What is the formula that calculates rebel progress according to unrest?

[bly08]

See title. Seems like a harmless equation to reveal, but is near impossible to derive from experiment.

 

[AVN]

Description given in the wiki

Each month a rebel faction has a chance to make progress towards a full-scale rebellion. The monthly chance that a rebel faction's progress will increase by 10% depends on the amount of unrest in all provinces associated with that faction and the national unrest; maxing out at 75% progress chance. Rebel progress can be found in the tooltip for that faction's progress in the Stability and Expansion tab. If the faction's progress reaches 100%, it will go into open rebellion and spawn troops in some of the provinces that had positive unrest. The tooltip for each faction's progress shows the current progress, monthly chance to increase it, the unrest in all provinces associated with that faction that have unrest greater than 0, and the estimated time until the progress reaches 100% and rebels are spawned.

If none of the provinces supporting a rebel faction has positive unrest, its accumulated progress will begin to decay by 10% per month thereafter. If unrest is then increased for any reason, the faction will resume gaining progress towards rebellion.

It is possible to reduce a rebel faction's progress to 0 at any time by accepting their demands. This will also remove any troops that faction has spawned. The demands are generally quite unpleasant, however, so this is usually an undesirable option unless the rebels have already rebelled or are on the verge of doing so.

It is also possible to check the country's subject's rebellion progress by ticking the box next to the current national unrest on the rebellion's page.

I suppose this info was once revealed by the devs, because I agree that it's near impossible to derive from experiment.
Based on my experiences with the game (I'm currently playing on 1.22.2) I think it's still correct.

 

[Vulkandrache]

Thats not what hes asking.
Its not uncommon to have a dozen provinces with the same rebel type at some 20 unrest.
But their monthly progress chance summs up to maybe 30-40%.
There has to be some steep drop-off point or a step-down function applied once the unrest gets too high in too many places.

 

[iquabakaner]

I don't think it's impossible to derive. You probably just need to record: number of provinces with unrest, unrest value in each province, national unrest?(if it's as the wiki mentioned), and progress chance, (I'm not sure if development in the provinces matters). Probably don't need a lot of samples to derive the equation, since there's no randomness involved.

 

[durbal]

Pretty sure it's just a simple probability function with the chance of success being the sum of all possible successful outcomes' probability.

In other words, if there are three provinces with corresponding unrest:
Province A - 15
Province B - 10
Province C - 5

Then you'd sum up the probabilities of the following outcomes of the D100 die roll being equal to or higher than the unrest level in each province.

Outcomes:

A - Yes    B - Yes   C - Yes ---  (0.15*0.10*0.05) = 0.00075
A - No     B - Yes   C - Yes --- (0.85*0.10*0.05) = 0.00425
...etc...

And iterate through all possible 2^n combinations of success/fail on the die rolls where n = number of provinces, summing probability of all successful outcomes.

 

[Less2]

Pretty sure it's just a simple probability function with the chance of success being the sum of all possible successful outcomes' probability.

In other words, if there are three provinces with corresponding unrest:
Province A - 15
Province B - 10
Province C - 5

Then you'd sum up the probabilities of the following outcomes of the D100 die roll being equal to or higher than the unrest level in each province.

Outcomes:

A - Yes    B - Yes   C - Yes ---  (0.15*0.10*0.05) = 0.00075
A - No     B - Yes   C - Yes --- (0.85*0.10*0.05) = 0.00425
...etc...

And iterate through all possible 2^n combinations of success/fail on the die rolls where n = number of provinces, summing probability of all successful outcomes.

This looks accurate, although you are calculating it in a very inefficient manner. The easy way to do it is to figure out the chance of the event not happening for all 3, then take the opposite of that, e.g.

1- (1-.15)*(1-.1)*(1-.05) = 27.3% chance.

Checking Ming's starting provinces and revolt risks they all come up pretty close with a small margin of error, which I chalk up to revolt risk being calculated to a finer precision than the tenths that are shown.