Testing how often rebels auto take the fort

[unmerged(6159)]

On occasion a revolt will lead to the rebels automatically taking the fort in the province rather than their having to beseige it. It ahs been repeatedly suggested that it would be nice to have some real data on how often this happens. The only real hints (from Johan) that we have are that it depends on the fort size, and the revotl risk. It has been suggested that it also depends on the number of rebels, although I'm not sure where this suggestion originated.

Because I really would like to get to the bottom of this I've started running some tests to establish how the probability of the fort falling to the rebels (which I'll call Pf) can be calcualted. This is ongoing work, I'll report it as I do it (I did all the stuff reported here yesterday).

My working hypotheses are
-Pf depends on fort size
-Pf depends on revolt risk
-Pf is independent of everything else. I'm keeping track of other things in my tests (province identity, preseince of an army or rebels, presence of leaders etc.) but I expect that these things don't matter
-Each of these relationships is linear and there are no cross terms

My current tentative conculsions are
1) When revolt risk is 0% rebels never take the fort.

My current guesses are
1) For minimal forts Pf is equal to the revolt risk
now proven wrong
2) For minimal forts Pf is equal to double the difference between the revolt risk and 3%.
also proven wrong
3) For minimal forts Pf is equal to the lower of:
-Double the difference between the revolt risk and 3%
-40%
Did not work for 5% revolt risk
4) For minimal forts Pf is equal to the lower of:
-Double the difference between the revolt risk and 2.5%
-40%
Cap niow shown to be higher than 40%
5) For minimal forts Pf is equal to the lower of:

• Double the difference between the revolt risk and 2.5%
• 42%

6) Pf at 100% revolt risk for a minimal fort is below the cap (estimated to be 42%)

NOTE: To be updated as I proceed.

update 1. First guess wrong
update 2. Second guess wrong
update 3. Third guess looking dicey.
update 4. Cap estimate wrong

 

[unmerged(6159)]

Method

I need to accululate a lot of test results to be able to get an accurate estimate of Pf. My procedure is to set up the conditions I want to test (revolt risk and fort size) and to fire off an event that causes lots of revolts. The results are then easily seen by the pop-ups - national shield means the rebels did not take the fort, rebel shield means they did.

I've chosen France in 1492. Lots of provinces with a range of properties, all the same religion, mostly state culture, lots of minimal forts. To increase the number of tests I fired a home made event in Jan 1492 that has France inherit Alsace, Strassbourg, Brittany, Savoy, and Navarre. I forgot that France is missing some shields.

So I have 27 provinces that revolt each time I fire the event from the console. Provinces that have properties that are different from the rest are:
-Alsace, which has 3% nationalism, 1% wrong culture revolt risk, and a 4/1/0 army in it. I've treated it as an independent test at a different revolt risk
-Morbihan, Bearn, and Armor, which have 1% wrong culture revolt risk. I've treated them as independent tests at a different revolt risk
-Bretagne, which has the 1% wrong culture revolt risk and a 6/1/0 army. I've also treated it as independent tests at a different revolt risk
-Savoie, which has a small fort, and 3% nationalism. I'm tracking these results, but doubt I'll make much use of them
-Ile de France which has a medium fort, -2% revolt risk for being the capital, and an army of 18/9/0 with Foix in command. Again unlikely I'll use the results from here.
-Languedoc which has an army of 22/5/0 with la Palice in command. I assume that I can use these results.
-Lorraine, which has a 9/1/0 army in it. I assume that I can use these results.

I know that I could disband the armies, but I'd rather keep them around and accumulate data.
I should perhaps add Gaelic, German and Basque culture to France. I may do this to get more results going forward.
I suppose I could also clear the nationalism. Not sure this is worthwhile either.

Between trials I exit EUII. As I understand it this is the ONLY way to reset the random number seed. I have used surrender and load for the first test of a sequence, but subsequent tests are always after quitting EUII.

I assume that the displayed revolt risk is correct.

 

[unmerged(6159)]

First Results

Without changing anything I fired the event 7 times. This gives me 175 revolts with 0% revolt risk. 161 of the revolts are with minimal forts. After 7 tests I got sick of this one.

