[quote="Captain_Orso"]In AACW it chits used to last twice as long, but that got 'fixed' in CW2 by general consensus.
QUOTE]
Now you all just agreed it really is twice as many hits. This is what I mean. If someone asks a question, we owe them an honest answer. If you don't mind posting a line of crap to newcomers, then here is a box of popcorn and please have a seat in the gallery, because I would like to talk to who thinks they actually know something and find out why they know it.
If the replacement chit has a finite number of hits when it replaces a whole unit and random otherwise, then why is that? It's either a gallon of milk all the time, or a magic gallon of milk, or randomly less than a gallon of milk, where you would be better off not buying any chits and merging units
-
GraniteStater
- AGEod Guard of Honor
- Posts: 1778
- Joined: Thu Oct 09, 2008 5:16 am
- Location: Annapolis, MD - What?
In math, it's called a step function. In this case, if x < N, then the limit of | N - x | is determined stochastically.
There, is everybody freakin' happy now? Now, just go buy chits when the UI tells you to, and behave yourselves.
There, is everybody freakin' happy now? Now, just go buy chits when the UI tells you to, and behave yourselves.
[color="#AFEEEE"]"Liberty and Union, now and forever, one and inseparable!"[/color]
-Daniel Webster
[color="#FFA07A"]"C'mon, boys, we got the damn Yankees on the run!"[/color]
-General Joseph Wheeler, US Army, serving at Santiago in 1898
RULES
(A) When in doubt, agree with Ace.
(B) Pull my reins up sharply when needed, for I am a spirited thoroughbred and forget to turn at the post sometimes.
-Daniel Webster
[color="#FFA07A"]"C'mon, boys, we got the damn Yankees on the run!"[/color]
-General Joseph Wheeler, US Army, serving at Santiago in 1898
RULES
(A) When in doubt, agree with Ace.
(B) Pull my reins up sharply when needed, for I am a spirited thoroughbred and forget to turn at the post sometimes.
-
W.Barksdale
- AGEod Grognard
- Posts: 916
- Joined: Tue Feb 05, 2008 8:17 pm
- Location: UK
Gray Fox wrote:If you don't mind posting a line of crap to newcomers, then here is a box of popcorn and please have a seat in the gallery, because I would like to talk to who thinks they actually know something and find out why they know it.
Really?
Gray Fox wrote:posting a line of crap to newcomers
On the contrary, we are trying to provide evidence to support our observations in game. We are doing this by sharing posts made in the past by the dev team and other reputable members of the forum on the subject.
Gray Fox wrote:If the replacement chit has a finite number of hits when it replaces a whole unit and random otherwise, then why is that?
My best guess is that it is because you cannot have a fraction of a chit in the game engine. On average the chit will be spent after using up an elements worth of hits anyway. (In AACW, it was 2x, apparently)
I really don't see why it is so hard to believe this.
"Tell General Lee that if he wants a bridge of dead Yankees I can furnish him with one."
-General William Barksdale at Fredericksburg
-General William Barksdale at Fredericksburg
Well my "best guess" is that I don't want to "believe" something, I want to know it. Again, it's deep in the code and no one knows, but here is what we suspect:
1. A whole unit and the X number of replacement chits I could buy for the same price have the same number of hits too, because that would be the single real world situation that a game should simulate.
2. A chit has a random chance of being used up for less than its total number of hits and a definite chance of being used up for a whole unit. This would always match obervations because a player would either see a chit is used or it isn't. Over the long run, it will supposedly work out that a chit is worth what it costs, because otherwise the theory makes no sense.
3. A chit has some hits but a random number of additional blanks, so that sometimes it is used up when it should not have been.
In #1 you buy a chit with X number of hits and you get (wait for it) X number of hits. I know that is icredibly unsettling for some of you.
#2 closely matches observations, because it is formulated to closely match any obervation. However, to make sense, it approximates #1 over the long run. Hmmm...I'll get back to that.
Clearly #3 shouldn't be what is coded. A chit would always have less hits than what you paid for it, and you would be better off not buying any chits and just building whole units and merging.
So the crowd favorite is #2. However, to make sense, #2 over the long run would actually be #1 in disguise. That's where reason trumps belief.
1. A whole unit and the X number of replacement chits I could buy for the same price have the same number of hits too, because that would be the single real world situation that a game should simulate.
2. A chit has a random chance of being used up for less than its total number of hits and a definite chance of being used up for a whole unit. This would always match obervations because a player would either see a chit is used or it isn't. Over the long run, it will supposedly work out that a chit is worth what it costs, because otherwise the theory makes no sense.
3. A chit has some hits but a random number of additional blanks, so that sometimes it is used up when it should not have been.
In #1 you buy a chit with X number of hits and you get (wait for it) X number of hits. I know that is icredibly unsettling for some of you.
#2 closely matches observations, because it is formulated to closely match any obervation. However, to make sense, it approximates #1 over the long run. Hmmm...I'll get back to that.
Clearly #3 shouldn't be what is coded. A chit would always have less hits than what you paid for it, and you would be better off not buying any chits and just building whole units and merging.
So the crowd favorite is #2. However, to make sense, #2 over the long run would actually be #1 in disguise. That's where reason trumps belief.
