-land units don’t help keep a city under control.

Okay, now that all that stuff above has been covered, let’s give some actual examples, so you can see what it means:

Example 1: Low culture capital
Consider a capital city with just a palace and no other cultural buildings. Suppose that the owner just sits there and builds no cultural buildings for 200 turns. How would this work out? Well, the palace produces 2 culture per turn, so at the start, the 9 initial city squares are going to get that amount for 5 turns (total 10), when the cultural radius expands. For the next 45 turns, the first two rings would be getting that 2 CPT and the inner ring would get an extra 20 per turn. Then the Radius expands and for the next 150 turns, the 3 city rings all get 2 culture, with the outer getting 20 extra and the inner getting 40 extra. So, let’s add this up. The city of course would end up at radius 3 with a flat 400 culture. The third ring would get a modest 300 points of plot culture, not too hard to invade. The second ring would get 3390. The inner ring, including the city square would get a whopping 7300. For another civ to get a majority in the area, they would need to beat that. If they took the city and just started culture bombing, they’d need around 6 great artists to gain that majority, unless of course they put some more culture in the city. The lesson? Sitting on a spot for a long time counts a lot with regards to cultural control.

Example 2: Cultural Nuke
Okay, suppose you’ve got a city that you’ve got a city that you’ve built up culturally, in order to flip an enemy capital, say, the city in the previous example, which is 3 squares away, the minimum distance between 2 cities on the same landmass (cities on different landmasses can be 2 squares away, oddly enough). You’ve decided that you’re okay with maximizing cultural output to increase culture bomb yield, so you crank the up the culture slider to 100%. You’ve really built the city up and it already has 900 culture. It also has 14 towns within it’s production radius. With 4 base commerce, +2 for free speech, +1 for printing press and +1 for financial, this is 8 culture per square, more than the 6 that an artist specialist gives you with sistine chapel, so you leave 14 people on towns for 113 CPT. One of your people is already an artist, and you have the other 7 join him, with sistine, that’s another 48 CPT. You’ve also got assorted buildings: 5 temples (+5), a Library (+2), a Theatre (+3), and 2 monastaries (+4). Add all the numbers up for 175 CPT Of course, you didn’t forget the cultural multipliers either: 4 cathedrals and the hermitage, not to mention Free speech, for a 400% bonus. 5 X 175 is 825 CPT. Yowza! Okay, so you send in your Great Artist and erm, detonate him. Every single square in the city radius istantly gets the equivalent of 20 turns of that 825 CPT, including the enemy capital that you are trying to flip. That’s 16500. Oh, and since the enemy capital is in the second to outermost ring of your cultural influence, it gets an additional 400 points from that 20 point per turn bonus.
Now, if you hadn’t assigned those artists and cranked you’d only have a base of 20, which, with multipliers, would become a mere 100 CPT. The total sum of 20 turns (with the same 400 bonus points) would be 2400. So, you got 7 times the effect for making a temporary adjustment to your production, which you will now switch back. Basically, you got 7 Great Artists for the price of one by exploiting a hole in the game mechanics. Now, if this doesn’t bother your conscience just a wee bit, remind me not to allow you in my house unsupervised.

Example 3: The English are Revolting
This following example actually happened in a recent game of mine. In this particular game, the English happened to be one of my neighbors and, as neighbors are wont to do, Viki decided to stick a knife in my back while I was off invading Mali. The main effect of this little skirmish was that I ended up owning one of Viki’s cities (Oh, and I called off my invasion of Mali and a few million people died and one of my cities got trashed from pillaging and repeatedly changing hands, but that’s not important). Deciding that it wouldn’t be worth the trouble to keep up the fight, I negotiated a peace treaty and resumed plotting to crush Mali at my earliest convenience.
This English city that I had captured was culturally very advanced and was something like 4 or 5 squares from their capital. Looking at the city, I noticed a high probability of revolt, somewhere around 9%. Now, if I had remembered the default ‘no city flipping after conquest’ setting, I might not have been so concerned, but I was thinking civ3 and I was afraid it was going to revolt back, so I started building culture and sending in more troops. With a garrison of 20 troops, a culture bomb, many buildings, and 29% of the population switched to my nationality, the !@#$% city was still trying to revolt. Several revolts later, I added a bunch of mech infantry and finally got the unrest under control, at which point my next invasion of Mali triggered an unnoticed defensive pact, forcing me to destroy the English as well and gain a domination victory, meaning no more chance of revolt, so all my anti-unrest measures were a waste of time anyway.
Anyway, let’s see what was going on. Sometime in the renaissance era (Most players were Industrial, but remember, the era is the players’ average era, rounded down) the city had a population of 14 and 4 of the 8 surrounding squares were still under english cultural control. So, multiply the population by 2 and the squares by 4 (renaissance being the 4th era) and we get a base revolt power of 44. Given that 29% of the city was my nationality, we multiply this by 1.59 (this is the approximate result of the nationality ratio equation given above), giving 69. In the interests of diplomacy, I had no state religion, while the city contained Elizabeth’s state religion, Confusianism. In fact, it was the Confusian holy city, but this doesn’t give any bonuses. Still, her state religion doubles her revolt power. Anyway, we get a revolt power of 138. Okay, the garrison at this point consists of 4 archers, 9 longbows, 1 horse archer, 2 grenadiers and 4 infantry. Add up the numbers and add 1 and we get 130. Hmm. All those troops aren’t quite enough. Now maybe if I had a state religion or could’ve gotten Elizabeth to drop hers, I’d have had an easier time.

Example 4: Modding Fun
The Mod “FallFromHeaven100” (not to be confused with “FallFromHeaven200”, which is too big for my modem, so I’ve never tried it) contains an interesting take on the missionary unit. Not only is it a medic I combat unit, at least some of the missionary units have the ability to create a tiny great work of art. 20 points of culture, to be exact. Now the intention of this unit was probably to allow a player to throw some quick culture in and get at least 1 culture level and stop any revolt in progress. However, due to the underlying cultural formula, this still gives 20 turns of culture to every square in the city’s cultural radius. Not only that, unlike the rare and hard to acquire Great Artist, you can build these guys cheaply in whatever numbers your cities can produce. Of course, while you’re busy dropping a mini culture bomb every turn or two, your enemies will be busy outteching your economic mess of a civilization. It can be a bit uncool when the enemy walks over your borders with heavy crossbowmen (power 13) while you’re still using archers (power 3, just like standard civ).

Source of information:
Most information given here was acquired by reading the source code in the civ4 SDK, available from Firaxis. The culture functions are contained in the files “CvCity.cpp” and “CvPlot.cpp”. “CvUnit.cpp” contains the code for great people.
A number of game values can also be ascertained (or modified) by reading the files in the Assets/XML directory, even if you do not have the SDK. Many of the numbers used in the culture source code are found in GlobalDefines.xml. Units/Civ4UnitInfos.xml contains various unit statistics, including cultural garrison power and great work value. If you do decide to modify the xml, be sure to keep a backup and if possible, figure out how to put your changes in your customassets folder, leaving the original one unmodified. I have no idea how to go about this, as I’ve never felt the need to actually modify any of the game’s values.

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