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DeepO
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supporting Candle'Bre
Jan 2002
time: 06:19
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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  ]
Last edited by DeepO on 04-06-2002 at 20:54
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playshogi
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If a city has 3 Greek and 3 Persian is the chance of flipping the same as if it had all 6 Greek?
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DeepO
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supporting Candle'Bre
Jan 2002
time: 06:19
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quote:
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
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DeepO
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supporting Candle'Bre
Jan 2002
time: 06:19
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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
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DeepO
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supporting Candle'Bre
Jan 2002
time: 06:19
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quote:
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.
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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.
quote:
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.
quote:
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 ?
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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.
quote:
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
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Fitz
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& Anarchist
Mar 2000
time: 21:19
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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.
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DeepO
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supporting Candle'Bre
Jan 2002
time: 06:19
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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
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Arrian
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Kneel before Grog!
Jul 2001
time: 00:19
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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
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DeepO
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supporting Candle'Bre
Jan 2002
time: 06:19
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Arian, I agree, but just one question: do you starve citizens because of going to the dark side, or because you believe it to be a good tactic?
Because, as shown above, it is not really helpful. Of course, pop rushing temples and garrison is a double solution (adding happyness or troops, while lowering foreign citizens), but pure starving for the fun of it doesn't help that much. You'd better make sure you get into WLTKD mode, so that those happy, foreign slaves actually are of some use to you, for production (if not totally corrupt), tax, science, whatever.
This doesn't rule out starving, though, if you don't have enough luxuries, starving will be the only reasonable way you get to WLTKD. And if your culture is already twice the enemies (or more), after your cityCulture rises above the previous cityCulture, one or two troops would totally negate the chance, making WLTKD not a necessity anymore.
DeepO
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Fitz
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& Anarchist
Mar 2000
time: 21:19
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It seems Arrian, that you are specifically talking about the early game when despotic pop-rushing is still available. This has a bunch of ramifications:
1) The AI culture as a whole is probably still low, especially compared to a human player.
2) The culture in any given city is probably low to 0, excepting of course the capitol, meaning that it is relatively simple to play catch up for that city.
3) The populations in general are low, and certainly below 12 to start with, if not 6.
4) Despotic pop-rush once out of resistance gives an easy means of reducing the native population even further.
Once your talking about a modern era size 17 conquest in Democracy, and the civ has had several 1000 years of culture in that city, and probably has caught up to a 2:1 or better ratio against you, it gets a little harder to keep that city.
Incidentally, I was wondering if Soren has put an Interger function on the Culture ratio (top or bottom). If so, there would be no effect until you get to *2 or *1/2 for that factor. I think it unlikely since a Int(CutureA/CultureB) will return 2, 1, 0 or etc but not a fraction, but still worth considering. Opinions on the likelyhood, and can anyone think of a simple C++ function that return 1/2 1/3 1/4 (interger on the bottom)? I do believe his comments made it sound like it is a decimal ratio, but all his examples were integers (possibly just for simplicity).
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DeepO
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supporting Candle'Bre
Jan 2002
time: 06:19
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quote:
Originally posted by Fitz
Incidentally, I was wondering if Soren has put an Interger function on the Culture ratio (top or bottom). If so, there would be no effect until you get to *2 or *1/2 for that factor. I think it unlikely since a Int(CutureA/CultureB) will return 2, 1, 0 or etc but not a fraction, but still worth considering. Opinions on the likelyhood,
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well, in one of his quotes on page 2, he said that it was needed that the AI would have a 3.5 ratio to the human... which was actually more then 3.5. Of course, it could be 7/2, but if you are working with decimal numbers, why is it needed to have a ratio of two simple integers? My guess is it was only for simplicity
quote:
and can anyone think of a simple C++ function that return 1/2 1/3 1/4 (interger on the bottom)? |
This is not a problem. There might be a nicer way, but for clarity the following:
code:
float r=3.45
float rCapped=1/((int)r) //rCapped is exactly 1/3
I believe this should work (C++ has been a while, though)
DeepO
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FrantzX
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"That's math staring right back at you."
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Capt Dizle
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The insults are unnecessary.
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04-06-2002 05:19
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