I'm the 51st shade of gray. Eat, pray, Charge!
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W.Barksdale
- AGEod Grognard
- Posts: 916
- Joined: Tue Feb 05, 2008 8:17 pm
- Location: UK
Gray Fox wrote:1. A whole unit and the X number of replacement chits I could buy for the same price have the same number of hits too, because that would be the single real world situation that a game should simulate.
You cannot have half a replacement chit. Or a quarter of a replacement chit. Or ANY fraction of a replacement chit.
Gray Fox wrote:2. A chit has a random chance of being used up for less than its total number of hits and a definite chance of being used up for a whole unit. This would always match obervations because a player would either see a chit is used or it isn't. Over the long run, it will supposedly work out that a chit is worth what it costs, because otherwise the theory makes no sense.
Gray Fox wrote:In #1 you buy a chit with X number of hits and you get (wait for it) X number of hits. I know that is icredibly unsettling for some of you.
Again, the game engine does not support a fraction of a replacement chit. That's why you need a probability calculation for a spent chit.
Gray Fox wrote:#2 closely matches observations, because it is formulated to closely match any obervation. However, to make sense, it approximates #1 over the long run. Hmmm...I'll get back to that.
Gray Fox wrote:So the crowd favorite is #2. However, to make sense, #2 over the long run would actually be #1 in disguise. That's where reason trumps belief.
It is a good way to model it if you cannot have fractions of replacement chits, isn't it? Moreover, it is substantiated by comments from the development team.
"Tell General Lee that if he wants a bridge of dead Yankees I can furnish him with one."
-General William Barksdale at Fredericksburg
-General William Barksdale at Fredericksburg
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GraniteStater
- AGEod Guard of Honor
- Posts: 1778
- Joined: Thu Oct 09, 2008 5:16 am
- Location: Annapolis, MD - What?
I told you, it's a step function. From everything I've read above, that seems to fit the bill.
On the semi-closed interval [H, H+1), a chit may expend n hits (or whatever the units are), where n>H; if n = H+1, then a 'full' expenditure is exhausted.
Yes, I'm expressing it as rationals, where it's really not, but I'm too lazy to express it properly. The idea should be evident, however. The determination of n is stochastic, i. e., a 'dice roll'.
On the semi-closed interval [H, H+1), a chit may expend n hits (or whatever the units are), where n>H; if n = H+1, then a 'full' expenditure is exhausted.
Yes, I'm expressing it as rationals, where it's really not, but I'm too lazy to express it properly. The idea should be evident, however. The determination of n is stochastic, i. e., a 'dice roll'.
[color="#AFEEEE"]"Liberty and Union, now and forever, one and inseparable!"[/color]
-Daniel Webster
[color="#FFA07A"]"C'mon, boys, we got the damn Yankees on the run!"[/color]
-General Joseph Wheeler, US Army, serving at Santiago in 1898
RULES
(A) When in doubt, agree with Ace.
(B) Pull my reins up sharply when needed, for I am a spirited thoroughbred and forget to turn at the post sometimes.
-Daniel Webster
[color="#FFA07A"]"C'mon, boys, we got the damn Yankees on the run!"[/color]
-General Joseph Wheeler, US Army, serving at Santiago in 1898
RULES
(A) When in doubt, agree with Ace.
(B) Pull my reins up sharply when needed, for I am a spirited thoroughbred and forget to turn at the post sometimes.
Barksdale, you're saying that a chit has no hits at all, just a percentage chance of being use. Then why does its cost vary by unit type. Why doesn't one chit fit all?
GS, your math statement comes from where exactly?
Each model approximates a reality. If it is 5% incrementally to 95% chance of being used up, then the average chance is only 50%. Chits would only replace half the number of hits that you would get by buying whole units and not using any chits.
GS, your math statement comes from where exactly?
Each model approximates a reality. If it is 5% incrementally to 95% chance of being used up, then the average chance is only 50%. Chits would only replace half the number of hits that you would get by buying whole units and not using any chits.
I'm the 51st shade of gray. Eat, pray, Charge!
-
W.Barksdale
- AGEod Grognard
- Posts: 916
- Joined: Tue Feb 05, 2008 8:17 pm
- Location: UK
-
GraniteStater
- AGEod Guard of Honor
- Posts: 1778
- Joined: Thu Oct 09, 2008 5:16 am
- Location: Annapolis, MD - What?
Gray Fox wrote:Barksdale, you're saying that a chit has no hits at all, just a percentage chance of being use. Then why does its cost vary by unit type. Why doesn't one chit fit all?
GS, your math statement comes from where exactly?
Each model approximates a reality. If it is 5% incrementally to 95% chance of being used up, then the average chance is only 50%. Chits would only replace half the number of hits that you would get by buying whole units and not using any chits.
GS, your math statement comes from where exactly?
I was a math minor. Google 'step function' - it's a simple concept, really. For all x from [0 to 1), f(x) = 0, until x = 1, then f(x) = 1; for the semi-closed interval [1, 2), f(x) =1, until x = 2, etc.
[color="#AFEEEE"]"Liberty and Union, now and forever, one and inseparable!"[/color]
-Daniel Webster
[color="#FFA07A"]"C'mon, boys, we got the damn Yankees on the run!"[/color]
-General Joseph Wheeler, US Army, serving at Santiago in 1898
RULES
(A) When in doubt, agree with Ace.
