14-01-2002 20:22									#1
	Culture-Flipping Exposed Support Apolyton, buy Alpha Centauri

Someone over at CivFanatics asked me about this, so I posted this there, figured it might be useful to players here as well...


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In response to the requests I received earlier this month with regards to how "culture-flipping" works, I sat down with Soren, the lead programmer on Civ III, and he explained which factors influence the probability of a city "flipping" and what the relative weight of each factor was.

The base values used to determine the chance of city flipping are as follows:

A) The number of foreign nationals in the city in question (resisters are counted twice), and

B) The number of the 21-tile city-radius squares of the city in question that fall inside your cultural borders.


These numbers are then further modified by a variety of factors, applied multiplicatively. Here those are, in order of importance:


1) The ratio of distances to the respective capitals of both cities. Basically, if you're closer to your capital than the other city is to its capital, you've got a better chance of getting a flip.

2) The ratio of total culture points of both civs. Obviously, the better your culture is versus the opponent civ, the better your chance of getting a flip are.

3) I didn't even know this, but apparently each city has a "memory" and remembers the total amount of culture generated by any civ who has ever occupied it. This is the 3rd most important factor, because if the "attacking" civ has more historical culture in the city than the "defender", the chance of that city flipping to the attacker are doubled. This is one reason that conquered cities often flip back to their previous owners.

4) Civil Disorder in a city doubles the chance of that city flipping.

5) We Love the King (or whatever) Day in a city halves the chance of that city flipping.

6) Lastly, the number of land-based combat units (e.g., any unit with at least 1 point of offensive and defensive capability) in the city in question are subtracted. This factor is relatively low on the totem pole and this shows you why cities can flip even with huge militias garrisoned in them.


Hope this helps.


Dan

	14-01-2002 20:37									#2
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Thanks for the info. I think most of the factors were known, but I appreciate the more concrete info, such as WLTKD reduces chances of flipping (which I knew) by 50% (which makes sense, but now I know for sure), etc.

The one factor I didn't know about is the "number of squares w/in a city's 21 radius that are within your cultural borders" bit. That is interesting, and explains several non-flips I've had - cities that I thought should have flipped to me, but never did. They were spaced so that they got their full 21 squares w/o my culture creeping in. The cities that I've deliberately placed close to AI cities in order to "culture bomb" tend to serve their purpose.

-Arrian

	14-01-2002 21:29									#3
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Very interesting. Next time I'm in a culture war, I'll be sure to plant some dummy cities 1 space away from the AI's cities that I'm looking to aquire. And seeing as how the number of garrison units is such a small factor once resistance is over, it would be best to just keep 1 defender (if even that) in newly conquered cities.

	14-01-2002 23:05									#4
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Extremely interesting, explained a lot for me.

	14-01-2002 23:25									#5
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i have never had a culture flip yet (i just raze cities instead of take em over since i hate the resistance and unhappines, so i just build my own ones)

reading your post, that it goes out of the available city squares and the number of foreighners, being multiplied by the other factors, is my assumption that a city without foreigners will never flip correct?
If so, i can stop worrying about that stupid culture but just stop adding captured workers to my cities.

	15-01-2002 00:08									#6
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I would assume that even if all 21 tiles were claimed, and no foreign nationals, the chance would still be greater than 0%. Otherwise culture wouldn't have any effect.

	15-01-2002 00:59									#7
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Dan

Very informative, and thanks a lot. Any chance you could do this another time using AI sneak attacks as the subject?

	15-01-2002 01:16									#8
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Info on sneak attacks would be nice to have... just to satisfy my curiousity. It certainly seems the AI does some sort of rough calculation of power, based only on number of units (not quality) and tends to be more likely to launch an attack if you are powerful and in possession of lots of resources/luxuries - basically, if you're winning. But a more exact explanation would be nice.

Also, it seems to me that if you play a more aggresive, warmonging game, so will the AI. I am currently playing such a game (I tend not to be a real warmonger, but finding Beijing UNDEFENDED, with a settler in it circa 2500 bc was just TOO GOOD to pass up). Well, since that nasty little opening, the game has been one war after another... with AI civs breaking ROP's and even MPP's to sneak attack me (poorly, and then get wiped out). I normally don't see that level of backstabbing.

