Research: the abilities of agents

[therother]

All right then, first research thread. This is the placeholder for the final results of this examination of the various abilities of agents.

[RedKnight]

Major update Nov. 12:

1) When you move spies into foreign cities (including allies! aha!), their Public Order goes down - watch and see.

2) P.O. goes down by 5% for each "eye" you have in the city (each spy-skill eye) to a maximum of 50%. Thus only the first 10 eyes matter. The number of spies does not - two 6-eye spies will only get you 50%, as will five 2-eye spies. This makes skilled spies a lot more cost effective vs. maintenance (100/turn).

3) While there's a 50% cap on spy Unrest, there's also an 80% overall cap on Unrest. So if the city is already in great turmoil, you may not get a full 50. Also, some traits (and buildings?) ward off Unrest, and can "eat" your first few eyes.

4) 1-eye spies become 2-eye on successfully entering a foreign city (including allied cities), thus causing 10% Unrest. Apparently it's like MTW command stars - the first successful action gives a promotion (and after that, they're harder to get). The initial city status screen will only show a 5% drop in P.O. but if you check again, you'll see it down by 10. Apparently the skill increase happens after the city screen pops up.

5) If there are "third party" spies in a city, they do not affect your success rate. For example if I as Julii spy on a German town that has a Brutii in it, the Brutii is ignored for success purposes. (Makes sense.)

6) If there are no indigenous spies in a city, a 1-eye spy will have a 93% success rate, and all others 100% success. If there are enemy spies in the city, the success rates will be worse, as follows:

                       My Skill

 Their   1    2    3    4   5    6    7    8    9    10
 Skill  --   --   --   --  ---  ---  ---  ---  ---  ---
    1   55   75   89   97  100  100  100  100  100  100
    2   40   57   71   83   91   97   99  100  100  100
    3   32   46   59   69   78   86   92   96   99  100
    4   26   39   49   59   68   75   82   88   92   96
    5   22   32   42   50   59   67   73   79   84   89
    6   19   27   37   45   52   60   66   71   77   82
    7   17   24   32   40   46   53   60   65   70   75
    8   15   22   29   35   42   48   55   60   65   69
    9   13   20   26   32   39   45   49   55   60   65
   10   11   19   24   29   35   40   46   50   55   60




(garbage text to make the window tall enough to see what matters, sigh)

For example, if I have a spy with 3 eyes and see a 42% success rate, I know he's got a spy with 5 eyes there.

These rates are for ONE indigenous spy.

NEWS FLASH - In my test game platform, I was working Brutii against Julii. A little playing around showed that Gauls have, for a 1-eye spy vs. a city with no indigenous spies, 75% success for a 1-eye, 93% for 2 eyes, and 100% for 3. When Gauls have spies there, the numbers are likewise slightly elevated. Conversely, Carthage did not have these slight increases. My preliminary guess is that there's a "cultural difference" that slightly increases the odds versus some races.

Before I spend tons more time on this, I want to figure out the spy-vs-spy equation for the simple matrix above. I bet the rest is simple variations of it. However, I can't figure out a simple equation for it, can you? For a discussion, I've posted a question in the Compuserve Science/Math forum here (I think you have to make a free account to join in, but they won't spam you and you don't need to install anything - there are some great math brains there).

7) Multiple indigenous spies will cause different rates which are more than the max single spy; preliminary testing shows it to be about halfway between the single highest spy of the lot, and the total eyes. While I've got some data, I want to discover the single-spy equation before proceeding. (There are tons of combination, while the 100 datapoints of the single spy matrix took hours of game research! With a working single-spy equation to start with, I should think multiples would only need a few points to see its nature.)

