KY means never having to say you understand

[GraniteStater]

I thought KY defaulted to the Union by Oct 61 or so, if no one grabbed it. In my PbeM with havi, the option was on the screen until Early Dec, so I clicked it finally - forbidden Regions until then, although northern KY was passable.

OK, so I don't understand. One of these days I'll learn how to play this game...

[ArmChairGeneral]

Starting in October 61 the game begins rolling to see whether KY enters and on which side. The chances favor the Union but it breaks for the South a fair amount too. If the event hasn't fired it will eventually default to the Union sometime in Spring 62, around when Corps can be formed.

[Jerzul]

Starting in October 61 the game begins rolling to see whether KY enters and on which side. The chances favor the Union but it breaks for the South a fair amount too. If the event hasn't fired it will eventually default to the Union sometime in Spring 62, around when Corps can be formed.

I thought I saw somewhere on the forum that there is only a 5% chance that KY sides with the CSA.

[GraniteStater]

Yes. I thought if 'Nothing Happened', either way, it defaulted to the Union in the autumn. Seen it before, but, I've been away for a good while.

[Gray Fox]

In the CW2 dBase, the file for KY secession lists a probability of "10", so perhaps 10% and has a window of 1861/08/01 to 1862/01/01.

[GraniteStater]

OK, so it goes until Jan '62. Thanks.

[Gray Fox]

My pleasure. You can download a copy of the dBase files here:

http://www.ageod-forum.com/showthread.php?35005-CW2-Excel-Database&highlight=cw2+dbase+files

[GraniteStater]

No, no! Not data!!!

Aaaarrgh!!! *Flees in horror and then returns to work - writing documents about technical procedures*

I play this to relax and have fun.

[ArmChairGeneral]

Fox, that makes sense. In most AI games it usually enters on one side or the other in the winter of 61. The Union AI doesn't always like to wait, and seems willing to take the penalties (although it doesn't actually do anything useful enough in Kentucky to justify the decision). But we can say concretely from the DB that it cannot go to the CSA at all after January 62.

If I understand the mechanism correctly (and I may not) it rolls each turn to check for secession. If this is the case, then the overall probability Kentucky will secede at some point during the window is higher than the 10% chance it has on each roll. With a 10% chance for success on each roll, on average it will take ten rolls before the first success, and there are ten turns between those two dates. (If the probability were instead 5%, then it would take an average of 20 rolls before the first success.) This would result in a 50% chance that KY secedes in a given game assuming the Union does not intervene. This might explain why the AI likes to intervene so much since it thinks there is an even chance of it going to the South anyway. That said, it does not feel like, in-play, that KY secedes quite that often.

Off-topic: This mechanism is common in computer games partly because it is easy to code and not CPU intensive and partly because the number of rolls before the first success is approximately normally distributed, (bell curve) so from a developer's perspective you get easy to program randomness that is highly predictable and simple to adjust. Paradox's Clausewitz engine (Crusader Kings, Europa Universalis, Victoria, etc.) utilizes it heavily, where they refer to the average number of failures before the first success as Mean Time To Happen.

[GraniteStater]

With a 10% chance for success on each roll, on average it will take ten rolls before the first success, and there are ten turns between those two dates. (If the probability were instead 5%, then it would take an average of 20 rolls before the first success

"Independence of events", if I recall Stats & Probbo 101. It's just as likely (or not) on the first as the tenth, or the nth.

A mother has ten male children in a row. The odds against having the eleventh being a boy are long - but the individual event is still 50/50. Same with coin flips.

On any given turn, it's still 1/10, I would think.

How long it goes on before the event happens (coin flips, babies, home runs), what you point out in the Paradox reference - well, ten occurrences doesn't strike me as a long train, but...it has been a while between chi squares for me.

[ArmChairGeneral]

GS,
Yes the rolls are independent, if they weren't it would be much more difficult to know the probability distribution.

In this case we are interested not in the likelihood of success on the next roll,(which as you stated is 10% every time) but rather the number of rolls it takes to get a success, which is modeled with the Geometric Distribution (or a Shifted Geometric Distribution depending on where you look it up). The expected value of a Geometric Distribution (i.e. the number of rolls it takes till the first success) is 1/p where p is the probability that the event will occur on any single roll. Paradox guys call this Mean Time To Happen, and in our case it is the mean number of turns before Kentucky secedes:

1/.1 = 10.

The Mean Time For Kentucky to secede is 10 turns, exactly the length of the window.

In my earlier post I incorrectly stated that the number of rolls before the first success (in our case, secession) is normally distributed about this mean; it is instead something a little more complicated. However, it is still highly predictable and it is quite easy to calculate the probability that the event will fire within a set number of trials. For what we are interested in (the probability that the event will fire in 10 turns or less) we use the Cumulative Distribution Function of the Shifted Geometric, which yields P(a success occurs in x turns or less) = 1-(1-p)^x where p = chance of success on an individual trial and x is the number of trial you conduct. In our case:

1-(1-.1)^10 = 1-.9^10 = .651 rounded to the thousandth.

So, IF the underlying mechanism is a 10% chance per turn between 8-01-61 and 1-1-62 that Kentucky secedes, then there is a 65.1% chance that KY will secede in any given game, assuming neither player chooses to intervene.

This seems a little high based on experience, although I have had plenty of games where KY does secede. Perhaps there is more to the event (like a concurrent roll for KY to join the Union during this period) or perhaps it only feels lower than 65% because the AI tends to choose intervention before the actual event fires.

