Culture Flip Formula

[Fitz]

I decided to cut this from the culture flip debate thread, in case anyone was interested and didn't feel like plowing through that thread.

Based on Soren's (post 1.21 I think) comments in this thread I came up with the following formula:

Chance of flip = ({[(# of foreign nationals, resistors count double)+(# of square in radii under foreign control)] * [2 if more culture in city by foreign civ, otherwise 1] * [2 if in civil disorder, 1/2 if in WLTK day, otherwise one] * [(Foreign civ total culture)/(Your civ total culture)]} - {1 per garrisoning military unit}) * / (Capitol distance factor {500 to 8000, average 2000})

According to Soren's comment in this thread, this chance is discrete for each civ's presence of territorial squares or citizens, and a garrison counts against ALL civs. So if you have a city with two other civ's citizens in it, there are two probabilities that it will flip (one to each), but the garrisons in the city count in full for each probability.

The capitols factor probably can probably be estimated in one of three ways:

1) we can assume there is a 1/4 and 4x cap on the number. Take the ratio of the distance of your capitol to the distance to their captitol (specifically {your distance/their distance}) and multiply that by 2000, then apply the cap if necessary (500 or 8000).

2) assume that the formula for capitols is graded to the map size, so that if you were at the maximum distance and they were at the minimum, it would = 500, and vise versa it would = 8000. This may or may not be the case, and is certainly the hardest to figure.

3) Play it safe for losing flips (but not gaining) and use method 1 only if you are standing to gain the city. If you stand to lose the city, start with a base 2000, increase by considerably less than the ratio if you are closer, and decrease by more if you are further (basically using method 1 for further, and 2 for closer).

For those who prefer a more algabraeic (sp?) formula:

Chance of flip = {[(N + S)*C*H*R] - T}/D

N = number of foreign nationals (resistors count as 2).
S = number of 21 city squares under foreign control
C = City Culture factor, 2 if foreign civ has generated more culture in this city, otherwise 1
H = Happiness factor, 2 for disorder, 1/2 for WLTK day, otherwise 1
T= number of garrisoning troops
R= national cultures ratio (Foreign civ total culture divided by your civ total culture)
D= Capitol distance factor (500 to 8000, 2000 average). Lower if they are closer, higher if you are

From this formula, we can derive the following information if we are interested in completely preventing a culture flip in a city:

Troops = {(N+S)*C*H*R}

or, in english, the number of troops to prevent a flip = 1 per foreign national (2 for resistors) and 1 per square controlled by foreign civ, *2 if they have had more culture in the city, *2 if the city is in disorder, *1/2 if in WLTKD, and * the ratio of cultures (their culture divided by your culture). Also, the chance of a flip is -0- if all the citizens are yours, and you control all 21 squares in its maximum production radii. Also note that the relative distances to the capitols does NOT affect the number of troops needed to stop a flip, just the chance of a flip if there is any chance at all.

Note: Given that the calculation for troops includes a ratio of cultures, which is not a number you can find anywhere in the game, the best you can do is estimate and overkill. The Histograph gives an eyeball approach to the numbers (ie 2 to 1, 10 to 1, etc), but that is the best you can do until they provide us with a method to see the exact value of each civs culture.

Edits: Formula adjusted due to DeepO's & Soren's comments on page 2 of thread. Comments about estimate of culture's affect on troops needed to negate flip added. Number of foreign nationals updated to double value of resistors.

[Cyclotron]

Thanks, Fitz. Useful info.

[Lucilla]

Thanks Fitz,

you might want to put a link in the new CivIII FAQ thread

[Fitz]

Thanks Lucilla. Did that.

[Coracle]

Whatever the formula is it doesn't matter unless they end this nonsense:

Cities that have been part of one large civ for millennia should never flip.

Garrisons should never vanish.

Razing cities must be drastically curtailed.

Borders should never flip over garrisoned fortresses, resources, improvements, or colonies.


BTW, about razing, Carthage in the Third Punic War is an extreme and rare example. It took a huge Roman force to do it, and the population was sold into slavery - an option that does not exist outside of the Ancient world. And there would have been a pollution tile left where it was.

[Tuberski]

Coracle, go play Civ 2.