7) Public Security traits (and buildings? are there any?) affect spy entry success - it is the only thing I have found so far that can affect it (I've tested Personal Security, Law, Unrest, and a host of other things - no effect). (However, if a governor has a trait which eats a few Unrest points, you may not cause Unrest with your first few eyes.) Traits with Public Security are as follows (research TBD re: how much points matter, but it's probably like 1 eye each):

   Group / Level Names / Effect Value

   CounterSpy
      Counter-Spy        +2
      Counter-Espionage  +3
      Spycatcher         +4

   Unjust
      Judgemental   +1
      Wrong-headed  +2
      Unjust        +3

   Xenophobia
      Distrusts_Outsiders  +1
      Hates_Strangers      +2
      Loathes_Foreigners   +3

   Xenophilia
      Welcoming_To_Foreigners  -1
      Likes_Strangers          -2
      Fascinated_By_Outsiders  -3






(garbage text to make the window tall enough to see what matters, sigh)

8) Spies in the "open field" (on campaign map, alone, not in cities or armies) have much steeper rates than those in cities, as follows. These are for Brutii vs. Julii:

                       My Skill

 Their   1    2    3    4    5    6    7    8    9   10
 Skill  --   --   --   --  --    --   --   --   --   --
    1   22   32   43   52   60   67   75   80   85   89
    2   11   17   22   27   32   37   43   48   52   56
    3    5    9   13   17   20   24   27   29   32   35
    4    3    5    9   11   13   15   19   20   22   24
    5    1    3    5    7    9   11   13   15   15   17
    6    1    3    3    5    7    7    9   11   11   13
    7    1    1    3    3    5    5    7    7    9    9
    8    1    1    1    3    3    3    5    5    7    7
    9    1    1    1    3    3    3    3    5    5    5
   10    1    1    1    1    1    1    3    3    3    5




(garbage text to make the window tall enough to see what matters, sigh)

9) In my current game, I have 15% Unrest in a dozen of my cities. At first glance, this would suggest that there were exactly 3 eyes' worth of spies in all these cities, but the Control cheat showed me that there wasn't a single spy in them. So if you see exactly 15%, it probably doesn't mean an enemy spy (although it could) - there seems to be something else that causes 15% in the game. Others have also seen this (see here) - possibility it is a "permanent cultural difference". If anybody has ideas, speak up!

More to come! Spy on - and give your exotic dancer a whirl for me.

[Tamur]

Nice info, thanks! I ran a couple of tests tonight and for some reason after four turns, public order began to go up again at 5% per turn (over four more turns, until I laid seige to the place in question). I know that during this time, the following did NOT change:

- the garrison of the enemy town
- the public order buildings in the town
- the number of enemy spies in the town

so that effect must be something besides these factors I'll do more checking as I have time.

Also, as I had guessed (but never taken the time to research), diplomats and diplomatic activity seem to have no effect at all on public order.

[R'as al Ghul]

I just checked back in froggies guide but this isn't mentioned there:
Sabotage:
Having a spy in a town you wish to sabotage is not only good in respect of intelligence provided about the buildings, but it also seems to increase your chances of sabotage. My current spy/assassin team in the region of Antiochia/ Damaskus/ Palmyra (plenty of work here!) is doing very well. While the 6-eye spy checks out the settlement and provides some good unrest, the assassin waits outside the town. (Assassins who don't kill or sabotage in a turn are practically wasted money.) As long as there's no enemy spy in this town, sabotage-chances are 100% for this combo. If there's a spy, he has to die first. Otherwise he will work against your odds of sabotage.
While killing off enemy generals is cheesy (AI needs all the help it can get), enemy troop facilities are fair game. Especially when they are egyptian.
However, an experienced assassin will not only damage a building to a certain percentage, making the repair quite cheap, but will completely destroy (100%) the building, so that a repair costs as much as a new one. You can really wreak havoc on your enemy this way. Not only will he need money to repair, but he cannot produce until repaired or you will have weakend his economy by sabotaging trade buildings or you will bring down public order by sabotaging happiness buildings plus dropping a spy in there. Very Nasty.

BTW, agents are expensive and should be moved with caution. From turn 2 until about 230BC I had a Seleucid spy standing near Seleucia (he was thrown out when I captured the city). Until now I've wasted 2-3 assassins and two spies on him. The little bugger won't die. I'm now training an experienced one to get rid of him, by the time he will probably have died anyway.

R'as

[Fridge]

What's the best way of training assasins?

I know going after rebel captains and army captains works, but do agents get retinues from staying in cities with Academies etc.? And for an untrained assasin, what's the best way of increasing his skills, sabotage or assasination?

Second question - what's the best way of stopping your armies (assuming no general) being bribed? Carrying a spy with them? Or a diplomat?

[Sinner]

All the agents can pick up ancilliaries from settlements with the appropriate buildings.

