Culture Flip Formula

[DeepO]

Sure thing... let's see. I'll calculate 2 things for every example: namely the number of troops you need to totally negate the CF chance, and an approximation of the chance each turn. For a more detailed breakdown on the different factors (plus extra examples), see page 4.

Example 1:
One of your cities is under cultural pressure from a neighbour, as there are 3 tiles within your city radius that are his. Your total culture is double his, and the city is roughly in the middle between his capital and yours.

The number of troops is calculated as follows:
- first you see how many 'bad elements' you have in the city. This is 3 (tiles) + no foreign citizens.
- Secondly, you'll see who has the most culture in that city. It is yours, so you have. No additional factor
- Thirdly, happiness. assume no WLTKD, nor disorder. No factor as well
- Fourth, you take into account total culture. Your's is double of his, so you divide the chance by 2. Result = 1.5
- And voila: the number of troops you need to fully negate the CF is 2 (bigger than 1.5).

Now, let's say you have only 1 troop in there, what would the CF chance be?
- You already now that the modified cultural pressure is 1.5 . Subtract 1(troop) from this --> 0.5
- this is then divided by the distance factor, which is 2000 as your capital is as close as his. So the total chance becomes 0.5/2000 = 0.025% each turn. On average, it will take 4000 turns before this city will flip. Or, during 200 turns (a realistic number in each game, there are 540 turns from 4000BC to 2050 AD), you have a 1 in 20 chance this city will flip on you... not really worth worrying about.

Example 2:
same city is under cultural stress, but this time it is much closer to the foreign capital, has 6 foreign tiles (still all of the citizens are yours), and your total culture is only half his.
- Bad elements = 6
- No additional factor because your culture in the city is bigger then his (you build the thing)
- For the moment, assume no WLTKD, nor disorder. No factor as well.
- Your culture is half his, so the 6 becomes 12, this is the total cultural pressure.
- Conclusion: you would need 12 troops in that city to fully counter flipping. This is a lot, but still reasonable.

Assume you only have 3 troops in, the chance would then become:
12-3 = 9 ... which has to be divided by the distance ratio which is in this example (very close to their capital) 500. So, the total chance would become 9/500, or 1.8%. This means that that city will on average take 56 turns to flip, a quite reasonable duration.

Now, in the example above, what would be the effect of a WLTKD?
- The number of troops needed to keep a hold on that city would half, so instead of 12 troops, you'd need 6.
- If you have 3 troops (like above), the chance would become(6-3)/500 = 3/500 = 0.6%. On average, the city would flip in 167 turns

If, on the other hand, there would be a disorder instead of a WLTKD, the number of troops you need is doubled. 12 --> 24.
- if you still have 3 troops there, the chance would be (24-3)/500 = 21/500 = 4.2%. On average, the city would flip in 24 turns...

From this example, it may be clear that happiness is everything, whatever you do, don't let a culturally pressed city fall into disorder!!

Example 3:
You conquered a foreign city, size 12, 8 resistors, next to capital, and with 5 foreign tiles. Your total culture is only half his, and there is normal happiness.
- 'bad elements': 12 foreign citizens + 8 resistors (they count double) + 5 foreign tiles = 25
- City culture was higher for the other one (it's his city): 25*2 = 50
- no happiness modifiers
- your total culture is half his, so you will need 50*2 = 100 troops to fully negate the CF chance.

If you only have 5 troops in the city (artillery doesn't count!), the chance would be (100-5)/500 = 95/500 = 19%. This city will on average fall back into the enemy hands in 5 turns, which is very high.

What could you do to counter this?
- The total culture is of course a big factor here, but that can't be changed over night. If your total culture would have been double of his, instead of half, you would only have needed 50/2 troops, or 25 troops to fully negate the CF chance.
With the same 5 troops present, the total chance would have been (25-5)/500 = 20/500 = 4%. On average it will take 25 turns, by which you should have conquered that capital easily
- WLTKD has similar effects: it would mean 50 troops need, and a (50-5)/500 = 9% chance (11 turns)
- starving citizens doesn't work well: you can only starve one citizen at a time, which won't be a resistor unless they're all resisting, and the chance only marginally improves. I only do this when you can pop-rush some culture building
- Rushing culture is good, not because of the effect it has on city culture (but this can be a factor when the conquered city didn't had any culture before), but because of the border expansion: if you have 5 less foreign tiles to worry about, your chance would become 80/500 instead of 100/500
- quelling the resistance is always good (but risky, as you need troops for this): losing 8 resistors would make the chance 68/500 instead of 100/500.

Any more examples? Let me know...