(B) Pull my reins up sharply when needed, for I am a spirited thoroughbred and forget to turn at the post sometimes.
-Daniel Webster
[color="#FFA07A"]"C'mon, boys, we got the damn Yankees on the run!"[/color]
-General Joseph Wheeler, US Army, serving at Santiago in 1898
RULES
(A) When in doubt, agree with Ace.
(B) Pull my reins up sharply when needed, for I am a spirited thoroughbred and forget to turn at the post sometimes.
Your math statement comes from where in the program? It's a quote from where?
What I am starting to suspect is that it is hard coded and it is some version of a random number. This means that you get less milk than you pay for. Someone else worked that out almost a decade ago and the salespitch became, "Oh no, you actually get twice the number of hits in a chit (because we are not going to recode it)." Otherwise chits are a cheat and you should only build whole units and merge.
What I am starting to suspect is that it is hard coded and it is some version of a random number. This means that you get less milk than you pay for. Someone else worked that out almost a decade ago and the salespitch became, "Oh no, you actually get twice the number of hits in a chit (because we are not going to recode it)." Otherwise chits are a cheat and you should only build whole units and merge.
I'm the 51st shade of gray. Eat, pray, Charge!
-
GraniteStater
- AGEod Guard of Honor
- Posts: 1778
- Joined: Thu Oct 09, 2008 5:16 am
- Location: Annapolis, MD - What?
Not in the program - I do enough at work without opening files in my spare time.
From the descriptions given. If y varies directly as x, then f (x) = ax + b, where a is a coefficient and b is an offset, and it is a linear function - I don't need a program to draw that conclusion.
If something increases, then doesn't vary, then increases, then stays steady, then increases, then remains the same, then increases...
that is most probably a step function. And yes, some randomness is present - that is what I mean by 'stochastic', i. e., not a discrete mapping, but a distribution of probabilities. In this case, the stochastic behavior is between the 'steps'.
From the descriptions given. If y varies directly as x, then f (x) = ax + b, where a is a coefficient and b is an offset, and it is a linear function - I don't need a program to draw that conclusion.
If something increases, then doesn't vary, then increases, then stays steady, then increases, then remains the same, then increases...
that is most probably a step function. And yes, some randomness is present - that is what I mean by 'stochastic', i. e., not a discrete mapping, but a distribution of probabilities. In this case, the stochastic behavior is between the 'steps'.
[color="#AFEEEE"]"Liberty and Union, now and forever, one and inseparable!"[/color]
-Daniel Webster
[color="#FFA07A"]"C'mon, boys, we got the damn Yankees on the run!"[/color]
-General Joseph Wheeler, US Army, serving at Santiago in 1898
RULES
(A) When in doubt, agree with Ace.
(B) Pull my reins up sharply when needed, for I am a spirited thoroughbred and forget to turn at the post sometimes.
-Daniel Webster
[color="#FFA07A"]"C'mon, boys, we got the damn Yankees on the run!"[/color]
-General Joseph Wheeler, US Army, serving at Santiago in 1898
RULES
(A) When in doubt, agree with Ace.
(B) Pull my reins up sharply when needed, for I am a spirited thoroughbred and forget to turn at the post sometimes.
W.Barksdale wrote:I think this thread has run its course.
Why, because Gray Fox is trying to get to the bottom of something that should be concrete? (All programing should have a hard answer somewhere, unless AGEOD is truly selling "Ghosts in the Machine") I agree his previous post was a little brusque but it is obvious he is simply looking for an answer that honestly should be there.
Gray Fox wrote:Your math statement comes from where in the program? It's a quote from where?
What I am starting to suspect is that it is hard coded and it is some version of a random number. This means that you get less milk than you pay for. Someone else worked that out almost a decade ago and the salespitch became, "Oh no, you actually get twice the number of hits in a chit (because we are not going to recode it)." Otherwise chits are a cheat and you should only build whole units and merge.
This is important to know. I get that most people play these games for the historical realism and not to power-game, but it would be important to know (especially for the resource-strapped South) if the chits are actually worth their cost? If Jeff Davis and James Seddon began to notice that their replacement soldiers were not all reaching the front line units to replenish them up to strength, but instead saw that building fresh units yielded more effectives on the front, that is how they would have prosecuted the war.
In the end, this is a game run by numbers programmed by people. It is beginning to boggle my mind how difficult it is to get answers.
I have heard, in such a way as to believe it, of your recently saying that both the army and the government needed a dictator. Of course it was not for this, but in spite of it, that I have given you the command. Only those generals who gain success can be dictators. What I now ask of you is military success, and I will risk the dictatorship.
-Abraham Lincoln, 1863, in a letter to Major General Joseph Hooker.
-Abraham Lincoln, 1863, in a letter to Major General Joseph Hooker.
-
GraniteStater
- AGEod Guard of Honor
- Posts: 1778
- Joined: Thu Oct 09, 2008 5:16 am
- Location: Annapolis, MD - What?
For CSA, chits for Replacements are most definitely worth it - the CSA replenishes twice as fast as the Union.
Twice As Fast...
