Culture Flip Formula

[DeepO]

Fitz, I was working on something similar, however I'm still typing. Could you wait a bit longer until I'm finished? I think we'll completent nicely...
Maybe it is a good thing to add a link to this post in the thread in your initial post, I wouldn't copy it completely.
DeepO

[Fitz]

Nah, I think I'm going to wait a week (in case someone comes up with new input) and then type up a nice long article for the column, including strategic considerations, offensive culture warfare, etc. I'll run it by you first before I submit it though.

[DeepO]

Thanks, I appreciate that. However, when my post is finished, you might want to use it in that article of yours
DeepO

[DeepO]

As we have a confirmed ((N+S)*C*H*R-T)/D formula, maybe it's nice to see what each of the different factors really does to the flipping percentage. This will use a lot of known information, but as this is a math oriented thread, I'll try to quantify it. This uses the current state of the art, if the formula somehow changes, I'll update this post.

Two examples will be used: Fitz's (Example A) and Coracle (Example B)
For clarity, you (or Fitz, or Coracle) play the Persians, the enemy is Greece

Example A:
Newly acquired city, 10 Greek citizens, 5 resistors, 3 Greek tiles, Greek city culture much bigger then Persian (as Fitz has just conquered it), no civil disorder, no WLTKD, Persian total culture 1.5 times the Greek total culture, 3 garrison troops. City right in the middle between Persian and Greek capitals.
Flip chance: ((15+3)*2*1/1.5-3)/2000=1.05%

Example B:
Newly acquired city, 5 Greek citizens, 5 resistors (Coracle is less liked by the AI's citizen, it just has to be ), 3 Greek tiles, Greek city culture much bigger then Persian (as Coracle just conquered it), Civil disorder, Greek total culture twice the Persian, 8 troops (sorry, no Samurai. Immortals also fine?). City next to Greece capital.
Flip chance: ((10+3)*2*2*2-8)/500=19.2%

N: number of foreign citizens, resistors double
There are a number of things you can do about this, first of all getting rid of resistors as fast as you can.
Coracle has a far better chance of doing this, for the sake of the argument, we assume next turn his 8 Samu..ehm..immortals have quelled all resistors. Second turn flip chance: ((5+3)*2*2*2-8)/500=11.2%, a 71% improvement.
For Fitz, we assume his 3 troops quell 2 resistors. chance: ((13+3)*2*1/1.5-3)/2000=0.917%, a 14% improvement.
all resistors gone: 0.717% chance, 46% improvement

After you removed all resistors, the Greek population could be removed. We assume building a settler (removing 2 citizens. Starving or poprushing could of course also work.
Coracle: ((3+3)*2*2*2-8)/500=8%, an additional 40% improvement
Fitz: ((8+3)*2*1/1.5-3)/2000=0.583%, an additional 22% improvement.

Conclusion
Quelling resistors is vital to improve your chance of holding your city. The higher the number of resistors in comparison to the foreigners, the more important it is. This is however risky, as you need many troops for it, so don't ever use offensive troops! It should be the first thing you do.
Further, diminishing population is a good tactic if you are in a bad situation (especially when you have a small city), otherwise there are other solutions which can be more effective.

For the rest of the comparison, we'll assume all resistors are gone, but you keep your citizens (so ex. A: 0.717%, ex. B: 11.2% flip chance),

S: Squares
Getting rid of the Greek squares can be done in several ways, by expanding your borders -- (rush)building a temple, conquering the next Greek city, it doesn't matter.
Fitz: ((10+0)*2*1/1.5-3)/2000=0.517%, 39% improvement
Coracle: ((5+0)*2*2*2-8)500=6.4%, a 75% improvement.

Conclusion
Try to remove enemy tiles from your city radius right after you dealt with resistors, or even at the same time if possible. Gains are greater when the number of foreign citizens is smaller. dealing with your borders is as good as dealing with foreign citizens, but are most of the times faster, and do not leave a ruined city behind (if you don't want that, of course)

C: City culture
In most cases this is not under your direct influence. Sometimes, building up culture fast by rushing can be helpfull, but only if there was not much culture in the conquered city to begin with (only for ancient era battles, or special cases). The gains can be great if you can do it (see next point for calculations), but most of the times it really is not worth the money / population. For big cities with a lot of acquired culture, it will take forever to get more culture then what was in there, and it only helps once you have more (it's like a light-switch, on/off, 2/1 factor)

H: Happiness
Suppose, through the use of luxuries, temples, entertainers, whatever you're able to get a WLTKD in the city.
Ex A: ((10+3)*2*0.5/1.5-3)/2000 = 0.283%, a 253% improvement!
Ex B: ((5+3)*2*0.5*2-8)/500=1.6%, a 700% improvement!!