---

I had to dig out some textbooks on this topic, I haven't messed with Bernoulli trials in a while since mostly I work with continuous functions. I would welcome anyone who is up to speed on this stuff to check my work.

[GraniteStater]

All right, that tears it. Now I'm coming after you with a slide rule.

They must've changed it from AACW, or from 1.03 here. It was October at one point (and remember, way back when, in AACW, the 'KY Rule' was a mod).

[Cardinal Ape]

All right, that tears it. Now I'm coming after you with a slide rule.

According to the database files a slide rule wielded by a Verizon employee in forum terrain against a force entrenched in an arm chair has less than a 5% chance to hit because math.

[GraniteStater]

Just for the record, I don't work for Verizon. I work for the people who keep Verizon (our biggest customer), T-Mobile, Sprint,and some others up & running. I edit the maintenance procedures.

So, if you want yer phone to work...watch it, bub

*****

The DB has a +5 attack value for Gatling slide rules.

[John S. Mosby]

I thought KY defaulted to the Union by Oct 61 or so, if no one grabbed it. In my PbeM with havi, the option was on the screen until Early Dec, so I clicked it finally - forbidden Regions until then, although northern KY was passable.

OK, so I don't understand. One of these days I'll learn how to play this game...

For me things like this are what makes the game so fun and interesting. You never know.

[GraniteStater]

Agreed.

[Cardinal Ape]

... The way it stands right now, how does the Union end up with a favorable KY?

The Union gets Kentucky to join by waiting patiently. Great answer, right? No? The details:

Sadly, the database file lies to us about the dates for which Kentucky is eligible to seceded to the CSA. The governing entry is located in the relevant campaign script, either April '61 or 1862 depending upon your start date. This secession event lists the min date as 1861/07/01 and the max date of 1861/08/05 with a probability of 10%. It also requires the CSA to have more NM than the Union.

If Kentucky does not secede the game will begin to make checks for it to join the Union. Two checks are required. The first is called 'Kentucky Warning' and it will start to make checks in March of '62 with a 50% chance each turn. Once this happens both sides will be warned that Kentucky is leaning towards the Union. Each turn thereafter a check will be made with a 25% chance for Kentucky to join the Union.

P.S. I don't know why the database file lists different dates.. I wonder if it got mucked up somewhere - that two turn window for Kentucky to join the South seems awfully small.

[GraniteStater]

The Union gets Kentucky to join by waiting patiently. Great answer, right? No? The details:

Sadly, the database file lies to us about the dates for which Kentucky is eligible to seceded to the CSA. The governing entry is located in the relevant campaign script, either April '61 or 1862 depending upon your start date. This secession event lists the min date as 1861/07/01 and the max date of 1861/08/05 with a probability of 10%. It also requires the CSA to have more NM than the Union.

If Kentucky does not secede the game will begin to make checks for it to join the Union. Two checks are required. The first is called 'Kentucky Warning' and it will start to make checks in March of '62 with a 50% chance each turn. Once this happens both sides will be warned that Kentucky is leaning towards the Union. Each turn thereafter a check will be made with a 25% chance for Kentucky to join the Union.

P.S. I don't know why the database file lists different dates.. I wonder if it got mucked up somewhere - that two turn window for Kentucky to join the South seems awfully small.

The grandaddy vanilla in AACW had no KY Rule at all. The whole thing was a mod at first. There might be some artifacts in the code.

I've noticed, in 1.06, that a frequent house rule about conscription seems to have been incorporated, also.

[RangerBooBoo]

So I've started/played 4 games in a row where KY has seceded. Does all the above mathy stuff mean I'm just unlucky or that even the good electronic citizens of digitized Kentucky know how bad of a Union player I am and just know where their best interests lie

[grimjaw]

OK, I'm going to go out on a limb here w/an explanation. I *think* CW2 uses a file to generate probabilities, rather than a random number generator called as part of a programming language. I have found a file in the directories that contains the probabilities, but I have not tried to edit it to see if I could produce 100% or 0% every time.

If that has anything to do with the easy secession, I don't know, but I did notice that even when I lowered some probability rolls to 5%, I was getting what seemed like a large number of 6 or higher. (and by that I mean I had events with a probability of success of 5%)

[Teatime]

What I find is that if you reload the previous turn and replay, or if you just start a new game without closing the game down, that you will often get the same result .. so the "random" generators seem to be something set when the game loads (I am not 100% sure of that but it appears that way from the frequency I have seen unlikely events trigger).

So if you really want to play without KY seceeding then reload your previous turn before the secession occurred, close game down and restart, load game and replay the turn

[Captain_Orso]

I know that I read way back in the AACW forum that there is some file somewhere which was used for generating random numbers, and that IIRC Pocus stated back then that repeating a turn would produce the same results. That was way back then, and even then I couldn't confirm it.

Now, I am sure that it is not the case. I've run too many tests, where I had a very simple set of units executing a very simple moves, possibly with combat involved. I ran the turn numerous times to gather a statistical variance, by simply running the turn, turning it back and running it again, without changing anything (same .hst file, same .ord files). There were always differences in the turn-executions. If some file were responsible for generating all random numbers, every repeat of the same turn would result in the exact same outcome; but it doesn't.

[grimjaw]

Regarding the possibility of the same probability being rolled each time, that should be easy to determine. It's logged as part of the turn resolution in the file with other things related to events, and it will show the number from the roll compared to the probability chance.