When I first learned that, I was grumpy for weeks. I still don't see why, exactly, but them's the breaks.
Think of a lot of things as Man-Days. Which is cheaper, getting the red out in those lovely UeberBrigades from VA, or building formations from scratch? Building anew takes Turns - replacing can be Right Now.
Especially if you're the CSA - I've spent too many Turns waiting around for the Army of the Potomac to get back to snuff for Another Try, only to find Longstreet & Co. waiting with rested full strength formations with fine morale and 100% Cohesion. Entrenched. With their buddies just itchin' to MTSG.
Use that advantage as the CSA. In the end, the Union has to dogpile, although a HiTek Union approach (*ahem*) can be a valid way of prosecuting the war.
Twice As Fast...
When I first learned that, I was grumpy for weeks. I still don't see why, exactly, but them's the breaks.
Think of a lot of things as Man-Days. Which is cheaper, getting the red out in those lovely UeberBrigades from VA, or building formations from scratch? Building anew takes Turns - replacing can be Right Now.
Especially if you're the CSA - I've spent too many Turns waiting around for the Army of the Potomac to get back to snuff for Another Try, only to find Longstreet & Co. waiting with rested full strength formations with fine morale and 100% Cohesion. Entrenched. With their buddies just itchin' to MTSG.
Use that advantage as the CSA. In the end, the Union has to dogpile, although a HiTek Union approach (*ahem*) can be a valid way of prosecuting the war.
[color="#AFEEEE"]"Liberty and Union, now and forever, one and inseparable!"[/color]
-Daniel Webster
[color="#FFA07A"]"C'mon, boys, we got the damn Yankees on the run!"[/color]
-General Joseph Wheeler, US Army, serving at Santiago in 1898
RULES
(A) When in doubt, agree with Ace.
(B) Pull my reins up sharply when needed, for I am a spirited thoroughbred and forget to turn at the post sometimes.
-Daniel Webster
[color="#FFA07A"]"C'mon, boys, we got the damn Yankees on the run!"[/color]
-General Joseph Wheeler, US Army, serving at Santiago in 1898
RULES
(A) When in doubt, agree with Ace.
(B) Pull my reins up sharply when needed, for I am a spirited thoroughbred and forget to turn at the post sometimes.
If, as W. Barksdale writes, there is no such thing as a partial replacement chit, maybe it works just as we have been told. Replace a whole element, use a whole chit. Chits cost differently for various types of elements since elements have different costs for conscripts, money or war supply. Replace damage to an element, roll a random number. If it is less than 5% (or any value you fancy), you lose the chit, otherwise is stays intact. A chit should be good for (on average) 20 replacements. Or 1, or 100, no telling. The only reason I can see for programming it that way is to give the CSA a better chance of replacing a loss than the USA.
I agree with Gray Fox, though, that it would be nice to know for sure.
I agree with Gray Fox, though, that it would be nice to know for sure.
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Captain_Orso
- Posts: 5766
- Joined: Tue Sep 01, 2009 5:02 pm
- Location: Stuttgart, Germany
There are no partial replacement-chits. One thing I stumble across in this game every time and again, is that it's principally a board game. It does use the accounting that a computer can do like when dealing with hits on elements. But those are specifically documented and displayed. If it's not, it probably doesn't exist in smaller denominations that what you can readily see.
Let's cut to the chase. I set up a test scenario with 4 Union and 4 Confederate division each with 16 line infantry regiments each missing 19 of their TOE 20 hits; that is exactly 1216 hits missing for each side. I also gave each side 10 line infantry replacement chits. Union units were inside Tolono, Il with a depot. Confederates units were inside Memphis with a depot.
I ran one turn without giving any orders and checked the results, and then started the scenario over again for a total of 20 iterations. These are the results:
[TABLE="class: grid, width: 1000, align: center"]
[TR]
[TD]Iteration[/TD]
[TD]Faction[/TD]
[TD]Missing Hits T1[/TD]
[TD]Missing Hits T2[/TD]
[TD]Hits Replaced[/TD]
[TD]Avrg. per chit[/TD]
[/TR]
[TR]
[TD]1[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]861[/TD]
[TD]355[/TD]
[TD]35.50[/TD]
[/TR]
[TR]
[TD]1[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]858[/TD]
[TD]358[/TD]
[TD]35.80[/TD]
[/TR]
[TR]
[TD]2[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]843[/TD]
[TD]373[/TD]
[TD]37.30[/TD]
[/TR]