Conclusion
This is huge! One of the best things you can do, in any situation, is making sure you get a WLTKD in a city. If this means you have only entertainers, and starve the city, who cares, at least it will stay yours.

Granted, I did make Coracle's example a bit too grave to begin with, by giving him a disorder in his city, only stopping the disorder would also give a ((5+3))*2*1*2-8)/500=4.8% chance, but even going from no disorder to WLTKD would yield a 300% improvement. This is the best, and easiest thing to do, but it requires micro management of all the cities in danger. So, Coracle, do this, and your problems would be solved
And, of course, avoid disorder at ALL times, a disorder is as bad for the flip chance as a WLTKD is good.

R: total Culture Ratio
Not much you can do instantly about this, but if you face constant problems with culture flipping, most likely your total culture is too low. Fitz doesn't have huge problems, as he has a 1.5 times better culture, whereas Coracle's problem is partly because his culture is only half of the Greeks.

If he would have had a 1 to 1 ratio on total culture, his chance of flipping would be 4.8%, a 233% improvement. But once he starts conquering, it is much too late to worry about his culture, he should have done this in the beginning of the game.

T: Troops
Suppose the number of troops doubles in the two examples.
A: ((10+3)*2*1/1.5-6)/2000=0.567%, a 26% improvement for 3 extra garrison
B: ((5+3)*2*2*2-16)/500=9.6%, a 16% improvement for 8 garrison.
Needed troops to get zero chance:
A: (10+3)*2*1/1.5=17.3, so 18 troops would take care of the flipping al together
B: (5+3)*2*2*2=64, 64 troops needed.

Conclusion
Troops normally do not give what you hoped for. Even if this conlusion plays right into Coracle's hand regarding his arguments on this board, he should understand that troops do not help in a very desperate situation. In certain situations (e.g. only one enemy square, no enemy citizens, to prevent a flip of a native city to the enemy) garrison troops can be good, otherwise don't bother with it. There are other, much more effective means of keeping your city.

However, it is the only way to get a zero chance in a conquered city, after using the other techniques. And they're needed to quell the resistance.

D: Capital distance factor
The only thing we do not have an exact formula for (yet). This can be used to play with, e.g. with Vel's Culture bomb tactic. As it has a direct effect on the chance, it is very easy to calculate. A city next to your capitol, with the other half a world away has a 8 times lower chance of flipping in the same situation as opposed to a city next to the Greek capital, half a world away from yours.

One tactic you could use this info for is to make sure that on a conquest round, you drive the enemy capital away asap, so that the cities you conquered a few turns back get safer. However, it might deminish the chance, but as we don't know the exact formula, I can't give any figures for it.

Final conclusion on how to keep a city from flipping

• The best immediate thing to take care of is to avoid disorder, use a WLTKD if possible.
• After that, getting rid of resistors and expanding borders (or making sure no-one's borders are inside your radius) is the most logical, and easiest thing to do.
• After that, starving or pop rushing population is good
• Last immediate remedy is adding troops. While it is the only way to stop flipping all together, it does not help in case you didn't look into the other solutions first.

Non-immediate solutions are :

• making sure you have a big total culture,
• and building cultural buildings in endangered cities.
• And even if it is not known by how much, cities far from your capital are more prone to flipping than those closer by.

I hope everybody gets a little help out of this information, sorry about the long post
Fitz, once you get around to that separate article (do I hear the word column?), feel free to use this. And thanks for the formula which got this whole thread started.

DeepO

[Edited to replace all 'Grecian' to 'Greek'. Sorry, it was 4 am last night ]

[playshogi]

If a city has 3 Greek and 3 Persian is the chance of flipping the same as if it had all 6 Greek?

[planetfall]

DeepO-- great analysis, I wish I had a better feel for the capital distance factor. I would add in the conclusion, as to what you can do--use the city governor. Have everything on the first tab no except for manage happiness. This does not work all the time, but does reduce the probability of the city going into disorder greatly. {Sorry no stats, just game experience. City going into disorder 2 turns in a row, and with governor, no disorder. Again this is assuming culture is at least about par with conquered city civ. May not work if culture is neglected. I have no idea about civ2, but trying to play civ3 without building culture is asking for more trouble.}

[DeepO]

Originally posted by playshogi
If a city has 3 Greek and 3 Persian is the chance of flipping the same as if it had all 6 Greek?

No, absolutely not. And the chance is lower then half of the combined. (strange, huh? but true...)

Example: city with 3 Greek, 3 Persian citizens, no resistors, no enemy squares, no disorder, 3 garrison, cityculture of Greek higher then your cityculture (assume you're Roman, and captured the city), Persian cityyculture lower (assume you added captured workers to your city), Totalculture of Persia, Rome, Greece equal, distance to the three capitals the same.