[Sultan Richard]

Hi--

I'm posting my first post here. But Fritz, shouldn't you rearrange the formula to find the number of troops required? Your rearrangement to find T leaves R, P and D somewhere out in the cold! So:

If original is:P=(((N+S)CH)-T) (R/D)
then I can rearrange to :P=R(CH(N+S))-T
.............................................D

(I'm not changing anything in your formula here, just making it look different)

And if we want to find the number of troops to have a probability if flip (P) of 0, we can make P=0 and rearrange as follows:

Where P=0:
0=R(CH(N+S))-T
............D

Multiply by D on both sides: 0D = R(CH(N+S))-T
and as anything multiplied by 0 is 0:0= R(CH(N+S))-T

Add T to both sides:
0+T = R(CH(N+S))
T = R(CH(N+S))


Also, as R, the ratio of their total culture with your total culture is a fraction, it could be written as:

As R = Tce
.........Tcp

Formula could be: T=Tce(CH(N+S))
.......................................Tcp

(Where Tc is Total Culture and e is Enemy and p is player; and Tcx is one number, not t*c*x)

Quod Erat Demonstadum

Sorry Fritz if I've over complicated it, so do you mind explaining how you got your version of T?

RK


EDIT: Fixed a few formatting/spacing errors. Dots used to fix paragraphing.

[Inverse Icarus]

the new formula should be if (N / N != 1) { flip(); }

[Sultan Richard]

umm..... I don't know how to get paragraph spacing in this! Please help!

[Tuberski]

Originally posted by Sultan Richard
umm..... I don't know how to get paragraph spacing in this! Please help!

Hit two or three times at the end of a paragraph.

[Switch]

So, is the algaebraic method the same as the other, just written differently, or is it actually simplified to give a rough estimate?

[nato]

Thanks for putting the formula so nice Fitz.

I have two questions then...

First, a quick one. Does a courthouse help at all with fighting culture flip? I thought it did.

Second, a longer one. A standard thing to do to prevent flipping in a newly conquered city is to rush cultural improvements, especially temples and cathedrals.

However, from the formula, it seems that generating culture in the city is only useful if it is more than the other civ generated. For most cities, you will kill the other civ entirely before you generate more culture than they did.

So is it worth the (sometimes large) expense to rush build culture buildings in a conquered city? It seems hopeless to hope that your culture generated will ever be greater than the original civs.

I suppose it is useful in that 1) makes some people content, and 2) eventually might expand your culture border ... For 1, luxuries do that for me usually, and for 2, I think I'll conquer the next city before that happens.

So does anyone think it is worth the expense of rushing temples and cathedrals in newly conquered cities?

[Cyclotron]

Originally posted by nato
However, from the formula, it seems that generating culture in the city is only useful if it is more than the other civ generated. For most cities, you will kill the other civ entirely before you generate more culture than they did.

So is it worth the (sometimes large) expense to rush build culture buildings in a conquered city? It seems hopeless to hope that your culture generated will ever be greater than the original civs.

I suppose it is useful in that 1) makes some people content, and 2) eventually might expand your culture border ... For 1, luxuries do that for me usually, and for 2, I think I'll conquer the next city before that happens.

So does anyone think it is worth the expense of rushing temples and cathedrals in newly conquered cities?

No. Unless you plan to end the war soon, all you need is a temple for borders. National culture is much more important than city culture, unless you plan to keep the city for a lot longer than your enemy did. It's very difficult to out-culture an opponent in one of his older cities... so don't try, and keep a high national cluture instead.

[DeepO]

Courthouses are for battling corruption, not to counter culture flipping. However, there's one indirect gain from them: if you have allocated some of your tax income to luxuries, it will be more easy to avoid civil disorders, and possibly to get a WLTKD as you (should) get more tax with a courthouse.

DeepO

[Akaoz]

Erm... Is there a rule of thumb as to how many troops you need in order to be sure the city will not flip?

-Alech

[nato]

Thanks for the answer cyclotron, I think thats how I'm feeling too. Oh all that money I spent rushing cathedrals!