DeepO

[edited to correct a small mistake]

[Charis]

Aye

Thanks for the comments, DeepO

> ... culture ratio thing, this isn't so bad as it looks. If
> you play for it, a ratio of 5 (yours being better then
> theirs) is achievable.

My bias towards deity and emperor is showing in that comment - it's achievable on lower diffs but I'm taking a beating on the culture ratio on deity

> If you conquer a city of 10, 5 of which rebel, and you
> don't control 5 of the tiles (a more realistic number
> then your 10)

I was thinking there of a situation capturing a front line enemy city on higher diff. If I control 11 tiles it's fantastic, 16 would be unthinkable :P

[ Edit: Actually though, once I capture the towns to either side of a spearhead city, having about 5-10 not under my control is pretty reasonable ]

> And I wonder where you got the (20*D) factor for the
> distance ratio... it should be map specific. AFAIK we
> only know it is in the 500-8000 range, with a middle
> value of 2000. Any info would be appreciated.

First, I just factored out the '2000' that you folks mentioned, and divided by 100 to make it "percent" instead of fraction. Then I separated out 'D' to be a simple ratio, and it makes perfect sense then to have D a real number, distance ration, capped at 4, rather than a nebulous 500-8000.

The revised formula also then suggests that a "20" plays a role in the formula. Perhaps not coincidentally, that's exactly how many tiles you have besides your capital for your people to work.

[ Edit - more on the '20' added ]
Let's look at that 20 a little more closely:

Chance of flip = {[(N + S)*C*H*R] - T} / (20*D) [percent]

If you look at it in basic terms, for equal civ culture, distance to capital, no troops forcing the matter, and no resisters, chance to flip eqn reduces to
%Chance = N / 20 (double if the old culture is higher)
So there's a one percent chance per turn of a flip when all the workers in a city are foreign nationals (all 20), and this chance is reduced by the number of foreigners divided by a full cities worth. That simple result is also why I like breaking out the 2000 and converting it down to 20.


Your four rules of thumb on what to do in general are spot on...
- Quell, rush temple, poprush if possible, get back to WLTK conditions

Your suggestion that loss of WLTKD by starving a city down and not keeping it under size 6 for so long is an interesting one. Whether it's correct depends on tile control. The more tiles you lack control, the less important the number of foreigners are and more important the WTLKD. But if you have full control, and roughly equal civ culture, #foreigners being 6 vs 1 is far more important than lack of WTLK.

Specifically, you have control over N and H and want the product of (N+S)*H to be as low as possible. N can be reduced to 1, or maintained at size 6 and kept happy.
Algebraically then, it becomes a toss-up when:
(1+S)*1 = (6+S)*1/2, rearrange to get:
S = 6. So... when the number of tiles outside your control is more than six, keep city size of 6 and go WLTKD. If number of tiles outside control is under 6, starve the city down to 1. (In the first case, there's no reason not to starve a large city down to six, speeding up via poprush or cash-rush workers)



That seems a handy result -
"A six tile sting? We love the King!
More control of your town? Starve it right down"

Charis

[Grumbold]

Has anything appeared in the editor options yet to allow you to modify the effect troops have on culture flipping? I'm not playing the game at the moment because I hate razing all big cities but don't see any alternative. If there's a way to increase the "weight" of modern units so that 3 mech inf can usually hold down a size 20 city I'll be very interested (like using the defence factor.)

[latenight]

Cost to flipping

Someone mentioned a return of Partisians. How about the following scenario--when a Culture flip is imminent, a message could be displayed that says "the Citizens of XYZ City want to join your Civilization but are held captive by Partisan resistors". To win the city, you must defeat the Partisians. Battle conditions would be slightly altered--there would be no destruction of City Improvements--only the destruction of the Partisians. Following their defeat, the City would revert to your control. I think it would also be fair to require a monetary payment of some kind to bring the City up to the full "standards" of your Civilization. Comments??

[DeepO]

Charis, I never compute in percentages, as it is just a way of representing a decimal number... '%' means 'divided by 100', literally. I agree it is a better representation as many things in life are in percent, but in a formula no-one will use it.

Further, your natural 20 might seem good, but I think this is just coincidence. This formula had quite a bit of balancing, and it changed I think even in the first patches. Plus, I'm sure that if it for some reason would be 50, you would be able to find another 'natural' relation

I'm not saying that your distance ratio isn't correct, it might be, but it is purely speculation at this point. We only know that the default is 2000, and it can go from 500 to 8000. More importantly, it is the least important part of the formula, as we need to know the factors that have a direct impact, and distance isn't one of them. Of course, if you move your capital closer to a city under pressure, you will have a easier time, but you need to put your capital so that it brings the best corruption, so you don't have much choice here.