One last thing. Dan, if you're following the thread, I have a request: if possible, I would really like to see my civ's diplomatic reputation, like in Civ II (despicable -> spotless). I bet others would, too.

Thanks,

-Arrian

	15-01-2002 01:27									#9
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solo
I mean you are greedy.
If Dan and Soren explain everything, what shall we do with our labs?
(part of the fun, at least for me, is discovering how this game works, and I know that I am not alone: if you have a look at my thread 'CiC' on civ2 strategy forum, you will notice that Xin Yu is busy explaining why and how the AI rushbuys in civ2, ...and he's doing that NOW)

(La Fayette, happy to have discovered 'size6', and willing to discover as many other ways to beat the AI as possible)

	15-01-2002 01:29									#10
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i guess that is now replaced by the mood of the foreign people.
polite, cautious, furious, are there more moods?

	15-01-2002 01:35									#11
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Not really, Darth, although your reputation will have an effect on the other civs' attitudes. Ever notice that sometimes civs start out "annoyed" at you? You haven't done anything to them, or anyone else, yet they're pissy. So it's not your reputation - the AI's attitude is also determined by relative power, cultural linkings (european, native american + americans, classical, ancient + zulus), etc. Sometimes they're mad at you out of jealousy - this is a sure sign you're doing well

-Arrian

p.s. I know my request is a minor, minor thing, and there are more important things that need to be addressed first.

	15-01-2002 01:49									#12
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Actually, according to the formula, an opponent's city must either have one of your citizens or must have a tile in its radius within your culture in order for it to defect.

Here's a distilled version of the formula as I understand it, specifically in terms of if an opponent's city will defect to you:

( ( Your nationals in city + tiles in city radius owned by you )*

( Distance to opponent's capital / distance to your capital ) *

( opponent's total culture / your total culture ) *

( If WLT*D, 1/2, else if Civil Disorder, 2, else 1 ) *

( If City generated more culture under your control, 2, else 1/2 ) ) -

Number of opponent's combat troops in city

((Citizens+Tiles) * CultureRatio * DistanceRatio * StatusFactor * HistoryFactor ) - Troops

So, let's say you captured Canterbury for a short time before the English took it back. While it was in your possession, it grew by 2 citizens to total 6, and built a temple and library. Your culture is (let's say) 200; the Brits, 120. Cantebury is 15 squares from London. In the short time you had it, the amount of culture produced exceeded that which it gained under the Brits. They are now stationing 3 spearmen in the city, and, since they haven't rebuilt the luxury infrastructure destroyed during the second war, the city has gone into civil disorder.

Not willing to enter another war just yet, you hope for a cultural flip back to your side and hope to help this along buy building the Forbidden Palace in the city-next-door, only four tiles away. Your borders consume 5 tiles of Cantebury's 21-tile radius.

According to the formula, the odds of regaining the city are:

( (2 + 5) * (15/4) * (200/120) * 2 * 2 ) - 3

( 28 * 3.75 * 1.67 ) - 3 = 172.35

I don't know what 172.35 is supposed to mean. What are England's "odds" of holding on to the city? I'll reverse the formula

( (4 + 16) * (4/15) * (120/200) * 1/2 * 1/2 ) + 3

( 5 * 0.267 * 0.6 ) + 3 = 3.8

3.8 to 172.35 is 2.2%, or 97.8% in your favor. That sounds pretty high... I haven't been paying close enough attention (or fighting enough wars) to know if this seems right.

Let's say that there was no war - your borders simply extend into Canterbury's radius - no citizens, no civil disorder, no wltkd, but your Forbidden Palace is 4 squares away.

( (0 + 5) * (15/4) * (200/120) * 1 * 1/2 ) - 3

Your factor = ( 2.5 * 3.75 * 1.67 ) - 3 = 12.67

Brits...
( (6 + 16) * (4/15) * (120/200) * 1 * 2 ) + 3
Brit's factor = ( 44 * 0.267 * 0.6 ) + 3 = 10.05

So, there's a 55.8% chance the city will defect to you, tested, I suppose, each turn. That sounds a little better to me, but still (in terms of my experience on Regent as Babs) a little on the high side...