[TR]
[TD]2[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]851[/TD]
[TD]365[/TD]
[TD]36.50[/TD]
[/TR]
[TR]
[TD]3[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]803[/TD]
[TD]413[/TD]
[TD]41.30[/TD]
[/TR]
[TR]
[TD]3[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]1019[/TD]
[TD]197[/TD]
[TD]19.70[/TD]
[/TR]
[TR]
[TD]4[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]856[/TD]
[TD]360[/TD]
[TD]36.00[/TD]
[/TR]
[TR]
[TD]4[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]906[/TD]
[TD]310[/TD]
[TD]31.00[/TD]
[/TR]
[TR]
[TD]5[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]788[/TD]
[TD]428[/TD]
[TD]42.80[/TD]
[/TR]
[TR]
[TD]5[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]825[/TD]
[TD]391[/TD]
[TD]39.10[/TD]
[/TR]
[TR]
[TD]6[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]804[/TD]
[TD]412[/TD]
[TD]41.20[/TD]
[/TR]
[TR]
[TD]6[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]857[/TD]
[TD]359[/TD]
[TD]35.90[/TD]
[/TR]
[TR]
[TD]7[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]860[/TD]
[TD]356[/TD]
[TD]35.60[/TD]
[/TR]
[TR]
[TD]7[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]797[/TD]
[TD]419[/TD]
[TD]41.90[/TD]
[/TR]
[TR]
[TD]8[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]750[/TD]
[TD]466[/TD]
[TD]46.60[/TD]
[/TR]
[TR]
[TD]8[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]841[/TD]
[TD]375[/TD]
[TD]37.50[/TD]
[/TR]
[TR]
[TD]9[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]754[/TD]
[TD]462[/TD]
[TD]46.20[/TD]
[/TR]
[TR]
[TD]9[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]753[/TD]
[TD]463[/TD]
[TD]46.30[/TD]
[/TR]
[TR]
[TD]10[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]733[/TD]
[TD]483[/TD]
[TD]48.30[/TD]
[/TR]
[TR]
[TD]10[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]811[/TD]
[TD]405[/TD]
[TD]40.50[/TD]
[/TR]
[TR]
[TD]11[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]839[/TD]
[TD]377[/TD]
[TD]37.70[/TD]
[/TR]
[TR]
[TD]11[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]797[/TD]
[TD]419[/TD]
[TD]41.90[/TD]
[/TR]
[TR]
[TD]12[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]898[/TD]
[TD]318[/TD]
[TD]31.80[/TD]
[/TR]
[TR]
[TD]12[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]864[/TD]
[TD]352[/TD]
[TD]35.20[/TD]
[/TR]
[TR]
[TD]13[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]954[/TD]
[TD]262[/TD]
[TD]26.20[/TD]
[/TR]
[TR]
[TD]13[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]1035[/TD]
[TD]181[/TD]
[TD]18.10[/TD]
[/TR]
[TR]
[TD]14[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]674[/TD]
[TD]542[/TD]
[TD]54.20[/TD]
[/TR]
[TR]
[TD]14[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]750[/TD]
[TD]466[/TD]
[TD]46.60[/TD]
[/TR]
[TR]
[TD]15[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]804[/TD]
[TD]412[/TD]
[TD]41.20[/TD]
[/TR]
[TR]
[TD]15[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]840[/TD]
[TD]376[/TD]
[TD]37.60[/TD]
[/TR]
[TR]
[TD]16[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]953[/TD]
[TD]263[/TD]
[TD]26.30[/TD]
[/TR]
[TR]
[TD]16[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]1042[/TD]
[TD]174[/TD]
[TD]17.40[/TD]
[/TR]
[TR]
[TD]17[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]745[/TD]
[TD]471[/TD]
[TD]47.10[/TD]
[/TR]
[TR]
[TD]17[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]996[/TD]
[TD]220[/TD]
[TD]22.00[/TD]
[/TR]
[TR]
[TD]18[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]940[/TD]
[TD]276[/TD]
[TD]27.60[/TD]
[/TR]
[TR]
[TD]18[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]820[/TD]
[TD]396[/TD]
[TD]39.60[/TD]
[/TR]
[TR]
[TD]19[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]729[/TD]
[TD]487[/TD]
[TD]48.70[/TD]
[/TR]
[TR]
[TD]19[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]751[/TD]
[TD]465[/TD]
[TD]46.50[/TD]
[/TR]
[TR]
[TD]20[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]803[/TD]
[TD]413[/TD]
[TD]41.30[/TD]
[/TR]
[TR]
[TD]20[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]774[/TD]
[TD]442[/TD]
[TD]44.20[/TD]
[/TR]
[/TABLE]
[TABLE]
[TR]
[TD]This makes for an overall average of 39.65 hits per chit for the CSA, and 35.67 for the USA. I'll let the mathematics experts voice in on the probability of these minor statistics.[/TD]
[/TR]
[/TABLE]
Let's cut to the chase. I set up a test scenario with 4 Union and 4 Confederate division each with 16 line infantry regiments each missing 19 of their TOE 20 hits; that is exactly 1216 hits missing for each side. I also gave each side 10 line infantry replacement chits. Union units were inside Tolono, Il with a depot. Confederates units were inside Memphis with a depot.
