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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.
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.
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