Duodecimal

Edit:

Per Mongoose, here's the first calculation without the Forbidden Palace. Let's say your capital is 25 squares away.
( (2 + 5) * (15/25) * (200/120) * 2 * 2 ) - 3 =
(28 * .6 * 1.67 ) - 3 = 25.1

The Brit's calculation also changes:
( (4 + 16) * (25/15) * (120/200) * 1/2 * 1/2 ) + 3 =
(5 * 1.67 * 1.67) + 3 = 13.9

So you have a 64.4% chance of the city reverting, instead of a 97% chance. If the garrison was doubled to 6, the odds of it reverting drops to 52.6% - compared to if you didn't outproduce the Brits in culture in that city - in which the odds plummet from 64.4% to 14.2%! (9.7 : 58.8)

Last edited by duodecimal on 15-01-2002 at 21:48

	15-01-2002 03:47									#13
	reversion after death Support Apolyton, buy Alpha Centauri

Quick question regarding this (I also posted this in the help section, but here's probably a better place):

Is there *ANY* likelyhood that a civ that's been wiped from the planet could come back via reversion? I wiped out 3 civs in my current game, and although in most of the cities I'm starving off all the resistors, I notice that even after a civ is gone, his population stays in the city I took over.

But, since the distance to capital = infinite, is there no possibility of it happening, even though my capital is literally across the world?

The reason I ask is right before destroying the Russians (huge earth map) who had their last city holed up in Newfoundland, and my capital on the southern tip of Africa, a city of theirs deep in Europe (a little west of Italy) reverted to them. All they had left was a size two city, 0 culture in that city, one spearman. I thought it was pretty cool that it did happen (made the war more realistic and interesting - I was an evil leader though, and raized the city so I could build my own their), but I was just curious if it could happen after the fact.

If anyone's seen it take place, let me know. Thanks!

-Rflagg.

	15-01-2002 07:45									#14
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Duodecimal, AFAIK, the Forbidden Palace does NOT substitute for the Palace in cultural reversion.

Anybody that can refute or confirm this? Dan, maybe?

Indeed, I read (at Civfanatics, I think) that somebody lost a city back to its original empire, even after having used a GL to rush the Forbidden Palace therein.

	15-01-2002 08:48									#15
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I remember government type matters. Despotism 1%, monarchy/republic 2%, democracy/communism 4%.

	15-01-2002 08:53									#16
	Re: Culture-Flipping Exposed Support Apolyton, buy Civilization: The Boardgame

quote: Originally posted by Dan Magaha FIRAXIS 6) Lastly, the number of land-based combat units (e.g., any unit with at least 1 point of offensive and defensive capability) in the city in question are subtracted. This factor is relatively low on the totem pole and this shows you why cities can flip even with huge militias garrisoned in them.

That should be a first factor, not a last.

If they had made it that only a city in disorder risked a flip, that would have solved most problems.

	15-01-2002 10:33									#17
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by the way, is anyone 100% sure of how distance is calculated in civ3?

sqrt(x^2+y^2)
or
x+y
or
max(x,y)

and then, do they use normal cartesian plane coordinates (like civ1's map used to be), or do they use the funky grid-at-45-degree-angle? (why does every game nowadays have to have this stupid pretend-its-3d-perspective diagonal grid? does it really add anything to the gameplay? )

this would also help in corruption calculations... maybe i should search for a corruption thread...

	15-01-2002 12:16									#18
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What I'm sure about distance...

Distance is the number of tiles between point A and B, each tile counting either 1 or 2 depending on its alignment. I'm not sure exactly how this is calculated. (X2 - X1) + (Y2 - Y1) doesn't work because of how every 3rd diagonal is treated.

Diagonals (1st,2nd,3rd..12th) = 2,2,1,2,2,1,2,2,1,2,2,1
All Verticals and Horizontals = 1

Diagonal, Vertical, Horizontal are meant in relation to the grid, which is turned 45 degrees. 12 Diagonals was the limit of my testing, because of map dimensions. Testing was done on edited maps with 25 commerce 25 production tiles to more accurately determine corruption percentages, which were used to determine the relation of diagonal tiles to non diagonal tiles. For instance, the corruption (out of 178 commerce) was exactly the same for a city placed 2 horizontal or vertical tiles away from the capitol as it was if the city was placed 1 diagonal tile away. The 2nd diagonal placement the same as the 4th horizontal or vertical placement, and a 3rd diagonal placement the same as a 5th horizontal or vertical placement. All testing was done with only the capitol and first city placement.