About the courthouses, I am sorry to be dense about this ... I see DeepO's answer, and I of course know courthouses are primarily for corruption. I can also see there is nothing in the formula about courthouses...

But do courthouses really have zero effect on culture flipping? I could have sworn I read somewhere that they help prevent it.

So can I stop rush building courthouses in newly conquered cities too (for the purpose of stopping culture flip)?

[Catt]

Fitz, good work. Very helpful.

nato, based on the Soren Johnson thread and the earlier Dan Magaha thread in January (on the strategy page), I think courthouses do not affect culture flipping. I thought I read somewhere that they did as well, but I think what we're both misremembering is that courthouses make cities more resistant to propoganda, which, for gameplay purposes appears as a flip, but which apparently operates on a distinct formula.

Catt

[nato]

Ah propaganda, that must be it Catt. Thanks. So a courthouse is of no help for normal purposes.

Wow, so now not only do I not need to rush build cultural buildings (except maybe a temple for borders), I also don't need to rush build courthouses in newly conquered cities.

I guess I'm no more resistant to culture flipping, but it is a lot cheaper to conquer now!

[Cyclotron]

If you want to actually get use out of your captured cities, however, you will need to rush a courthouse anyways.

[Capt Dizle]

Coracle is correct. Even if the community eventually discovers the correct formula for flipping it will not justify this horrid game concept.

The idea of a province peacefully defecting to another empire (civ) is perfectly acceptable in certain circumstances. The current implementation leading to huge cities flipping and huge garrisons vanishing into thin air is simple the worst gameplay element I have ever seen in a civ game.

Logic dictates that if a city wants to flip it would have to revolt and defeat the occupying enemy troops. Firaxis could implement this by returning partisans to the game.

I also agree with Coracle that borders should not expand over enemy fortresses. A fortress and its ZOC that has any tile in the border of its civ should effectively block the expansion of other civs borders; likewise a colony should do the same irregardless of its location.

[Switch]

Originally posted by jimmytrick
I also agree with Coracle that borders should not expand over enemy fortresses. A fortress and its ZOC that has any tile in the border of its civ should effectively block the expansion of other civs borders; likewise a colony should do the same irregardless of its location.

well, that would actually NOT be quite a good decision. Then people could just surround their borders with fortresses and never worry about other civ's exoansion into their territory.

[notyoueither]

Nevermind.

[Capt Dizle]

Originally posted by SwitchMoO


well, that would actually NOT be quite a good decision. Then people could just surround their borders with fortresses and never worry about other civ's exoansion into their territory.

People shouldn't have to worry about another civ's expansion into their territory unless it is by force of arms, if they had fortified their perimeter. And this business of letting settlers come in and found a city in someone else's borders is silly.

[DeepO]

Originally posted by nato
Wow, so now not only do I not need to rush build cultural buildings (except maybe a temple for borders), I also don't need to rush build courthouses in newly conquered cities.

Well, there are special cases in which rushing every possible cultural building is still helpful. If a city flipped to your side, it is very likely that it's culture was rather low (e.g. a temple for 50 turns, meaning 100 culture). To prevent it from flipping back (which happens once in a while), building up your culture quickly can be a good thing. If, in the same example, you rushbuild a temple, library and cathedral, it only takes about 15 turns before your culture outranks the previous culture, after which there is minimal risk of flipping back.

The same holds for conquered cities early on in the game: most of the times there was only a temple inside, which makes it easy to outrank that culture fast.

Big, late game cities do not need rushbuilding after the first temple or library (if you're scientific); it's a lost case after all. There only garrison troops help, or annihilation of the enemy, or ethnic cleansing.

DeepO

[wrylachlan]

is it the number of tiles under the control of the civ you might flip to? The number of tiles controlled by any foreign civ (near a three-way border)? or the number of tiles NOT controlled by you (like if you've advanced 2 or 3 cities into a civ, the 1st city has some no-mans land around it, does this count against you)?

Also, since rushing cultural building allows you to quickly control all the tiles, I would say it is certainly not a waste. Also in the long run it helps with the total cutrure difference.

As for courthouses and happiness structures, these cause WLTKD which cuts down on flipping, so they are important too.