As to starving: I'm not saying it wouldn't affect the chance, but in my eyes it is the least effective option you have. I never deliberately starve (outside poprushing), and I very rarely have problems with culture flipping. With decent overall culture and a few troops, the effect of a WLTKD is always way bigger then any starving you might do. I don't say you need to bring each city you have into WLTKD, and that is not the only reason why you don't starve, the most important reason is that you lose the possibility of good production in that city. Sure, you can reduce it back to 1 pop, but by the time you get a size 12 city down to 1, you should have conquered the whole civ anyway. And when there is no foreign city left, all foreigners of that nationality are considered your own.

Starving, and razing is only needed when you have a lousy culture, so instead of complaining about that, you might want to check if your civ can use a few more temples and libraries. I'm very positive that on Emperor (my preferred level) you can have 5 times the culture of the next civ, I do this a lot. And this is not purely a builder approach, it's just that from time to time you mix in a cultural building between some troops and you're fine. Of course, this means that conquered cities need to have some production to build those things, if these cities are busy starving to death, you don't have production enough to build anything, and you're likely to concentrate on some troops instead of culture.

As to 11 foreign tiles being normal: you know it would be a problem, so change your battle tactics to compensate. Wars in Civ should be as short as possible, and if possible this means that neighbouring cities should be next in line. Never make a very jagged front line, where one of your cities is sided by 3 enemy cities for 20 turns in a row, that is a bad tactic for multiple reasons (flipping one of them). the shorter front line you have, the easier it is to control it. Note that flipping is not something that happens in 1 turn, or 2 turns, it is a long process in many cases. Whatever war you're fighting, you should make sure that in 5 turns time you can advance the whole frontline at least 1 city, or you would better sue for peace, and build up forces to come in one big sweep. That's why you will very rarely see a city with 10 foreign tiles, maybe it will be so for 1 turn, never longer.

Grumbold, I mentioned this before (i'm not sure if it was to you), but if you want to edit culture flipping out of the game, start a scenario in which you start with 100,000 culture, and disable cultural victory. The only problem you might be facing is that loads of cities will flip to you, but just rebuff the rebels, and your fine. You're missing out on a critical aspect of the game, but that's your choice. I would strongly oppose any changing to the formula where troops become more important, the whole idea of CF is that Civ III is not a war game. As it is now, with some decent culture building, 1 or 2 troops will prevent all problems, I think in the past 5 games only some 5 cities flipped on me... and I'm playing huge maps on Emperor where I end with some 100 foreign cities each game. That is not a problem to me, it keeps the game interesting.

latenight, that was indeed proposed, amongst other 'solutions' a few times already, but this wil not change. The reason is that it means a total shift in how CF works right now, so maybe for Civ IV. Please don't degrade this thread into a 'I don't like flipping' thread, we had hundreds of these already. So far this has been the only thread where the idea was to understand flipping, not to change it. I'm not saying that I'm very fond of the end implementation of flipping, but the concept is very good (IMO), and it is as it is: learn to work with it, instead of wanting to change it.

DeepO

[Theseus]

DeepO, I like it when you translate to concrete, in-game strategy and tactics!!

I'll chime in: Whether by land or sea, I almost NEVER capture one city at a time, but rather two adjacent, and where possible I work from the outside (i.e., sea / ocean) in. This is especially true for intercontinental invasions, where distance to capitol can be a much bigger factor, cities are bigger, and culture is higher.

[DeepO]

Well... there is one exception to this short front line: cultural spearheads. But I only use these when I'm not planning on a military takeover, and have extreme culture (10 times the enemy's culture or higher). The idea is to build a few cities in between the AI cities, and build up culture fast in there with one goal: to let the neighbouring cities flip to you. It is a long term strategy, and given the randomness of flipping it can take a few turns, 100 tuns, or it won't ever happen.

How to do it: build a few cities as close to a target city as possible, in a checkers pattern (so that an enemy cities is 'walled in' from at least 3 sides.). Then start building up culture, so that all the tiles which could be yours are yours as your culture is bigger. Remember: a tile that is only 1 space away from the enemy, and two spaces away from you will never be yours. Tiles that are 2 tiles away from both parties can be won culturally. If you are careful, you can make their cities have 3 or 4 tiles at most for their own, all the other tiles in their city view yours. If your culture is high enough, you will gain those cities, even if they are right next to their capital.

If you want to speed it up, you can make sure that their luxuries supply varies by trading with them, and when they want to renew wait a few turns (2) before trading it back to them. This will mean that in certain villages they will get into disorder, which more or less doubles the flipping chances to you. Something that is also very useful in certain situations is pillaging the road towards these cities: if they are walled in, the road towards them comes through your territory. So pillage it, watch them go into disorder, and build it again. Repeat a few times, and the continuing disorder will most likely flip them to you. Nasty tactic, but certainly no exploit.

