Found on reddit (!) - https://www.reddit.com/r/civ3/comments/cn6trs/how_to_make_the_probability_of_a_culture_flip_0/ - This entire post is a C&P, and the concluding link is good.
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Culture flips that take cities away from you are frustrating in part because of their seemingly sporadic nature. However, culture flips are not actually random, and it is possible to completely avoid them. I'll show you how.
The formula for determining the probability of a culture flip is:
((ycd / ecd) * (ec / yc) * (fn + to + r) * (hc > cc ? 2 : 1) * (cd ? 2 : 1) * (wlkd ? 0.5 : 1)) - us
// where
// ycd is "Your capital distance"
// ecd is "Enemy capital distance"
// ec is "Enemy Culture"
// yc is "Your Culture"
// fn is "Foreign Nationals"
// to is "Tiles Occupied"
// ycd is "Resistors"
// hc is "Historic Culture"
// cc is "Current Culture"
// cd is "Civil Disorder"
// wlkd is "We Love the King Day"
// us is "Units stationed"
There's a lot to take in here, but luckily most of it doesn't matter. The most important thing to note is that the bulk of this equation is contained in one large product. This means that if we can get just one of the operands to equal zero, the entire equation (excluding units stationed, but this can only ever decrease the probability of a culture flip, so we can safely ignore it) becomes zero. So let's run down the list and find which values could become zero.
Firstly, we can ignore hc, cc, cd, and wlkd because these values are only involved in ternary operations that can't produce a zero.
If we set the distance to your own capital to zero, the probability of flipping becomes zero, which explains why your own capital can't ever flip, but this doesn't help us with the other cities. If you can figure out how to set the enemy capital distance to infinity, then congratulations! You've successfully avoided a culture flip, and not just because the product becomes zero, but also because you crashed the game.
If you can get the enemy culture down to zero, flipping will be avoided. Unfortunately, this can only be accomplished by eliminating them from the game entirely. Not exactly new information there.
The part of the equation that we can actually influence down to zero is the (fn + to + r) section. Foreign nationals, resistors, and tiles occupied can all be taken care of in one way or another. If you have any takeaway from this writeup, remember this: a city with zeros in all three of these categories cannot flip, ever.
For now, let's ignore foreign nationals and resistors which both only exist in captured cities (an exception being if you join a captured worker) and focus on tiles occupied. There are 21 tiles a city can occupy. These are the city center, the 8 tiles in the immediate ring around the city, and 12 more tiles in the outer ring of the city. If all of these tiles are kept within your territory, or more accurately, if none of these tiles fall under enemy territory, the tiles occupied value will equal zero and the city won't ever flip. Conversely, the more tiles you take away from an enemy city, the more likely it is to defect to you. Here's some ascii art demonstrations:
aaa bbb
aaaaabbbb
aaAaabBbb
aaaaabbbb
aaa bbb
In the above situation, city A and B are bordering, but only A could ever possibly flip B, because A occupies 3 potential tiles of B, while the reverse is not true. Again, this is all assuming no foreign nationals or resistors, which require their own topic.
aaabbb
aaaabbbb
aaAabBbb
aaaabbbb
aaabbb
Now one tile closer, B and A both have potential to flip each other, and it will fall to the RNG gods to see which if any flips first.
Finally, here's an imgur album of an in-game demonstration of the tile occupation principles: https://imgur.com/a/d4p33mv
------------------------------------------------------------------------------------------------------------------------------------------------
Culture flips that take cities away from you are frustrating in part because of their seemingly sporadic nature. However, culture flips are not actually random, and it is possible to completely avoid them. I'll show you how.
The formula for determining the probability of a culture flip is:
((ycd / ecd) * (ec / yc) * (fn + to + r) * (hc > cc ? 2 : 1) * (cd ? 2 : 1) * (wlkd ? 0.5 : 1)) - us
// where
// ycd is "Your capital distance"
// ecd is "Enemy capital distance"
// ec is "Enemy Culture"
// yc is "Your Culture"
// fn is "Foreign Nationals"
// to is "Tiles Occupied"
// ycd is "Resistors"
// hc is "Historic Culture"
// cc is "Current Culture"
// cd is "Civil Disorder"
// wlkd is "We Love the King Day"
// us is "Units stationed"
There's a lot to take in here, but luckily most of it doesn't matter. The most important thing to note is that the bulk of this equation is contained in one large product. This means that if we can get just one of the operands to equal zero, the entire equation (excluding units stationed, but this can only ever decrease the probability of a culture flip, so we can safely ignore it) becomes zero. So let's run down the list and find which values could become zero.
Firstly, we can ignore hc, cc, cd, and wlkd because these values are only involved in ternary operations that can't produce a zero.
If we set the distance to your own capital to zero, the probability of flipping becomes zero, which explains why your own capital can't ever flip, but this doesn't help us with the other cities. If you can figure out how to set the enemy capital distance to infinity, then congratulations! You've successfully avoided a culture flip, and not just because the product becomes zero, but also because you crashed the game.
If you can get the enemy culture down to zero, flipping will be avoided. Unfortunately, this can only be accomplished by eliminating them from the game entirely. Not exactly new information there.
The part of the equation that we can actually influence down to zero is the (fn + to + r) section. Foreign nationals, resistors, and tiles occupied can all be taken care of in one way or another. If you have any takeaway from this writeup, remember this: a city with zeros in all three of these categories cannot flip, ever.
For now, let's ignore foreign nationals and resistors which both only exist in captured cities (an exception being if you join a captured worker) and focus on tiles occupied. There are 21 tiles a city can occupy. These are the city center, the 8 tiles in the immediate ring around the city, and 12 more tiles in the outer ring of the city. If all of these tiles are kept within your territory, or more accurately, if none of these tiles fall under enemy territory, the tiles occupied value will equal zero and the city won't ever flip. Conversely, the more tiles you take away from an enemy city, the more likely it is to defect to you. Here's some ascii art demonstrations:
aaa bbb
aaaaabbbb
aaAaabBbb
aaaaabbbb
aaa bbb
In the above situation, city A and B are bordering, but only A could ever possibly flip B, because A occupies 3 potential tiles of B, while the reverse is not true. Again, this is all assuming no foreign nationals or resistors, which require their own topic.
aaabbb
aaaabbbb
aaAabBbb
aaaabbbb
aaabbb
Now one tile closer, B and A both have potential to flip each other, and it will fall to the RNG gods to see which if any flips first.
Finally, here's an imgur album of an in-game demonstration of the tile occupation principles: https://imgur.com/a/d4p33mv