I ran one turn without giving any orders and checked the results, and then started the scenario over again for a total of 20 iterations. These are the results:
[TABLE="class: grid, width: 1000, align: center"]
[TR]
[TD]Iteration[/TD]
[TD]Faction[/TD]
[TD]Missing Hits T1[/TD]
[TD]Missing Hits T2[/TD]
[TD]Hits Replaced[/TD]
[TD]Avrg. per chit[/TD]
[/TR]
[TR]
[TD]1[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]861[/TD]
[TD]355[/TD]
[TD]35.50[/TD]
[/TR]
[TR]
[TD]1[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]858[/TD]
[TD]358[/TD]
[TD]35.80[/TD]
[/TR]
[TR]
[TD]2[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]843[/TD]
[TD]373[/TD]
[TD]37.30[/TD]
[/TR]
[TR]
[TD]2[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]851[/TD]
[TD]365[/TD]
[TD]36.50[/TD]
[/TR]
[TR]
[TD]3[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]803[/TD]
[TD]413[/TD]
[TD]41.30[/TD]
[/TR]
[TR]
[TD]3[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]1019[/TD]
[TD]197[/TD]
[TD]19.70[/TD]
[/TR]
[TR]
[TD]4[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]856[/TD]
[TD]360[/TD]
[TD]36.00[/TD]
[/TR]
[TR]
[TD]4[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]906[/TD]
[TD]310[/TD]
[TD]31.00[/TD]
[/TR]
[TR]
[TD]5[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]788[/TD]
[TD]428[/TD]
[TD]42.80[/TD]
[/TR]
[TR]
[TD]5[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]825[/TD]
[TD]391[/TD]
[TD]39.10[/TD]
[/TR]
[TR]
[TD]6[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]804[/TD]
[TD]412[/TD]
[TD]41.20[/TD]
[/TR]
[TR]
[TD]6[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]857[/TD]
[TD]359[/TD]
[TD]35.90[/TD]
[/TR]
[TR]
[TD]7[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]860[/TD]
[TD]356[/TD]
[TD]35.60[/TD]
[/TR]
[TR]
[TD]7[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]797[/TD]
[TD]419[/TD]
[TD]41.90[/TD]
[/TR]
[TR]
[TD]8[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]750[/TD]
[TD]466[/TD]
[TD]46.60[/TD]
[/TR]
[TR]
[TD]8[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]841[/TD]
[TD]375[/TD]
[TD]37.50[/TD]
[/TR]
[TR]
[TD]9[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]754[/TD]
[TD]462[/TD]
[TD]46.20[/TD]
[/TR]
[TR]
[TD]9[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]753[/TD]
[TD]463[/TD]
[TD]46.30[/TD]
[/TR]
[TR]
[TD]10[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]733[/TD]
[TD]483[/TD]
[TD]48.30[/TD]
[/TR]
[TR]
[TD]10[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]811[/TD]
[TD]405[/TD]
[TD]40.50[/TD]
[/TR]
[TR]
[TD]11[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]839[/TD]
[TD]377[/TD]
[TD]37.70[/TD]
[/TR]
[TR]
[TD]11[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]797[/TD]
[TD]419[/TD]
[TD]41.90[/TD]
[/TR]
[TR]
[TD]12[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]898[/TD]
[TD]318[/TD]
[TD]31.80[/TD]
[/TR]
[TR]
[TD]12[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]864[/TD]
[TD]352[/TD]
[TD]35.20[/TD]
[/TR]
[TR]
[TD]13[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]954[/TD]
[TD]262[/TD]
[TD]26.20[/TD]
[/TR]
[TR]
[TD]13[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]1035[/TD]
[TD]181[/TD]
[TD]18.10[/TD]
[/TR]
[TR]
[TD]14[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]674[/TD]
[TD]542[/TD]
[TD]54.20[/TD]
[/TR]
[TR]
[TD]14[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]750[/TD]
[TD]466[/TD]
[TD]46.60[/TD]
[/TR]
[TR]
[TD]15[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]804[/TD]
[TD]412[/TD]
[TD]41.20[/TD]
[/TR]
[TR]
[TD]15[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]840[/TD]
[TD]376[/TD]
[TD]37.60[/TD]
[/TR]
[TR]
[TD]16[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]953[/TD]
[TD]263[/TD]
[TD]26.30[/TD]
[/TR]
[TR]
[TD]16[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]1042[/TD]
[TD]174[/TD]
[TD]17.40[/TD]
[/TR]
[TR]
[TD]17[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]745[/TD]
[TD]471[/TD]
[TD]47.10[/TD]
[/TR]
[TR]
[TD]17[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]996[/TD]
[TD]220[/TD]
[TD]22.00[/TD]
[/TR]
[TR]
[TD]18[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]940[/TD]
[TD]276[/TD]
[TD]27.60[/TD]
[/TR]
[TR]
[TD]18[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]820[/TD]
[TD]396[/TD]
[TD]39.60[/TD]
[/TR]
[TR]
[TD]19[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]729[/TD]
[TD]487[/TD]
[TD]48.70[/TD]
[/TR]
[TR]
[TD]19[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]751[/TD]
[TD]465[/TD]
[TD]46.50[/TD]
[/TR]
[TR]
[TD]20[/TD]
[TD]CSA[/TD]
[TD]1216[/TD]
[TD]803[/TD]
[TD]413[/TD]
[TD]41.30[/TD]
[/TR]
[TR]
[TD]20[/TD]
[TD]USA[/TD]
[TD]1216[/TD]
[TD]774[/TD]
[TD]442[/TD]
[TD]44.20[/TD]
[/TR]
[/TABLE]
[TABLE]
[TR]
[TD]This makes for an overall average of 39.65 hits per chit for the CSA, and 35.67 for the USA. I'll let the mathematics experts voice in on the probability of these minor statistics.[/TD]
[/TR]
[/TABLE]
-
Cardinal Ape
- General of the Army
- Posts: 619
- Joined: Wed Mar 07, 2012 1:59 am
Captain_Orso wrote:I set up a test scenario...