Chance to flip to Greece: (3*2*1*1-3)/2000=0.15%
Chance to flip to Persia:
(3*1*1*1-3)/2000=0%
Total chance: 0.15%

Chance if there were 6 Greece citizens, no Persian, same situation otherwise:
(6*2*1*1-3)/2000=0.45%

If you would have 3 Greek citizens, 3 Persian squares, the outcome would be the same.

DeepO

[DeepO]

Thanks Planetfall,

What I find most intrigueing about the analysis though, is that I should take the manage citizens mood governer off line. Avoiding disorder is certainly very important, but, making sure there is a WLTKD is even more important, and gives the biggest control over the flipping.
Sadly, there is no governor option to 'manage citizens into WLTKD', which could be an idea for next patch.

And yes indeed, trying to play CivIII without building up your culture is asking for trouble, as Coracle's example shows. It can be done, but the game punishes you for it, and one of those punishments is the bigger chance of flipping cities.

DeepO

[DeepO]

Oh, BTW, I too would like to have more of a feel for the Capital Distance Factor. But, it only changes the overall percentage, directly correlated, which is not that important for a player.
What I tried to do is give hints on how to deminish the chance (in percentage improvement), what the exact chance is is less important.

One problem is that I don't see hints on how to figure out the formula for the distance, I guess it should come from Soren if we really want to know it. And he already said it goes from 500 to 8000, with an average of 2000.

DeepO

[playshogi]

In the example of 3 Greek and 3 Persian, I was assuming I was Persian. The idea was to lower the chance of a flip by joining some of my settlers/workers to the city. However, what you are saying is that if I'm Persia and I join 3 Roman workers to the 3 Greek city I just captured I can lower the chance of a flip back to Greece? ? (assuming the Roman capital is way distant and culture is way lower by far). Just out of curiosity, if I join a Russian worker to any city and Russia has been eliminated from the game (so it has no capital) what is the formula ?

For the capital distance formula- if the distance is equal then D=2000 so if the Greek capital is 4 squares away and mine is 8 squares away, I'd assume D=1000? or if my capital was more than 16 or more squares away then D=500. Conversely, if I'm 4 and Greece is 8 then D=4000.

[DeepO]

Originally posted by playshogi
In the example of 3 Greek and 3 Persian, I was assuming I was Persian. The idea was to lower the chance of a flip by joining some of my settlers/workers to the city.

O, sorry, I misunderstood you. If you are Persian, adding Persian citizens does not net you anything, it is simply not taken into account in the equation. Of course, the difference between having 6 Greek citizens, and 3 Greek citizens is noticeable, look at the 'N : Number of foreign citizens' part of the analysis for more info.

However, what you are saying is that if I'm Persia and I join 3 Roman workers to the 3 Greek city I just captured I can lower the chance of a flip back to Greece? ? (assuming the Roman capital is way distant and culture is way lower by far).

No, that's not correct. I was saying it is preferable to have 3 Greek and 3 Roman than to have 6 Greek (or 6 Roman). This is always true, whereever their capital is and whatever their total culture is.
The only use for it in a game, though, is that it is stupid to join captured Greek workers into a former Greek city. If you're battling on two fronts (Greek and Roman), and want to join captured workers into cities, join Roman workers into the Greek cities and vice versa.

Just out of curiosity, if I join a Russian worker to any city and Russia has been eliminated from the game (so it has no capital) what is the formula ?

The added chance is 0. Russians will not count in any way, as there is no possibility to flip to their side. This is one of the surest solutions: eradicate the other civ. From that point on, their citizens will count like your own.

For the capital distance formula- if the distance is equal then D=2000 so if the Greek capital is 4 squares away and mine is 8 squares away, I'd assume D=1000? or if my capital was more than 16 or more squares away then D=500. Conversely, if I'm 4 and Greece is 8 then D=4000.

Possibly... there is no reason why it has to be linear. It could use a kwadratic formula, or use tresholds, or... I couldn't tell. It might for instance take the size of the map into account, instead of just the ratio between the two capitals.
Plus, what is distance in this respect, is it metric distance or new-york like distance? E.g. a city 3 tiles up and 4 tiles to the right, is that 5 tiles apart, or 7?

Your formula could be a rough estimate, but as it doesn't matter much (nobody wants to know the real chance of flipping, only how to lower the chance), I don't care for now.

DeepO

[Fitz]

Excelent DeepO, very excellent indeed. I think though, that in certain situations troops will work just fine. No, they do not have the hugest effect, but if everything else is done right, then they will work just fine.