The rebels did not take the fort once.

My tentative conclusion is that if revolt risk is 0%, the rebels never take the fort.

At a 95% confidence level this means that the probability of the rebels taking the fort when revolt risk is 0 is less than 1.84%

edit: Added statistical numbers

update 1: Fired the event another 6 times, for a total of 13 times. As a result I have 338 revolts with the rebels never taking the fort. At a 95% confidence level the probaility of them doing so in this scenario is now less than 0.88%. I'm going to stop testing this and call that zero.

 

[unmerged(6159)]

Second Results

I adjusted the catholic tolerance slider to get 5% revolt risk in France. On the slider change Berri and Gascogne revolted. In neither case did the rebels take the fort. I saved this game, and ran 13 tests from the console. The results are:
Test 1: Fort taken in Armor
Test 2: Forts taken in Picardie, Nivernais, Maine and Languedoc
Test 3: Forts taken in Poitu, Morbihan, Bretagne and Alsace
Test 4: Forts taken in Limousin, Nivernais, Champagne and Alsace
Test 5: Forts taken in Cevennes and Armor
Test 6: No forts taken
Test 7: Gascogne
Test 8: Normandie
Test 9: Lorraine, Guyenne, Berri
Test 10: None
Test 11: Morbihan
Test 12: Normandie
Test 13: Morbihan, Dauphine, Armor

Overall I have 275 revolts with minimal forts at 5% revolt risk. 16 times the fort fell. The ratio is therefore 5.82%. There are also 52 revolts with minimal forts at 6% revolt risk. 7 times the fort fell.

I then went back to the original save, and adjusted the tolerance slider to get 7% revolt risk. I had to do this a few times to avoid having 4 or 5 rebel armies on the map in my test save. Ultimately I had a change where there was one revolt in Vendee, and the fort didn't fall. This I then saved and ran 13 tests from the console. The results are:
Test 1: Fort taken in Bretagne
Test 2: No forts taken
Test 3: Champagne and Alsace
Test 4: Poitu, Morbihan, and Bourgogne
Test 5: Nivernais and Auvergne
Test 6: Languedoc
Test 7: Dauphine, Cevennes, Bearn
Test 8: Berri
Test 9: Morbihan, Lyonnais, Auvergne, Armor
Test 10: Savoie, Poitu, Orleannais, Morbihan, Auvergne, Alsace
Test 11: Bearn
Test 12: None
Test 13: Maine, Gascogne, Alsace

Overall I have 274 revolts with minimal forts at 7% revolt risk. 16 times the fort fell. The ratio is therefore 5.84%. There are also 52 revolts with minimal forts at 8% revolt risk. 7 times the fort fell.

So the beliveable results are that at 5% we have 5.8% chance of the rebels taking the fort, and at 7% we have a 5.8% chance of the rebels takign the fort. From the binomial distribution the uncertainty in each of these numbers is 1.4%. At the 95% confidence level we can rule out that Pf for either revolt risk is greater than 8.6% or lower than 3%.

My working guess is "For minimal forts Pf is equal to the revolt risk".

Next step is to run tests at revolt risks like 11% and 16% revolt risk, and get more data on the two cases I've already tried.

 

[unmerged(45766)]

I need to accululate a lot of test results to be able to get an accurate estimate of Pf. My procedure is to set up the conditions I want to test (revolt risk and fort size) and to fire off an event that causes lots of revolts.

For that event, I suggest that you make a command line for each of your province, and that you specifically target each provinces by one line. If you use -1 for the targetting, you risk having two or more revolts in the same province, which could give less useful results, as you won't know which of those revolts succeeded in taking the fort.

Well, maybe that's what you're already doing ?


To change the RR, I suggest you use tailor-made events, firing them through the console, to up and down the RR. It's less troublesome than tolerance slider, as each move on it triggers a RR-check.

 

[unmerged(53580)]

I don't know if you already have done this, but you should do several attempts with the same parameters before reaching any conclusions.

 

[unmerged(58610)]

From my experience war exhaustion not only increases the revolt risk but also is taken into account when deciding whether or not rebels get control of the fort. I am convinced one of my 0% provinces revolted and the fort defected when the only factor that could have affected it was war exhaustion. Unfortunately I did not check that the revolt risk was still 0% at the time the revolt occurred.