And correct me if I'm wrong, but don't happy citizens assimilate faster? Which means that happiness can cut down on the number of foreing nationals which means less culture flipping.

[wrylachlan]

Originally posted by Tuberski
Coracle, go play Civ 2.

Or Pac-Man... oh wait, it's not realistic that pac-man can eat all those dots. For him to be able to eat all of them his total volume would have to be greater than the sum of all of them. And Ghosts! Come on folks, lets get back to reality here.

[DeepO]

Originally posted by wrylachlan
is it the number of tiles under the control of the civ you might flip to? The number of tiles controlled by any foreign civ (near a three-way border)? or the number of tiles NOT controlled by you (like if you've advanced 2 or 3 cities into a civ, the 1st city has some no-mans land around it, does this count against you)?

It's the number of tiles within your possible city radius. The city radius is the area you could put citizens onto in your city screen (so 21 squares, apart from the city tile itself)
Further, if there are several nationalities of squares and/or citizens in your city, the chance is calculated several times, not once with the total # of citizens+squares. This effectively lowers the chance, as the garrison units you had in the city count double (or triple in case of 3 different nationalities).

And no-mans land does not count in any way... but still you'd better have a border increase just to prevent others from gaining territory, at which point it would become an isssue

DeepO

[Edited to add a paragraph]

[Fitz]

Ignoring all the comments about the realism of the flip ...

Okay, first, I'm basing all this on my interpretations of Soren's comments. If he left out anything (ie courthouses precluding flips) then I haven't included it.

The algabraeic formula is identical to the written one. Nothing removed or "simplified".

Sultan, you've made some mistakes on the troops thing, which I believe to be that you forgot to multiply T by R when rearranging your formula (equation 2 or 3 I think).

If P(robability of flip) = (((N+S)*C*H)-T)*R/D and we want 0 chance of a flip, then

0 = (((N+S)*C*H)-T)*R/D
multiply both sides by D and
0 = (((N+S)*C*H)-T)*R
divide both sides by R and
0 = ((N+S)*C*H)-T
subtract T from both sides and
T = (N+S)*C*H

So that means 1 troops be forign national or square, *2 if more culture from the otehr civ, *2 if in civil disorder, and *1/2 if in WLTKD, just as I said, to prevent a flip.



Courthouses should have no effect other than raising your overall national culture, and possibly towards exceeding another nations culture in that city. Ditto temples. Oh yeah, and eapanding your borders, which can (and frequently does in my games) change the S (squares) factor of the equation.



DeepO, sounds like you got the # of squares thing down.

However, on multiple nationalities, I am guessing it works like this:

Each troops only counts once towards negating chance of a flip. However, each chance to flip is calculated seperately. How the troops are assigned to negating the chances I wouldn't know. Probably equally, or assigned to one until equal negations to the other (ie if one has ten citizens and another 3 squares, first seven cancel the citizens).
Either that, or there is an overall chance of flip determined once, then who the flip goes to is determined next based one chances of flipping to each individually. This makes more sense to me, but don't know if this is the way Firaxis would have done it. The only problem with that is how the formula breaks down to include the distance/culture ratio portions.

Regardless, SOREN IF YOU ARE LISTENING PLEASE TELL US WHICH WAY IT WORKS. Important info.

So, as an example, lets assume you have equall culture and distance to two other civs, the eqyptians and the persians, and you just took the city from the persians. You have less culture than the persians had in this city, it has two persian citizens, three squares are covered by the eqyptians, and there are no WLTKD or disorder effects. You have 3 garrison units there.

Assuming method 1, we can guess that the garrisons will be assigned 2 to persians and 1 to egyptians. Chance of flip to persians: (2*2*1-2)*1/2000= 0.1% Chance of flip to egyptians: (3*1*1-1)*1/2000= 0.1% .

[Arrian]

Courthouses don't produce culture. I do remember reading somewhere that they reduce the chances of a flip, but that could be incorrect.

I applaud your efforts, Fitz, because this is pretty complicated stuff.

Coracle/Jimmy: this thread is specifically for the discussion of the culture flip formula, NOT A DISCUSSION OF WHETHER OR NOT INCLUDING CULTURE FLIPPING WAS A GOOD DESIGN DECISION. Your views on the second matter are well known.