	15-01-2002 15:29									#19
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quote: Originally posted by duodecimal Actually, according to the formula, an opponent's city must either have one of your citizens or must have a tile in its radius within your culture in order for it to defect. Here's a distilled version of the formula as I understand it, specifically in terms of if an opponent's city will defect to you: ( ( Your nationals in city + tiles in city radius owned by you )* ( Distance to opponent's capital / distance to your capital ) * ( opponent's total culture / your total culture ) * ( If WLT*D, 1/2, else if Civil Disorder, 2, else 1 ) * ( If City generated more culture under your control, 2, else 1/2 ) ) - Number of opponent's combat troops in city ((Citizens+Tiles) * CultureRatio * DistanceRatio * StatusFactor * HistoryFactor ) - Troops

Your formula suggests that a city can only defect to a civ which has culture in that city. Otherwise ( opponent's total culture / your total culture ) would be 0, giving the formula a result of 0. Now, we know that cities regularly defect anyway, so there must be some kind of default value here.


Also, the formula shows that the number of units in the city has a minimal effect on the final value.

	15-01-2002 16:09									#20
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no, with total culture he means total culture from your whole civ. Somewhere later in his formula he states that the chance is either halved or doubled, depending on who created most culture in the city.

totally different matter:
English is not my native language, and i don't know if it's your's. The word "default" you just used in your post, is it used correctly there?
The only meaning of default i know is something like standard value.

	15-01-2002 16:20									#21
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(( YourNonResistingNationals + ( YourResisters * 2) + Tiles) * CultureRatio * DistanceRatio * StatusFactor * HistoryFactor ) - Troops

Hurry said:

quote: Your formula suggests that a city can only defect to a civ which has culture in that city. Otherwise ( opponent's total culture / your total culture ) would be 0, giving the formula a result of 0. Now, we know that cities regularly defect anyway, so there must be some kind of default value here.

Well, it's not *my* formula, just a restatement to make it seem simpler - though I could have misunderstood Dan Magaha.

There are safegaurds against zero/infinite values...

A civilization always has culture - thanks to the palace. If you just built a city, and your only other city was your capital and it's taken, then the capital is instantly rebuilt and generates culture. This keeps the CultureRatio and DistanceRatio arguments from generating zero or infinite values.

The other two arguments default to one, two, or one-half depending on conditions (though I'm reversing the formula Dan gave us in order to get the number for someone keeping a city).

The only things that will make a formula come out to zero are if you have no citizens and no tiles in the enemy city, or if the number of troops perfectly balances everything else.

As stated by others, there are questions -

Distance - calculated by smallest number of tiles between two points, by Pythagorean theorem? (If so... how are X and Y calculated if it's not also just a tile count?), or Aeson's horizontal/vertical = 1, diagonal = 2 except every third diagonal = 1? I prefer the first one since the other two don't relate to unit movement...

Forbidden Palace - counts in distance calculations, or no? There may have been a lot of other factors causing the reversion in Mongoose's scenario besides distance... I know that in one of my Bab games, I had cities defect that were right next to my opponent's capital. That was on a standard map... I usually play on Huge now and hardly ever see cultural reversion anymore (especially after the patch... ?)

Government type and cultural government preferences - where do these enter into the equation?

National history - Where does the issue of whether or not you have waged war against a culture enter into the odds that a city in that culture will defect to you? I recall vaguely hearing something about this affecting defection chances...

Duodecimal

	15-01-2002 18:10									#22
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quote: Originally posted by mengo76 by the way, is anyone 100% sure of how distance is calculated in civ3? sqrt(x^2+y^2) [...] (why does every game nowadays have to have this stupid pretend-its-3d-perspective diagonal grid? [...]

After my observation the corruption-relvant distance is calculated in the euklidic metric (sqrt(x^2 + y^2)).
To calculate, e.g., the placement of my (forbidden) palace I zoom out (z-Key) and look at the small word map in the lower left corner: On standard maps the left and right border (white line) gives the area for the last useful city if you position your screen on the (planned new) palace. In north and south the main screen must corrected 4 tiles in the opposite direction. (click 4 tiles down your planning point for a new palace, then left-top-right is the area of useful cities.) To the corners you have to go slidly inside to form an ellipse of non-corruption.

