Well technically its a (theoretical) 50% unrest timer that decreases by potentially more than 1% each turn.
Its a 100% racial factor, which decreases by 2% naturally, or more by adding your own people. Basically each turn the city calculates how many in the city are not your race, and that divided by 2 is the unrest factor.
Season 1. CityX has 20 Quendar and 0 Altarians. 100% race factor, 50% unrest factor.
Season 2. City X has 20 Quendar and 1 Altarian. Assimilation is 2%, so there are (19.58) Quendar and (1.42) Altarians. This represents persons of mixed culture. (really just a convenient explanation for using non-integers, in order to keep the clean and efficient percentage based system)
Presented to the player as 93% Quendar and 7% Altarian.
This gives an additional 47% base unrest (rounded to nearest integer)
Season 3. City X has 19.58 Quendar and 2.42 Altarians. After Assimilation is factored in this becomes 19.14 Quendar and 2.86 Altarians.
Presented to the player as 87% Quendar and 13% Altarians.
Which gives the city an additional 44% base unrest to the city.
Season 4. City X has 19.14 Quendar and 3.86 Altarians. After Assimilation this becomes 18.68 Quendar and 4.32 Altarians.
Presented to the Player as 81% Quendar and 19% Altarian.
Which gives an additional 41% base unrest to the city.
In this case, with a growth rate of 1 citizen per season, and starting with 0% native population, you get an ACTUAL 3% unrest reduction per season as opposed to the theoretical 1% unrest reduction. This is because the city size is so small (only 20 citizens).
It is only when you reach really, really large cities that unrest reduction approaches 1% per season,.
(1% reduction is a minimum, and as city size approaches infinity, it will get closer to a mere 1% reduction. Alternatively, if growth becomes 0 you will always get baseline of only 1% reduction, regardless of starting penalty)
Example 2. (Very large city)
Season 1. City Y has 400 Urxen and 0 Altarians. 100% race factor and 50% unrest factor.
Presented to player as 100% Urxen and 0% Altarians.
50% added to base city unrest.
Season 2. City Y has 400 Urxen and 1 Altarian. Assimilation is still 2%, so we actually have 391.98 Urxen and 9.02 Altarians.
Presented to player as 98% Urxen and 2% Altarian.
49% Unrest (1% decrease!!!)
Season 3. City Y has 391.98 Urxen and 10.02 Altarians. After Assimilation, 383.94 Urxen and 18.06 Altarians.
Presented to Player as 96% Urxren and 4% Altarians
48% Unrest (1% decrease once again!)
Season 4. City Y has 383.94 Urxen and 19.06 Altarians. After Assim, we get 375.88 Urxen and 27.12 Altarians.
Presented as 93% Urxen and 7% Altarian.
As you may be able to see, we are approaching a drop in 2% unrest pretty soon, because obviously we are not yet at infinity. Seeing as this is such a large city, there will almost certainly be a number of growth buildings, which would increase the reduction of Unrest even further. (imagine 2 new altarians per turn, or even 5 new altarians per turn, when added to the "assimilated Altarian" numbers) -> Might not make a huge difference, but as growth increases, reduction of unrest increases as well.
In Example 1, Assimilation had a smaller effect than growth ... therefore we had a reduction of 3% unrest per turn ....
While in Example 2, growth was smaller than assimilation, so we had a reduction of 1% unrest per turn.
I would hypothesize that if Growth and Assimilation are equal, we may see a 2% reduction of unrest per turn.
The reason keeping track of race numbers is important, is for dealing with a "Reconquering" scenario. For instance, if you lost a city 5 seasons ago, and are now taking it back ... You will now have at LEAST 10% foreign population in the city, giving you a 5% unrest penalty.
if you wait too long to retake your old city (say, somewhere between 15 turns and 50 or more turns) you could be dealing with an entirely foreign (entirely assimlated) city ... and you will have to assimilate it back just as long as the conquerors had to do.
Therefore, the longer you wait, the harder it will be to retake lost cities. (economically in any case)
A global penalty for global non-native populations is possible/potentially interesting ... but I am not sure if it is worth it.
Perhaps global racial factor should be added directly? So if your nation is 50% foreign, all cities get +50% unrest? This would be the equivalent of suddenly conquering a nation just as large as yours is.
Depending on several factors ... this would decrease at a rate of anywhere between 1% - 3% per turn (assuming conquered population exaclty equals your own) ... making it a phenomena that can last anywhere between 17 and 50 Seasons
For a war that DOUBLES the size of your empire (over the course of 1 turn), a 17 - 50 season penalty seems fair to me. And obviously, if you are just annexing a comparatively small nation the penalty is far less.
A fitting affect, do you agree?
This included with "Free garrison" units would make defensive armies a bit less costly, while making conquering an "Investment" instead of a "Haha we now win"
On further inspection, this would make a small nation taking over a giant nation extremely costly ... but then again we always have the "Raze" button
If we have Magnar not have any assimilation due to flavor reasons, we should likely reduce their personal conquest unrest factors by half, and have them go away at a fixed rate.
On the other hand, ignoring the Magnar exception, if we have the ability to CASH RUSH slave pens .... ... then we could at least get production out of these new cities
(as Slave Pens would not work on native population, but only foreign, it would only be worthwhile to build them in new cities)
-> If we also go with Slave Pens 'removing the unrest' ... perhaps it should only remove the global unrest. Meaning that you have to choose between assimilating a city long term, or using it solely for production in the short term.
You would have to get rid of the slave pen in order to slowly assimilate the city, but upon doing so you would also get a hit to your global unrest.
In this case, if you conquer a new civ, it might be a good idea to cash rush slave pens in most of the cities, and leave just a few alone ... So that little by little you can slowly assimilate the entire nation without being hit by the global penalty "all at once".
This makes the Slavery tech (or whatever its called) VERY important .... at least for Conquerors. Conquerors that don't just RAZE that is