Thank you!
I don't have much time at the moment to evaluate...
Were all the infantry chits consumed in each iteration? Historical attrition on?
It is fairly obvious to see the Union's penalty on replacements with all the 100's being theirs. (A small clarification: The CSA does not get a bonus to replacements. The British, Indians, French, Haitians, CSA, and everyone else who is not the Union all function normally. It is only the Union that gets the penalty.)
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Captain_Orso
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GraniteStater
- AGEod Guard of Honor
- Posts: 1778
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A real quick & dirty crunch (each set separately) yields a standard deviation of ~ [sqrt 5], which means most events don't vary very much; it can, at times, have a good outlier.
So, it is random (duh), penalizes the Union most of the time, but not always; can, at times, hit one out of the park or ground out weakly to the pitcher.
And the Union still collects these at half the rate of the CSA.
The game is borked!!! Hopelessly broken!!!
Where's my M-64 Laser Cannon? That was in development! Unfair to the Union!
So, it is random (duh), penalizes the Union most of the time, but not always; can, at times, hit one out of the park or ground out weakly to the pitcher.
And the Union still collects these at half the rate of the CSA.
The game is borked!!! Hopelessly broken!!!
Where's my M-64 Laser Cannon? That was in development! Unfair to the Union!
[color="#AFEEEE"]"Liberty and Union, now and forever, one and inseparable!"[/color]
-Daniel Webster
[color="#FFA07A"]"C'mon, boys, we got the damn Yankees on the run!"[/color]
-General Joseph Wheeler, US Army, serving at Santiago in 1898
RULES
(A) When in doubt, agree with Ace.
(B) Pull my reins up sharply when needed, for I am a spirited thoroughbred and forget to turn at the post sometimes.
-Daniel Webster
[color="#FFA07A"]"C'mon, boys, we got the damn Yankees on the run!"[/color]
-General Joseph Wheeler, US Army, serving at Santiago in 1898
RULES
(A) When in doubt, agree with Ace.
(B) Pull my reins up sharply when needed, for I am a spirited thoroughbred and forget to turn at the post sometimes.
-
W.Barksdale
- AGEod Grognard
- Posts: 916
- Joined: Tue Feb 05, 2008 8:17 pm
- Location: UK
Thank you Captain_Orso. Some numerical analysis:
How many hits does an infantry replacement chit give out on average?
It appears that each chit can give out ~40 hits in an infantry element, as noted earlier. To be sure, is there any chance you could do that experiment ten more times? (This is so the law of large numbers will take affect, ~30 iterations)
What is the probability that an infantry replacement chit will be spent?
You cannot answer this question with the current experiment because all of the chits have been spent.
To do this may I suggest you try a different experiment? Run a test with one infantry element for both sides, each missing one of their TOE 20 hits and each with one replacement chit, noting if the chit was spent. (30 times) Then repeat again with missing two of their TOE 20 hits. (30 times) After I see those results I can tell if more runs are needed with 3 missing hits etc.
How many hits does an infantry replacement chit give out on average?
It appears that each chit can give out ~40 hits in an infantry element, as noted earlier. To be sure, is there any chance you could do that experiment ten more times? (This is so the law of large numbers will take affect, ~30 iterations)
What is the probability that an infantry replacement chit will be spent?
You cannot answer this question with the current experiment because all of the chits have been spent.
To do this may I suggest you try a different experiment? Run a test with one infantry element for both sides, each missing one of their TOE 20 hits and each with one replacement chit, noting if the chit was spent. (30 times) Then repeat again with missing two of their TOE 20 hits. (30 times) After I see those results I can tell if more runs are needed with 3 missing hits etc.
"Tell General Lee that if he wants a bridge of dead Yankees I can furnish him with one."
-General William Barksdale at Fredericksburg
-General William Barksdale at Fredericksburg
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Captain_Orso
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W.Barksdale wrote:Thank you Captain_Orso.
W.Barksdale wrote:Some numerical analysis:
How many hits does an infantry replacement chit give out on average?
It appears that each chit can give out ~40 hits in an infantry element, as noted earlier.
As far as line infantry chits are concerted.
W.Barksdale wrote:To be sure, is there any chance you could do that experiment ten more times? (This is so the law of large numbers will take affect, ~30 iterations)
Okay, not only an additional 10 iterations, I've done an additional 20
1 CSA 1216 824 392 39.20
1 USA 1216 988 228 22.80
2 CSA 1216 570 646 64.60
2 USA 1216 752 464 46.40
3 CSA 1216 764 452 45.20
3 USA 1216 870 346 34.60
4 CSA 1216 727 489 48.90
4 USA 1216 832 384 38.40
5 CSA 1216 767 449 44.90
5 USA 1216 870 346 34.60
6 CSA 1216 616 600 60.00
6 USA 1216 895 321 32.10
7 CSA 1216 757 459 45.90
7 USA 1216 754 462 46.20
8 CSA 1216 790 426 42.60
8 USA 1216 938 278 27.80
9 CSA 1216 975 241 24.10
9 USA 1216 857 359 35.90
10 CSA 1216 824 392 39.20
10 USA 1216 1025 191 19.10
11 CSA 1216 488 728 72.80
11 USA 1216 931 285 28.50
12 CSA 1216 752 464 46.40
12 USA 1216 809 407 40.70
13 CSA 1216 937 279 27.90
13 USA 1216 988 228 22.80
14 CSA 1216 693 523 52.30
14 USA 1216 938 278 27.80
15 CSA 1216 881 335 33.50
15 USA 1216 955 261 26.10
16 CSA 1216 899 317 31.70
16 USA 1216 861 355 35.50
17 CSA 1216 846 370 37.00
17 USA 1216 752 464 46.40
18 CSA 1216 862 354 35.40
18 USA 1216 952 264 26.40
19 CSA 1216 858 358 35.80
19 USA 1216 919 297 29.70
20 CSA 1216 729 487 48.70
20 USA 1216 757 459 45.90
W.Barksdale wrote:What is the probability that an infantry replacement chit will be spent?