-Arrian

[DeepO]

Originally posted by Fitz
However, on multiple nationalities, I am guessing it works like this:

Each troops only counts once towards negating chance of a flip. However, each chance to flip is calculated seperately. How the troops are assigned to negating the chances I wouldn't know. Probably equally, or assigned to one until equal negations to the other (ie if one has ten citizens and another 3 squares, first seven cancel the citizens).
Either that, or there is an overall chance of flip determined once, then who the flip goes to is determined next based one chances of flipping to each individually. This makes more sense to me, but don't know if this is the way Firaxis would have done it. The only problem with that is how the formula breaks down to include the distance/culture ratio portions.

Fitz, the tiles in the city radius is actually the easiest factor, well, apart from counting the foreign citizens
I just reread the Soren thread to get some clues, but there's not much info about this in it. However, I found another problem (more on that later)

My guess for using garrison is that it counts each time in full. Why would the calculations use a part of the garrison? I see no reason for it... It's easier if you just make the calculation each time, for each nationality, regardless whether there are more nationalities involved.

This would mean that, in your example the chance of flipping to the persians is 0.05%, the chance of flipping to the Egyptians is 0. Which shows that, even with only 3 garrison units and 5 foreign citizens+tiles, the total chance is very low (once every 2000 turns on average!). Compare this to 2 persian citizens + 3 persian tiles --> chance of .35%, 7 times as high.

I don't know which of us two is right, although I do like my method better If however garrisons are divided to counter different nations, they should be divided equally (meaning 1.5 for both Persia and Greece). You can't expect a quite complicated formula to dived the garrisons first, then calculate the chances, the roll the dice... it's IMO one step too much.

But now something else: as I reviewed the original thread once more, I noticed a few descrepancies:

Originally posted by Soren Johnson Firaxis
The only way a city of, say, size 2 would revolt if you had 14 troops in the city was if their total culture was 3.5 times your total culture, which is pretty unlikely.

Originally posted by Soren Johnson Firaxis
well, it would be more useful to see a pic (or better yet, a save...) from just before the flip. If there are tiles of Greek territory in the city radius, they count just as much as citizens. So if there were four Greek squares in your radius and four Greek citizens, you would have needed 16 combat (don't count artillery) units (assuming your overall culture is at least equal to their's) to have no chance of a flip. Of course, the probability goes down with each unit added to the city. So if you had 14 units, the probability of a flip was probably < 1%. But it happens...

I should also add that in the scenario I just outlined, if you had twice the total culture of the Greeks, you would have only needed 8 units. If you had 3 times their culture, 6 units. 4 times, 4 units...

Originally posted by Soren Johnson Firaxis
The capital factor affects how big the "die" is, if that makes sense. For example, in the case above, there are 4 greek citizens and 4 greek tiles. That equals 8, which is then doubled because Greek culture _in that city_ is greater than Roman culture in that city. So that is 16. Let's say Snoopy has 4 units and has twice as much total culture as the Greeks. That would be 16 - (4 X 2) = 8. So if we "roll" an 8 or less, the city flip.

(only Soren's quotes mentioned, look at the thread for more info)
If you look at the above quotes, you see that it doesn't fit your formula. (close, but no sigar ). My guess is that the totalCultureRatio should shift into your brackets, although I'm not sure to which place it should actually go.

Either it should become
(((N+S)*C*H)-T*R)/D
or
(((N+S)*C*H/R)-T)/D
not
(((N+S)*C*H)-T)*R/D

(with R the totalCultureRatio = yourTotalCulture / enemyTotalCulture)

Possibly it shifts between those 2 formulae depending on whether R is bigger then 1, or smaller then 1, otherwise it's the first one.

This has a grave impact on the chance, and makes R a deciding factor to calculate the number of troops to get to 0 chance. So, depending on your total culture, you should add more (or less) troops...

Conclusion: We still don't know it

Let me know if I'm right on this, or if I overlooked something...

Originally posted by Fitz
Regardless, SOREN IF YOU ARE LISTENING PLEASE TELL US WHICH WAY IT WORKS. Important info.

I couldn't agree more.

DeepO

[edited for clarity]