As far as training up assassins, now that you mention it I can't recall ever having one improve after a sabotage mission. That could just be circumstance, but maybe it's a bug or design feature, I'll check when I get home.

[*Ringo*]

As far as training up assassins, now that you mention it I can't recall ever having one improve after a sabotage mission. That could just be circumstance, but maybe it's a bug or design feature, I'll check when I get home.

I've had assassin's traits increase on a sucessful sabotage.

Second question - what's the best way of stopping your armies (assuming no general) being bribed? Carrying a spy with them? Or a diplomat?

I'd like to know this also as refusing a bribe can lead to the "True Roman" trait line... which is very useful.

*Ringo*

[therother]

Second question - what's the best way of stopping your armies (assuming no general) being bribed? Carrying a spy with them? Or a diplomat?

This is an open research area. It seems that a spy simply adds cost to the deal: the higher the valour, the more he costs. Culture may also play a part in the cost. Assassins do a similar job.

It's slightly different for a diplomat, as someone who has 4 less negotiation skill than him can't bribe him. (There have been suggestions that this bribe shield may extend to family members as well - Edit: Tamur has now confirmed this here). So a high valour diplomat not only adds a fair amount to the bribe cost, thereby making it less attractive, he also provides a complete bribe shield against much less experienced diplomats.

There is preliminary info in my posts at the bottom of this thread.

Edit:

I've had assassin's traits increase on a sucessful sabotage.

Do you know what kind of trait increase it was, i.e. from which spying trait branch?

[mfberg]

What's the best way of training assasins?

Enemy/Neutral/Allied Diplomats are good training and the world is full of them. Assassination success level depends on subtlety vs. influence.

mfberg

[Quillan]

Like others, I have never had a skill increase from a successful sabotage. As to training assassins, I find that captains are an easier target than diplomats, so I usually start with captains and then move to diplomats once the agent has gained a couple of points of skill.

[RedKnight]

Anyone interested in Spy info, see where I just did a major update to my message (second in this thread). I'm editing in place so that things don't get spread all over - this is what we should do in these research threads. However, edits don't cause an email notification, so I'm tacking this on, for those interested. Therother is checking with Tosa to see if it might be possible for edits to cause a notice.

TGIF

[zhuge]

                       My Skill

 Their   1    2    3    4   5    6    7    8    9    10
 Skill  --   --   --   --  ---  ---  ---  ---  ---  ---
    1   55   75   89   97  100  100  100  100  100  100
    2   40   57   71   83   91   97   99  100  100  100
    3   32   46   59   69   78   86   92   96   99  100
    4   26   39   49   59   68   75   82   88   92   96
    5   22   32   42   50   59   67   73   79   84   89
    6   19   27   37   45   52   60   66   71   77   82
    7   17   24   32   40   46   53   60   65   70   75
    8   15   22   29   35   42   48   55   60   65   69
    9   13   20   26   32   39   45   49   55   60   65
   10   11   19   24   29   35   40   46   50   55   60




(garbage text to make the window tall enough to see what matters, sigh)

Before I spend tons more time on this, I want to figure out the spy-vs-spy equation for the simple matrix above. I bet the rest is simple variations of it. However, I can't figure out a simple equation for it, can you? For a discussion, I've posted a question in the Compuserve Science/Math forum here (I think you have to make a free account to join in, but they won't spam you and you don't need to install anything - there are some great math brains there).

7) Multiple indigenous spies will cause different rates which are more than the max single spy; preliminary testing shows it to be about halfway between the single highest spy of the lot, and the total eyes. While I've got some data, I want to discover the single-spy equation before proceeding. (There are tons of combination, while the 100 datapoints of the single spy matrix took hours of game research! With a working single-spy equation to start with, I should think multiples would only need a few points to see its nature.)

I'd like to know if there's any progress on deciphering the data for success rates of spies when pitted against enemy spies.
Fully agree that getting a rough idea of the general formula would be very helpful so that we can extrapolate it for more complex cases.

I've looked the general formula provided by Jim Irwin in the forum you linked but I couldn't reason out how he arrived at that. Well, I'm no mathematician in RL, anyway...