I believe that rebels will never automatically capture your capital based on observation of my own capital revolts and those in enemy capitals whether under my control or not.

On a gut level, I think the calculation ought to factor in your stability and base morale plus/minus any modifier for your garrison.

 

[unmerged(6159)]

For that event, I suggest that you make a command line for each of your province, and that you specifically target each provinces by one line. If you use -1 for the targetting, you risk having two or more revolts in the same province, which could give less useful results, as you won't know which of those revolts succeeded in taking the fort.

Well, maybe that's what you're already doing ?

Yes that's what I'm doing

To change the RR, I suggest you use tailor-made events, firing them through the console, to up and down the RR. It's less troublesome than tolerance slider, as each move on it triggers a RR-check.

I think I will be doing this. However, it's not necessarily a bad thing to have a couple of cases of pre-existing rebels in the province. I'd bet that this doesn't matter, but having those data points in the data set would (ultimately) allow that assumption to be tested.

I don't know if you already have done this, but you should do several attempts with the same parameters before reaching any conclusions.

I'm not sure what this means. For each of the sets I've listed above I have 13 (or 7) trials from the exact same savegame. So there definitely are multiple tests with the same parameters.

From my experience war exhaustion not only increases the revolt risk but also is taken into account when deciding whether or not rebels get control of the fort. I am convinced one of my 0% provinces revolted and the fort defected when the only factor that could have affected it was war exhaustion. Unfortunately I did not check that the revolt risk was still 0% at the time the revolt occurred.

I won't be testing this any time soon. All the tests I'm listing have zero war exhaustion.

I believe that rebels will never automatically capture your capital based on observation of my own capital revolts and those in enemy capitals whether under my control or not.

That feels right to me too. In 33 tests Ile de France has not fallen yet. On the other hand it has a medium fort too. As I get more data this should be testable. If true it reduces the significance of my first (and only) tentative conclusion, as Ile de France was tested 7 times, and if it can't fall those tests aren't statistically useful.

On a gut level, I think the calculation ought to factor in your stability and base morale plus/minus any modifier for your garrison.

What do you mean by "modifier for your garrison"? Army present in the province? This I will be able to test. I doubt stability is a factor as it already strongly affects revolt risk. All my tests are at the same stablity (I think it's +1, I will confirm). All my tests are at 100% maintenance. It's a fair amount of work to test these, so unless I uncover evidence that I missign something I don't plan to test them. Perhaps I'll run a sequence of tests at 50% maintenance. But given I only have 6 armies present (and two of those are in provinces that don't have minimal forts) it'll take a lot of tests to see if that matters. My guess is that none of these matter.

 

[unmerged(58610)]

In supply, ie connected with the rest of your holdings and that the enemy is not blockading the port, if coastal. The presence of armies either friendly or hostile ought to modify the garrison's ability to hold the fort in the event of a revolt.

Even the month of the year could have a minor effect. You could test whether or not a revolt in the province that previously took the fort automatically takes the fort with a greater than expected frequency.

 

[unmerged(3921)]

Interesting investigation. Issac, I do have some end point observations for you. With revolt risk at levels in excess of 100% (have observed this at over 800% revolt risk), rebels still do not take the fort automatically. Therefore this argues against a direct RR = chance of fort seizure mechanism. It is my anecdotal observation that if there is an army garrison in the province, the chance of fort seizure is lower.

 

[unmerged(45766)]

I think I will be doing this. However, it's not necessarily a bad thing to have a couple of cases of pre-existing rebels in the province. I'd bet that this doesn't matter, but having those data points in the data set would (ultimately) allow that assumption to be tested.

Indeed, that's another layer of data.

I believe that rebels will never automatically capture your capital based on observation of my own capital revolts and those in enemy capitals whether under my control or not.

That feels right to me too. In 33 tests Ile de France has not fallen yet. On the other hand it has a medium fort too. As I get more data this should be testable. If true it reduces the significance of my first (and only) tentative conclusion, as Ile de France was tested 7 times, and if it can't fall those tests aren't statistically useful.

