Culture flip limit?

[darious001]

Well, is there. I have two cities surrounding one Persian city. It's about two times closer then my two cities are to our respective capitals. It was set up in the BC's, it's now around the 1400's. My two cities have been putting out a lot of culture buildings, and are at the culture level three right now, it just hit two a little bit ago. It's been there so long, that it should have cultured fliped. There was another city that was set up a bit farther away, and that flipped within four centuries. I'm just wondering, what is it that's taking so long for it too flip. It had only three squares to it's self for most of that time. Yet it hasn't flipped, it's quite annoying. There's also one other city that should have flipped, yet that one wouldn't either. Any reason for it. Anyone know.

 

[Shabbaman]

Hello Darious, I took this straight from the faq:

the full formula (this is from Sorenson, who is responsible for this programming):

P=[(F+T)*Cc*H*(Cte/Cty) - G]/D

where:
P = probability that it will flip this turn
F = # foreignors, with resistors counting double
T = # working tiles under foreign control
Cc = 2 if foreign civ has more local culture than you, 1 otherwise
H = .5 for WLTKD, 2 for disorder, 1 otherwise
Cte = Total culture of the foreign civ
Cty = Total culture of your civ
G = # garrison units
D = factor based on relative distance to capitals

Now reorganizing this gives the required garrison as:
G = (F+T)*Cc*H*(Cte/Cty)

As you can see there is a nice set of extra factors there. Now when you take a city Cc is likely to be 2 for a long while. And then there is the culture ratio. And this is a true ratio so it could be 1.1:1, 2:1, 5:1 depending on how much culture each of you has

The national culture factor is probably the reason why some seem to have no problem with culture flips and others do. Since if you have strong national culture, this value might be approaching 1/2, which can keep the garrison down at a 1:1 ratio. However, if conversley the AI civ in question has double your culture, you are going to need 4 units for every foreignor and tile to prevent a flip.

If you attempt a cultural attack:

P=[(F+T)*Cc*H*(Cte/Cty) - G]/D

then F=0 most of the time (no foreigners there...)
and T=<21, you mention only three squares for the city, so that would make a T value of 18 (which is extremely high!)
Cc=2 (probably)
H=1
(Cte/Cty)= 2/1 if you've got twice as much culture as them.
D=

It's about two times closer then my two cities are to our respective capitals.

thus D=2 I think (it's closer to his capital then to yours?)

G will be something like 3...

P = ((18 * 2 * 1 * 2 )- 3)/2 = 34.5

I assume that you should read this as a chance of 0.345 that it flips to you that turn. If you misinterpreted the working tiles overlap, this lowers the chance dramatically!

I hope that I didn't make errors in this calculation, feel free to correct me.

Greetings!

 

[RX2000]

I h8 math.

 

[Yndy]

Originally posted by Shabbaman
G will be something like 3...

AI reacts against a cultural attack so he probably added enough G to counter all the culture push you added. I've seen this many times. He may have 10 units in that city which would diminish the flip chance.

Basically if a city which you attack does not flip within 20 turns it will probably not flip for a long, long time. I tried a cultural attack against an enemy city and I gave up after 50 turns or so. After 50 more turns he flipped both my attacking cities.

 

[Shabbaman]

Originally posted by Shabbaman
Cc=2 (probably)

I made a mistake here: 2 is if foreign civ has more local culture than you, 1 otherwise, so it's 1! Since the foreign civ is the local civ.

That lowers the chance again, of course.
Plus, if what Yndy says is correct, there might be a bunch of defenders...

P = ((18 * 1* 1 * 2 )- 10)/2 = 13

 

[TheNiceOne]

Shabbaman, you made a few errors in your calculation, so I'll try as well, starting with:
P=[(F+T)*Cc*H*(Cte/Cty) - G]/D

F=0
T=17 (I guess he meant that the city had 3 in addition to the actual city square).
Cc=1 (2 means that you have generated more culture than the Persians in that city, which you obviously havent).
H=1 (No WLTKD or Civil Disorder)
Cte/Cty = 2 (You have twice as much total culture)
G=3 (I'll use your number)
D=4000 (D must be a number between 500 and 8000, and its formula is probably 2000*Dy/De, capped at 500 and 8000. With your capital (Dy) twice as far away as the Persian, this becomes 2000*2/1 = 4000).

This gives:
P = (17 * 1 * 1 * 2 - 3) / 4000 = 0.00775

P is now the chance that it will flip any given turn, i.e. 0.775% chance of a flip each turn, which means that on average, it will take it 129 turns to flip.

So there's no cities that should flip. It has a very small chance of flipping each turn. Sometimes you're lucky and get the flip after a turn or two, and sometimes you'll never see the flip. It's still 20% chance that it will not flip for the next 500 turns.

Flips works best early on if you manage to make a swift culture lead. It is possible to have 10 times higher culture than an opponent early on. If this was true, the above formula would instead become:
P = (17*1*1*10-3) / 4000 = 4.2% chance of a flip each turn.