Looking at row 5 and comparing the differences between the values yield: 10, 10, 8, 9, 8, 6, 6, 5, 5 which appears to indicate that rounding up/down may make quite a difference as I would have expected a smoother decline.
Values generated by smooth curves will be in decimals and that rounding up/down issue may cause substantial disparities.
For example, for row 1, although the last few figures are all the same: 100, this may be just a manifestation of rounded up values near an upper asymptote for sigmoid or inverse hyperbolic tangent curves.

I've dabbled with sigmoid (for probit analysis) and inverse hyperbolic tangent curves before, but I think they may not be applicable here, or need to be heavily modified. As you've mentioned, the curves do not appear symmetric...
Some kind of curve fitting tool would be nice I think. Wonder if Mathlab or some other application might help?

Hope we can make some progress. I think it's a tough problem to crack.

[RedKnight]

I've kicked it around a fair amount and found a very good parabolic fit vs. lone spies in cities, but unfortunately it doesn't work well at all for spies in open field. Let me post it here, and maybe it'll spark insights.

My big clue into the workings came from, not Jim Irwin's idea on Compuserve, but by plugging the terms from Excel's polynomial regression equations from my spreadsheet into a quadratic equation editor such as found here. If you plug in the terms for the first five rows (each curve is My Spy Skill from 1 to 10; the first five rows are vs. TheirSkill 1...5), you'll find that they are going something like

(X+1)(X-6)
(X+1)(X-11)
(X+1)(X-16)

etc., where My Spy Skill is X... but the equations have a constant in front of them ("A" in the quadratic) that I couldn't make much sense out of.

Note: I cut off the curves, for the graph, at the point where the value reached 100 (for TheirSpy=1 and 2). More on this later.

The second clue was when the quadratic page reminded me I could take the derivative of the equation and find it's maximum - interestingly, the maxima of the first five curves were 5, 7.5, 10, 12.5, and 15 (it was moving to the right by 2.5 each time). Eventually it dawned on me that this constant "A" was in fact simply the value of Y at maximum X - in other words, the equation's results at the highest point on the parabola. By using this as a denominator, you lock the results into being 100 at their highest point.

Terms:

M = My Spy Skill
T = Their Spy Skill
A ~ 1 = First constant (in left hand term)
B ~ 5 = Second constant (modifier in right hand term (RHT))
C = 1 = Third constant (added to T in RHT)
D = 1 = 4th constant (added to RHT)

as follows.

First, the governing equation:

(M+A)(M-((B(T+C))+D) (Eq. 1)

Then the denominator simply needs to be equal to the maximum value that the numerator can reach; this will cause it to be 100% at the maximum (top of the parabolic arc). So we take the derivative with respect to M (omg! calculus in the real world?? nah - RTW is just a game!) then solve for M to get its value at maximum:

Multiply terms so we can get derivative:

=(M+A)(M-((B(T+C))+D)
=(M+A)(M-(BT+BC+D))
=(M+A)(M-BT-BC-D)
=M^2-MBT-MBC-MD +AM-ABT-ABC-AD

derivative with respect to M is:

2M-BT-BC-D+A (Eq. 2)

Solve for M:

0=2M-BT-BC-D+A
-2M=-BT-BC-D+A
2M=BT+BC+D-A
M=(BT+BC+D-A)/2 (Eq. 3)

This shows the point where M is a maximum. So we plug this into the equation, IOW, substitute the value of M (from eq. 3) into eq. 1, as the denominator. Or:

Eq. 1
-------
Eq. 1, substituting eq. 3 for M

let's simplify the denominator a little:

Eq. 1, with Eq. 3 substitued for M:

= (Eq3+A)(Eq3-((B(T+C)+D))
= (Eq3+A)(Eq3-BT-BC-D)

= (( (BT+BC+D-A)/2 )+A)(( (BT+BC+D-A)/2 )-BT-BC-D)

put 1/2 in front of each term, so you can multiply the insides by 2:

= 1/2*(BT+BC+D-A+2A) * 1/2*(BT+BC+D-A-2BT-2BC-2D)

notice how a lot of stuff gets subtracted in the second parens...

= 1/4*(BT+BC+D+A)*(-BT-BC-D-A)

pull out the negative and behold, you have a square...