No, I've already seen capitals falling to rebels immediatly. Several times.

 

[unmerged(6159)]

Interesting investigation. Issac, I do have some end point observations for you. With revolt risk at levels in excess of 100% (have observed this at over 800% revolt risk), rebels still do not take the fort automatically. Therefore this argues against a direct RR = chance of fort seizure mechanism.

Yes. Yesterdays tests proved this. I'll post them later.

It is my anecdotal observation that if there is an army garrison in the province, the chance of fort seizure is lower.

I will be able to test this hypothesis when I have more data. I can tell you right now that it isn't a huge effect.

Indeed, that's another layer of data.

By using the data this way I'm trying to get somethign for nothing. At the risk that the initial results may lead me in the wrong direction.

No, I've already seen capitals falling to rebels immediatly. Several times.

In yesterday's test Ile de France fell nine times, so I can confirm that the capital hypothesis is proven incorrect.

My first report for today is that I ran the 0% revolt risk another 6 times. i now have a total of 325 trials, with the fort never falling. With 95% confidence the chance of a minimal fort falling to rebels when revotl risk is 0 is now less than 0.88%. I'm comfortable calling that zero.

 

[unmerged(11427)]

I look forward to see the results of your test. Nice work so far.

 

[unmerged(58610)]

I am slightly disappointed. You've demonstrated capitals can fall. Still, that's the whole purpose of these tests.

 

[unmerged(6159)]

Third Test

Yes it's all about dispelling illusions. Including my own!

This time I adjusted the catholic tolerance slider to get -5% revolt risk in France, and then fired an event that raises the revolt risk by 5% three times, so that the revolt risk is 10% everywhere that is has French culture, no nationalism, and is not the capital. As such there are no rebels on the map when I fire the test event. I ran 13 tests from the console. The results are:
Test 1: Fort taken in Maine, Dauphine, Berri, and Alsace
Test 2: Forts taken in Maine, Bretagne, and Bourgogne
Test 3: Forts taken in Lyonnais, Langudoc, Cevennes, and Alsace
Test 4: Forts taken in Caux, Bretagne and Auvergne
Test 5: Forts taken in Vendee, Maine, Limousin, Dauphine, and Cevennes
Test 6: Provence, Poitu, Maine, Bourgogne, Auvergne, and Alsace
Test 7: Vendee and Normandie
Test 8: Maine, Lyonnais,Guyenne, and Alsace
Test 9: Nivernais, Langudoc, Guyenne, Berri and Armor
Test 10: Normandie and Limousin
Test 11: Poitu, Langudoc, Guyenne, Caux, Bourgogne, Auvergne, and Alsace
Test 12: Maine, Bourgogne and Bearn
Test 13: Maine and Gascogne

Overall I have 273 revolts with minimal forts at 10% revolt risk. 41 times the fort fell. The ratio is therefore 15.0%. The 95% confidence range for Pf (10% RR, min fort) is between 10.7% and 19.3%. This excludes 10%!

There are also 65 revolts with minimal forts at 11% revolt risk (including Lorraine from the 7% test. 7 times the fort fell.