 

[Shabbaman]

Thanks, very nice indeed!
I see I interpreted the brackets wrong, and I'm glad you explained the distance modifier. This way, the chance produced makes more sense

 

[darious001]

Umm, it had only one guy there for a very long time. My total culture, well, it's about ten times the amount of the three other countries combines. More like six, but close enough. There's about five guys in there now, and the city is sporting five other tiles, besides the one it's on.

 

[darious001]

I did the calculations. More questions arise.

P=[(F+T)*Cc*H*(Cte/Cty) - G]/D

where:
P = probability that it will flip this turn
F = # foreignors, with resistors counting double
T = # working tiles under foreign control
Cc = 2 if foreign civ has more local culture than you, 1 otherwise
H = .5 for WLTKD, 2 for disorder, 1 otherwise
Cte = Total culture of the foreign civ
Cty = Total culture of your civ
G = # garrison units
D = factor based on relative distance to capitals

P=
F=10
T=5
Cc=1
H=1
Cte= .7 millimeters 1594.65
Cty= 14 31893
G= 3
D=11/7 1.5714

[(10+5)*1*1*(1594.65/31893{This was the best I could get, it comes to about .05})-3]/1.5714 {It‘s eleven away from mine, and 7 from the other.}=-1.431844215349369988545246277205 {That might explain it, the number is negative.}


Did I mess up, or did I cause an anomaly in the game.

 

[Shabbaman]

Hey, quick response: chances can't be negative! You screwed up, obviously!

EDIT:

P=
F=10
T=5
Cc=1
H=1
Cte= .7 millimeters 1594.65
Cty= 14 31893
G= 3
D=11/7 1.5714

F=10, means that there are 10 citizens with another nationality than the civ the city currently belongs to. I think in your case, F=0

EDIT:
Darious, you misinterpreted the formula: where in the text is mentioned 'your' civ, is meant the civ who the city belongs to. I've used a spreadsheet to calculate it, with the following values:

f	0
t	5
cc	1
h	1
cte	31893
cty	1595
g	3
d	3142.857143

Then, P=0.030, or about 3%

 

[darious001]

Alright, updated, it comes to about -8.7501590938017054855542828051419e-4

That's with the new distance number. Which is 3142.8.

 

[Shabbaman]

Nice one
If you meant 17 tiles under YOUR control, the chance is more like 10% btw.

 

[darious001]

Thanks for the help. Should have flipped by now still.

 

[Thierry]

Another consequence :

To prevent Flipping you must have the probability = 0
=> With the same culture, for one of your city, you must have :
G = T + F !

Or in general G = (T + F) * Your culture / Their Culture

So, with has many units has their are foreigners or denied squares, you run no risk...

Whatever the distanc from your palace !

Interesting, I often thought that when I settled a very distant city in a foreign 'hole' it would easily flip... It seems distance makes it faster, but doesn't change the balance...

With 4 more culture, you can have a small city safe with 3 units (which you would put in garrison anyway on a distant isolated outpost)

 

[TheNiceOne]

Since you have that much higher culture, it should flip soon. With 15 tiles under your control (20-5 is 15, right?) and 5 military units, the chance is still 9.3% each turn, if your distance and culture ratios are correct, which means that on average it will take you 11 turns before the flip.

Thierry: You're correct, but note that for captured cities, you need twice as many military units even after any resistanse/civil disorder is over, since the enemy has produced more culture than you in that city.

 

[Gothmog]

Re TheNiceOne: where did you get this info?

Quote: " D=4000 (D must be a number between 500 and 8000, and its formula is probably 2000*Dy/De, capped at 500 and 8000. "

I have been looking around for the base value of D (the inverse of the chance of a flip with all other things being equal) with no success, although I know I saw it somewhere before. You are saying the base chance is 0.05%, which sounds about right to me. Also where did you get the 500-8000 cap? This corresponds to the distance value only ranging between 1/4 and 4. Is this in the editor somewhere or what?

Thank you for this piece of information, but I would like to know how you arived at it.

 

[Thierry]

So, for a captured city, once you've starved it to size 1, and once it's no longer surrounded by ennemy cities, 2 units is enough, if you have the same culture as the ennemy ?

 

[Shabbaman]

Originally posted by Thierry
So, for a captured city, once you've starved it to size 1, and once it's no longer surrounded by ennemy cities, 2 units is enough, if you have the same culture as the ennemy ?

Look at this, from the previous example, with somewhat altered stats:

f	1
t	0
cc	1
h	1
cte	15000
cty	15000
g	1
d	3142.857143

With 1 garrisoned unit, the chance of a flip is equal to 0. That's right, the big O!

Note that distance doesn't matter here, since the numenator is 0.

 

[JAWiseman]

What excactly does this mean:
"T = # working tiles under foreign control"

Is that the number of tiles of encroachment of enemy cultural border, or number of squares in the encroaching cultural border than are actually being worked by the enemy?

The word "working" in the definition confuses me...

 

[DaveMcW]

Shabbaman:
In the captured city example Cc=2. Thierry is correct.


JAWiseman:
The closest 20 tiles to a city count towards a culture flip. It is impossible to work a foreign-owned tile.