You cannot answer this question with the current experiment because all of the chits have been spent.
To do this may I suggest you try a different experiment? Run a test with one infantry element for both sides, each missing one of their TOE 20 hits and each with one replacement chit, noting if the chit was spent. (30 times) Then repeat again with missing two of their TOE 20 hits. (30 times) After I see those results I can tell if more runs are needed with 3 missing hits etc.
It took me a while to understand what you are getting at. Assuming that the expected situation--at least in my mind--is that each chit is expended by the formula: 1/x = 'percent chance of consuming the chit', where x = 'the Hit-TOE of the element receiving the replacement' you'd have to run this test at least 80 times each with 1 hit missing and again with 2 hits missing.
Ummmm.... Sorry, not me
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W.Barksdale
- AGEod Grognard
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W.Barksdale
- AGEod Grognard
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If anyone wants to mod the scenario with one infantry element each side at half strength (10 hits of TOE 20) and one replacement chit I'll run test and post the analysis.
"Tell General Lee that if he wants a bridge of dead Yankees I can furnish him with one."
-General William Barksdale at Fredericksburg
-General William Barksdale at Fredericksburg
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Captain_Orso
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W.Barksdale
- AGEod Grognard
- Posts: 916
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Captain_Orso wrote:Actually, I don't see what the difference would be. With just one chit being used per turn, or 10 chits a couple hundred times, you still wind up with the same statistic. The only difference is in how long it takes to accumulate the information.
Yeah sure it could work. Can you set up 10 (or 20) infantry elements at half strength with 10 (or 20) chits? Or a different strength if you think it is better.
As long as some of chits are spent and others not I think I can do the numerical analysis.
"Tell General Lee that if he wants a bridge of dead Yankees I can furnish him with one."
-General William Barksdale at Fredericksburg
-General William Barksdale at Fredericksburg
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Captain_Orso
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I can, but it would make no difference. Hypothetically a chit might replace a single hit before being consumed, or 1000 hits--it's not likely, but it's possible. In the end, there are a finite number of hits being replaced--discovered after each test iteration--, and a finite number of chits being consumed--defined by the test--. Which hits are replaced on which element during which turn and by which chit makes no difference.
The important thing is to understand what the player can expect on the average.
The important thing is to understand what the player can expect on the average.
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W.Barksdale
- AGEod Grognard
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Captain_Orso
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It's not a question of wanting to know, it's a question of how to best discover it.
Running a test in which 1 chit is used to replace hits over and over again until the chit is consumed will give you very limited information. The one thing this test would reveal would be the most extreme results, ie a chit being used only once and being consumed, or a chit being used far more than the premised 40 times times before being consumed. But the test would still have to be run hundreds of times to be able to build a reliable statistic, and the extreme outliers would still say nothing really, because they will still be within the realm of possibility.
But I can put this together pretty quickly if you'd like to play around with it. I can set the scenario up with both sided having 0 replacement chits in their pools and enough resources to purchase as many chits as you wish.
I can also set it up that the number of hits each line infantry element has is modified by an event, and not through the scenario setup. That way you could edit the event to start with what would would like to use for your test-bed.
Running a test in which 1 chit is used to replace hits over and over again until the chit is consumed will give you very limited information. The one thing this test would reveal would be the most extreme results, ie a chit being used only once and being consumed, or a chit being used far more than the premised 40 times times before being consumed. But the test would still have to be run hundreds of times to be able to build a reliable statistic, and the extreme outliers would still say nothing really, because they will still be within the realm of possibility.
But I can put this together pretty quickly if you'd like to play around with it. I can set the scenario up with both sided having 0 replacement chits in their pools and enough resources to purchase as many chits as you wish.
I can also set it up that the number of hits each line infantry element has is modified by an event, and not through the scenario setup. That way you could edit the event to start with what would would like to use for your test-bed.
-
W.Barksdale
- AGEod Grognard
- Posts: 916
- Joined: Tue Feb 05, 2008 8:17 pm
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Captain_Orso wrote:It's not a question of wanting to know, it's a question of how to best discover it.
Set it up the test as you think best. I'll do the analysis and present the conclusions.
"Tell General Lee that if he wants a bridge of dead Yankees I can furnish him with one."
-General William Barksdale at Fredericksburg
-General William Barksdale at Fredericksburg
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