Next I fired the event that raises the revolt risk by 5% three more times, so that the revolt risk is 25% everywhere that is has French culture, no nationalism, and is not the capital. Still no rebels on the map when I fire the test event. I ran 13 tests from the console. From here on out I'm giving a three letter abbreviation as LOTs for forts fell to the rebels. The results are:
Test 1: Pic, Orl, Nor, Mor, Mai, Lyo, Lim, Lan, IdF, Guy, Bre, Bou, Ber, Arm, Als
Test 2: Pic, Orl, Nor, Lim, IdF, Guy, Gas, Cha, Cev, Bre, Ber
Test 3: Ven, Sav, Orl, Mor, Mai, Lyo, Lim, IdF, Guy, Cha, Cev, Bre, Ber, Als
Test 4: Ven, Sav, Pic, Nor, Niv, Mor, Mai, Lyo, Lan, IdF, Guy, Gas, Dau, Ber, Bea, Arm
Test 5: Sav, Pic, Niv, Mai, Lyo, Lor, Lim, Lan, Guy, Auv, Arm, Als
Test 6: Ven, Pro, Poi, Nor, Niv, Lyo, Lor, Gas, Cha, Bre
Test 7: Pro, Poi, Orl, Nor, Mai, Lyo, Lor, Lan, IdF, Dau, Cau, Arm, Als
Test 8: Sav, Pro, Poi, Niv, Lor, Lan, IdF, Guy, Gas, Bre, Auv
Test 9: Sav, Pro, Poi, Niv, Mai, Guy, Bre, Bou, Auv, Als
Test 10: Ven, Orl, Niv, Lor, Lan, Gas, Cha, Bre, Bea. Auv
Test 11: Nor, Guy, Cha, Cau, Bre, Ber, Bea, Arm, Als
Test 12: Sav, Poi, Orl, Nor, Mor, IdF, Cev, Bre, Bou, Bea
Test 13: Sav, Pic, Nor, Niv, Mor, Lyo, Lim, Lan, IdF, Guy, Gas, Cau, Bre, Ber, Bea, Arm

Overall I have 273 revolts with minimal forts at 25% revolt risk. 112 times the fort fell. The ratio is therefore 41.0%. The 95% confidence range for Pf(25% minimal fort) is 35.1% to 47.0%. This defintely excludes 25%.

There are also 52 revolts with minimal forts at 26% revolt risk. 26 times the fort fell.

Looking for a new guess as to what the function might be. Has to fit my 5 data points!

edit: typo - RR was 25% for the scond test.

 

[unmerged(45766)]

So, your last string of tests apparently leads to the assumption that PF rises faster than RR, but based on my first-hand knowledge (conforted by others experience of chinese revolts) that even above 100% a fall isn't automatic (at least until 800% RR), Pf is somehow capped.

Graphically, it doesn't look like a simple equation, even one with caps, as it's neither linear nor exponential. o

 

[unmerged(11427)]

Looking for a new guess as to what the function might be. Has to fit my 5 data points!

It seems to be growing faster then linear function at the begining. Steepnes has to be smaller at higher %RR. Someone said that at 100% RR not all forts will fall.

More points are needed.

 

[unmerged(6159)]

To summarize here are the results that have half way decent statistics. Confidence levels are 95%.

0%		0%-0.9%
5%		3.0%-8.6%
7%		3.0%-8.7%
10%		10.7%-19.3%
25%		35.1%-47.0%

The question I'm asking myself is - what sort of function would the person who coded this be likely to use. Would they be concerned about limiting CPU usage? Straight line and exponential are the most obvious functions to use, but these results don't really match either.

I gave this some though and came up with the following wild guess:
"Pf is equal to twice the difference between the revolt risk and 3%"
( I assum there is some sort of cap to explain the problem at 800% revolt risk. But first things first )

This gives the following table

0%		0%
5%		4%
7%		8%
10%		14%
25%		44%

Which has good consistency with my results to date. Of course that means very little as I have only 4 points and the model already has two degrees of freedom.

I have no idea why this function might have been chosen, except for the 3% RR from nationalism. Anyone know if you can lose the fort to purely nationalism rebels? I do have 40 tests at 3% and the rebels have never taken the fort.

Next stop - test 2% revolt risk.

 

[unmerged(11427)]

From the programming perspective, I would choose linear with cutoff at some level (say 80% chance at 100% RR). I would force it to go through (0,0).

%fort taken = a*%RR
%fort taken = MIN(%fort taken,80%)

If CPU time was not an issue I would choose one of the functions with asymptotic line:
1) Inverse tangent (goes through zero and asymptotic line is pi/2)
2) Einstein's forumula for heat capacity at low temperatures (goes through zero and has 1 as asymptotic line)

I would like to know %fort taken for higher %RR, like 50%, 80% and 200%. Maybe we could establish if it is asymptotic or cutoff.

 

[unmerged(760)]

a formular that would fit your empiric data is:

Pf=RR*2-6

though this one is linear, and does not take fort size into account (maybe its +/- X instead of just 6, depending on size?). for the cap i suppose its not directly in the formular, but seperate.

edit: oh i just saw you have assumpted that one verbally....