As it was explained in the civ2-manual the "perspective" grid is isometric, means that the distances measured euklidic matches a distance measured in tiles.
It's a matter of taste if it for you more intuitiv. Guess it is so for the most player.

	16-01-2002 01:09									#23
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I have observed in my games that having no unhappy people in the captured city greatly reduces the chance of reversion. In fact, creating entertainers till the unhappy people are gone sometimes will stop an imminent reversion. I have seen other posts commenting on this in vel's threads. This factor isn't on the list, apart from wltkd, which wasn't relevant in the games to which I refer. Is this factor proxying for one of the factors mentioned? I don't see which one.

	16-01-2002 01:55									#24
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quote: Originally posted by DrSpike I have observed in my games that having no unhappy people in the captured city greatly reduces the chance of reversion.

I bet only laborers are counted as citizens in the equation!

Duodecimal

	16-01-2002 02:33									#25
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If so, that would explain it. It does seem kinda arbitrary though, as well as nicely exploitable............

	16-01-2002 03:32									#26
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quote: Originally posted by DrSpike I have observed in my games that having no unhappy people in the captured city greatly reduces the chance of reversion. In fact, creating entertainers till the unhappy people are gone sometimes will stop an imminent reversion. I have seen other posts commenting on this in vel's threads. This factor isn't on the list, apart from wltkd, which wasn't relevant in the games to which I refer. Is this factor proxying for one of the factors mentioned? I don't see which one.

maybe there is another reason:

I guess im not the only one, but when something goes horribly wrong, i tried reloading the last auto save, and then doing it again, a certain battle for example. If you do this, it will always turn out exactly the same.
This means, either the game makes chance calculations one turn ahead and will only use the outcome if you actually take the specific chance (like a battle) or, the game uses the recently happened moves in its chance calculations when a chance has to be calculated.
The last one seems to be true, because otherwise the computer would need to make many needles calculations. And did i experiment a little with it and if you can for example fight 3 battles and if you alter the order, the outcome will be different.

now if you have a city flip, simply reloading the last game and trying again will not help i guess, since as i just explained the outcome will be the same, the same calculation is made.

However, if you make some entertainers, the recent moves are different, and the outcome of the chance calculation might be different.

Don't forget, a city flip is based on chance, it is not something that WILL happen at a certain point. So this way, you just make a new calculation and your city might not flip. The chance in this calculation might be the same as it was in the former calculation though.

I hope this was a little understandable.

This system also makes me wonder how much value chances actually have. since obviously, the chance calculations are not purely random calculations.

	16-01-2002 03:42									#27
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Darth

My point was the number of unhappy people doesn't seem to correspond to any of the factors Dan outlined, except wltkd, which wasn't in progress in the games I mentioned. In your terms, if what was changed after a reload wasn't relevant to calculating the chance of reversion why was the outcome different?

	16-01-2002 12:14									#28
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if you change something the outcome will be different, because another calculation is made. Not because there are more people happy or something. That was my point

	16-01-2002 13:16									#29
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Darth Sidious, duodecimal: Thanks for pointing out my misreading of the formula.

Now, I want to point out another factor from Danīs post:

quote: The base values used to determine the chance of city flipping are as follows: A) The number of foreign nationals in the city in question (resisters are counted twice),

How are population of destroyed civs counted? As your own pop or foreign? In other words, would a city of size 12, with 6 own, 5 destroyed and 1 actual foreign pop in fact count as it had 6 foreign population?

And no, my native language is not english either, so I canīt comment on my use of proper or improper english.

	16-01-2002 14:16									#30
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Hurry and Darth Sidious,
I couldn't help but stick my nose in. English IS my first tongue, so I feel obliged to comment on the use of "default" (although English being someone's native language CERTAINLY does not qualify them to say they know anything about that confusing language ).

"Default" has been used by Hurry as to mean a "base" or "starting" value. This seems fine to me, as you may think of your computer's configuration - Windows has a default setting, which is one without the additional drivers etc that your Normal setting has. In theory, you start with a default setup and add things like device drivers to get your normal setup.

I fully expect arguments from native English and non-native speakers alike on the definitions of "default", "setup" and other words I have used like maybe "tongue" - but ignoring boring things like dictionary definitions, to this native English speaker in Kiwiland, your use of "default" was perfectly understandable.

Hmm. I seem to have gone a little off thread topic and hope I didn't waste too many people's time with this rambling drivel.