The only problem is that when you do this, you have to make sure your cities are well protected against flipping with a few extra troops. And, you need to set aside enough funds to rush culture in those cities, once an AI city is under cultural attack it will prioritize culture as well. Plus, each time you gain a few tiles, the AI will like you a little less.

DeepO

[Grumbold]

Originally posted by DeepO
Grumbold, I mentioned this before (i'm not sure if it was to you), but if you want to edit culture flipping out of the game, start a scenario in which you start with 100,000 culture, and disable cultural victory. The only problem you might be facing is that loads of cities will flip to you, but just rebuff the rebels, and your fine. You're missing out on a critical aspect of the game, but that's your choice. I would strongly oppose any changing to the formula where troops become more important, the whole idea of CF is that Civ III is not a war game. As it is now, with some decent culture building, 1 or 2 troops will prevent all problems, I think in the past 5 games only some 5 cities flipped on me... and I'm playing huge maps on Emperor where I end with some 100 foreign cities each game. That is not a problem to me, it keeps the game interesting.
DeepO

I dont want to take out flipping as a design element. What I would like to do is retain flipping as a long term risk associated with poor culture, but increase the value of units to a level I am comfortable with to reduce the chance of immediate flips while at war in the late game when cities are size 20+. If I can crush a city's defenders and citizenry with 3 artillery and 3 armor I don't expect to have to stuff 40+ units into it to prevent its loss. Tagging unit weight to unit defence value would help achieve this, with mech inf proving far more capable at holding down rebellious citizenry than warriors or pikemen. Tying down 4-6 Mech inf as occupation forces makes sense to me in a way using 20+ miscellaneous units or parking a couple just outside to retake and not occupying the city at all simply does not.

Ok, I'm lazy so I haven't done the math on this now more exact formula but an earlier post of yours certainly shows 1-2 troops should not "prevent all problems". I like culture, but I'd not normally achieve 5x the opposition. Say more like 2x...

Charis, don't get overexcited on the 30 troops * culture ratio thing, this isn't so bad as it looks. If you play for it, a ratio of 5 (yours being better then theirs) is achievable. If you conquer a city of 10, 5 of which rebel, and you don't control 5 of the tiles (a more realistic number then your 10) you would need 8 troops to totally negate the chance. I agree, this still is a large number, but I mentioned before that troops are for fighting, and not for countering culture flipping. With a WLTKD you would only need 4 troops... but I haven't seen WLTKDs with rebellions going on.

Really all I was asking was whether the editor yet had more flexible ways of adjusting culture than the brute force on/off switch. If it had, it would have revived my interest in playing the game again.

[DeepO]

I'm sorry for the confusion, when I said 1 or 2 troops prevented all problems I should have said they will prevent any serious problem, down to the point where flips don't bother me as they are so rare. If you have twice the culture of the civ you're crushing, a good rule of thumb is that you need as much troops as there are foreign citizens (+ tiles + resistors) to have a 0% chance in a city without WLTKD. But, you can manage with a lot less if you are willing to let 1 or 2 cities flip per game.

I do agree that the implementation isn't everything, and the idea of having certain troops being better against flips is a good one, but again, this is hardly the thread to discuss that. So if you want to work with the implementation as it is now, you just use a bunch of outdated or obsolete units to garrison cities. I always end with most of the initial warriors and spearmen I built in the ancient era, I agree that it would be better if I was able to upgrade them and use them instead of spending upkeep each turn, but they do have their uses, they aren't lost.

Also, please forgive me if I sound irritated from time to time when it comes to flipping, but over the past few months I responded to so many posts on this issue that you lose hope. That's why I constrain myself only to answer strategic questions, and try to explain to people how this formula works, I don't want to get involved in the same arguments again.

DeepO

[Grumbold]

Np. Thanks

[mojo1442]

I have three questions on the exact interpretation of the given formula:

1. Does an army count as one garrison troop or do all individual units of the army (w or w/o leader) count?

2. Do entertainers count as foreign citizens?

3. Do air units count as garrison?

4. Are foreign citizens assimilated over the years?

Johannes

[mojo1442]

ok that were 4 questions ;-)

[alexman]

1. If you assume that the garrison for culture flip purposes is the same as the garrison for military police purposes, then all individual units within an army count, including the actual army unit. If the army is empty, it doesn't count at all though.
   
2. Although I have not tested this, I would bet the answer is yes, if they are in fact foreign. Otherwise it would be too easy to avoid flips by assigning specialists.
   
3. Again, if garrison is the same as for MP purposes, the answer is no.
   
4. Yes, and the rate is between a 1 and 4 percent chance per citizen per turn, depending on your government.