Lets take a low level game I believe I referenced earlier (regent? Warlord? ::shrugs:. Still earliesh in the game, just got knights, and since it is 16 civ huge map, not everywhere is settled yet. I started rushing temples very early, while the AIs concentrated on lots of settlers. I actually came out pretty well in expansion, but lots of my latest cities are interlaced with the surrounding AIs. And my culture is at least ten times all the other AIs at this point.

So, to take examples:

1) Persian city. Size 6 (Persian citizens), 12 squares in eqyptian territory (surrounded), higher Persian culture, assume normal happiness, my (Egyptian) culture has 10:1 ratio. Troops needed to stop the flip for the Persians = ((0+12)*1*1*(10))=120. Even if you give a linear distance factor of 2:1 (use 4000) closer to the persian capitol, flip chancewithout troops = 3% per turn. given it took about 20 turns to flip (71% chance with no troops), I can only assume they had some there. Even so, they couldn't have anywhere near 120 troops there.

2) After one Persian city flip, I decided to build a settler (actually disbanded the city to move to a better location). I moved it over near to another city to keep the Cultural preasure on. Now let look at the danger for me loosing that new city back to the Persians:

Egyptian city, 1 Persian citizen, 6 squares in Persian territory (both before and after first 10 culture points), Never more Persian culture in city, normal happiness, culture 10:1 in Egyptian favor. Troops to hold = ((1+6)*1*1*(1/10)) = 0.7 which is easily covered by a single defender.

3) Back to that first city. I can't rememeber for sure (two days since I played), but lets assume for a second (regardless of reality) that the citizens stayed Persian. How many troops do I need to prevent it from flipping back? Well, now it is 100% in Egyptian territory, we can also assume that it never produced any Persian culture (since it never expanded). So Troops = ((6+0)*1*1*(1/10)) = 0.6 troops, which is actually less than the city in example 2.

Lessons? The relative strength of your culture is critical. Getting a 10:1 on Monarch or higher is not a reasonable proposition, but you certainly should be shooting for 2:1 to reduce the troops you need by half and double the requirements of your neighboring civs. In addition, the relative Civ cultures factor is the only part of the equation that can exceed *2 or go below *1/2. Whatever you do, don't let yourself get behind in the culture game, be you a builder or a warmongerer.

Obviously, this requires early planning, and just goes to show another reason that both Religious and Scientific Traits are powerful, given their cheaper cultural producing buildings.

That's the strategic side to accompany DeepO's tactical considerations of citizens, territory and happiness.

[DeepO]

Thanks Fitz, I was hoping you'd like it

What you are describing is exactly one of the special cases for the use of troops which do have a great impact. The Persians have no chance just using troops to 'battle' your aggresive culture, while, as your culture is so overwhelming, you can use it to good effect.

Mind you, a 10 to 1 ratio for total culture is very impressive on Monarch, on Emperor I'm always battling to not get in the disadvantage. And then you have a whole other picture.

Maybe an explanation for the AI holding on is that it used the WLTKD-tactic I described above. With a WLTKD, the chance would be ((0+12)*1*0.5*10-0)/4000=1.5% for a not defended town. Given 2 defenders (which seems to be the AI-preferred garrison for normal cities), that would be 1.38%. This sounds too low for a 20 turn holding on, but it could be a combination of WLTKD and normal happyness, or it was just bad luck

My conclusion stays that Happyness is underrated as a tactic to hold on to your cities, it always gives a more than 200% improvement. Of course, the totalCultureRatio can be a lot more important, but it is both not immediate, and very hard to come by at higher levels. But I salute you you're able to crank it up so high

DeepO

[Cyclotron]

A really great analysis you guys have going here. I've always just pushed up my national culture, but WLTKD looks very favorable now. I also think including an "induce WLTKD" would be a good setting for the governor.

[Arrian]

High Culture + Luxuries = easier warmongering. As a builder who converted to the dark side, I almost never experience flips. My culture (monarch) is usually double or more the closest AI, and often 3, 4 or 5x the weakest.

The keys to keeping captured cities:

1) push those borders back by moving fast. Eliminate civ if possible.
2) put down resistance and starve the city.
3) make sure that the city stays happy (kinda amusing as you are starving them)
4) rush a temple. Happiness + a border expansion, not to mention more culture.

This is one of the reasons why I have come to prefer ancient era warmongering. The AI gets off to a very slow start on culture, ESPECIALLY the non-religious civs. Many of the AI's cities have not linked up, culturally, with their other cities. I capture a city, and only the core cities ever even have resistors. Step one, rush spearman (1 pop). Step two, rush temple (wait 10 turns, 1 pop, or if you want, 2 pop from scratch).

-Arrian