= -((BT+BC+D+A)^2)/4 (Eq. 4)

Final equation (Eq 1 divided by Eq 1 with Eq 3 subbed for M) is:

(M+A)(M-BT-BC-D)
= -----------------
-(BT+BC+D+A)/4

-4(M+A)(M-BT-BC-D)
= -----------------
(BT+BC+D+A)^2

In all my playing, I found that C and D both always equal pretty much 1, so this simplifies (for lone spies in cities, only!) to:

-4(M+A)(M-BT-B-1)
= ----------------- (Eq. 5)
(BT+B+1+A)^2

For a rough approximation, I found that A=1 and B=5 was quite nice. However, by successive aproximation, the best fit I could get (least error vs. game data) was A=.975 and B=5.2. I figure that 1 & 5 may be right from the programming perspective, but small rounding errors in the bowels of the equation, too little for the developers to worry about, made this second set be a better fit. (That or the equation is actually a lot more complicated - but in small ways that don't make much difference, and which could be very hard to pick out.)

An example of the equation at work: For My Spy Skill (M) = 1 and Their Spy Skill (T) = 1, Eq. 5 is:

-4(M+A)(M-BT-B-1)
= ----------------- (Eq. 5)
(BT+B+1+A)^2

-4(1+1)(1-5*1-5-1)
= -----------------
(5*1+5+1+1)^2

-4*2*(1-5-5-1)
= -----------------
(5+5+1+1)^2

-4*2*-10
= --------
12^2

80
= ---
144

= .5556

versus actual game value of 55, for Me=1 and Them=1.

Also you have to programmatically cut off values when they reach 100 - but this is easy because you can compute the location of the maximum via Eq. 3 and see if you have exceeded it. E.g. for Row 1 (T=1):

M=(BT+BC+D-A)/2 (Eq. 3)
=(5*1+5*1+1-1)/2
=(5+5)/2
=5

which we can readily see is indeed the place where Row 1 goes to 100.

Like I said, these fit the game data extremely well for lone spies in cities - but fall on their face for spies in the open. For one thing, there's so little data in the Spies In Open matrix that Excel has trouble generating regression lines. (Little vertical movement, and lots of stepstairs due to being in single digits a lot.) So I can't see any pattern from their quadratic results. I tried playing with them a lot but still can't make it fit.

I left my spreadsheet at work, where I have all this math plugged in - I'll post it come next week.

A couple more things -

* I have a testbed game with Julii and Brutii each having ten spies of skill 1 to 10. If anybody wants a copy, email me at mikestar@speedfactory.net (which will make replying easy).

* In my original big post (with the raw data), I made a FLASH concerning how Gauls are different (and other cultures may well have other levels of difference, too). The above equation may easily extrapolate to them; you can see how Gaul's no so different. Spies in Open Field seem to be an especially tough case. I wish I had time to collect data vs. e.g. Gaul, but I won't in the next few days. (You'd probably have to jack around Gaul's spies' skills, or whatever other races you wanted to test versus.) For what it's worth, I was thinking this might be linked to the permanent 15% unrest discussed elsewhere - like, some game value essentially meant "there's +1 Culture difference for Julii vs. Gauls, which means all Gaul cities have +15% unrest, and all spy attempts are shifted slightly harder by tweaking the equation x amount" - but the discussions suggest that the 15% is not faction specific; it's city specific. So it leads to a question of whether this shift in the spy values is versus cities or factions. If it is versus factions, there has to be a faction-vs-faction table somewhere. Anyway, I wouldn't be surprised if C or D are what is changed, or maybe A or B is bumped up or down by 1.

[lottrbacchus]

spies and assassins get ancillaries from temples of fun, bardic circle, and awesome temple of justice (lol). they have to stay there for a whole turn to have a chance. it's usually 15% per turn.

assassins also have the chance to pick up an ancillary after a successful assassination, and a 10% chance of getting a poisoner if someone unsuccessfully tries to knock off your assassin and some other conditions are met.

assassins are SUPPOSED to get from 1-3 points in goodconspirator from sabotage, but i haven't seen it. maybe i need to experiment more and pay closer attention.

2 points of goodconspirator gives you +1 subterfuge, so 2 successful sabotage missions should give you the trait 'plotter' (i think). then you need 4 and 8 points to get +2 and +3 subterfuge.