10-10-2003 02:45									#1
	GCA and "The Odds" Increase the size of your Attachments

Since we're talking about this in multiple threads I thought it might be wise to centralize it here.

I propose that this thread be used to create a post - I'll create two placeholders after this one - for someone with more time and mathematical aptitude to calculate the probability of what GCA is pulling off turn-by-turn, and then the overall probability of ALL events up to the current date. I propose that at such time as the overall probability drops below 5 percent, we alert Mongoose that there is a problem, and when the overall probability of all successes of GCA drops below 1 percent, we formally challenge their play and provide our evidence. I further propose that if on any turn GCA manages something in the less-than-1 percent column, and this happens twice total, we also formally challenge their play.

At the very least, let's try and get all our information/discussion for what appears to be the growing case against GCA in one thread, for ease of reading, cleaning up the other threads, and in the future, ease of reference.

	10-10-2003 02:46									#2
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Dummy post one for "Turn by turn" probabilities - maybe Area X can pick this up, or the mighty Rush?

	10-10-2003 02:46									#3
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Dummy post two for "Overall probability of the successes so far."

	10-10-2003 02:54									#4
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Like I've mentioned elsewhere, I think we should only take into account their attacks on our Numidian Mercenaries, and only as long as they do not trigger a GA.

We have very little information concerning how many units they're throwing at us. The only thing that is concretely fishy (if such is possible) is the fact that our GA has not been triggered yet, because it means that their Horsemen are not losing.

GCA could have spent a bunch of units destroying jagjef and the other Swordsman (forget its name right now). We have no proof either way. We do know that they are not spending more than one Horseman per Merc. however. Once our GA is triggered, we'll have no means of reasonably calculating odds, because we'll have very little idea what is hitting us (just one reason why I like combat reports in PBEM).

If our GA is triggered next turn, I'm afraid we'll have to continue playing as though they're not cheating, because we will no longer be able to gather sufficient proof.


Dominae

	10-10-2003 03:05									#5
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1) I agree with Dominae, only count mercs because thats the only unit we can prove they didn't lose any battles against.

2) Always give them the benefit of the doubt with odds. If we don't know some details assume the worst case for us: ie) assume they had an elite unit, assume it only survived with 1 pip. Doing this will force all the error in our calculations to be in their favor, further reducing the doubt.

3) Not everyone is into number crunching. Even with tons of mathematics and the odds being in the .0000001% range this would be a very hard case to sell unless they admit it. Given that, I think the best way we can deal with this is to just win the war and relegate it to irrelevance.

	10-10-2003 03:48									#6
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I disagree that we won't be able to get any proof as to anything after our GA is triggered (by whatever means). For one thing, how will they know that we are in our GA, we outproduce them now as it is. Nothing shows, for them, that we are in our GA. The only way to be fully certain, is to have a look at one of our cities, via espianage, but we will remain at war with them until the last, so that's not an option.

They can get Intel from others, but I doubt that CFC is going to do that for them and GWT is too interested in their own war to even spend the monies to investigate one of our cities for GCA.

No, they won't know when our GA will be triggered, unless they know that they lost a battle against a NM. They will certainly keep themselves to the beleif that they will try to prevent our GA.

E_T

	10-10-2003 04:05									#7
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quote: Originally posted by wervdon 2) Always give them the benefit of the doubt with odds. If we don't know some details assume the worst case for us: ie) assume they had an elite unit, assume it only survived with 1 pip. Doing this will force all the error in our calculations to be in their favor, further reducing the doubt.

Agreed that we should assume full 5-HP elite horses unless we can concretely prove otherwise. As far as calculating the odds, just calculate the odds of them winning each single combat, then the odds of all of those combats being won; the pips themselves don't matter, which unit dies is what's concrete and knowable.

	10-10-2003 04:52									#8
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quote: Originally posted by E_T No, they won't know when our GA will be triggered, unless they know that they lost a battle against a NM.

That's not the point. The point is that, until our GA is triggered, we know that any victory by GCA over one of our Mercs was a one-shot deal (not that they could attack the same unit twice, since we still have my Mercs left), and therefore we know that whenever they're attacking our big stacks they're doing so losslessly. Whether or not they want to trigger our GA is irrelevant here.


Dominae

	10-10-2003 05:44									#9
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Except that it is highly unlikely that they want to trigger our GA, and that attacking with a horseman against a huge stack including catapults and numidians is the best way to CAUSE the GA. No math there, but much more "sellable" proof for those who won't like the math.

By the way - I really apologize for being the guy to suggest all this work and not be able to do it myself, I'm no number cruncher on this level at all, barely even remember how.... but is someone going to pick up the banner and run with this? Please?

You'll get a shrine in Apolyton lore or something!

	10-10-2003 06:07									#10
	Inflate your Upload Space

I think Dominae can do a fine job. If others can help him, great.

I am somewhat of two minds on this issue. One one hand I would not like to see us focus on GCA's conduct and inhibit our own sound planning and actions. That is part of why I have tried to tone down discussions of GCA and this topic in the past.

On the other hand, suspicious incidents are piling up. First there was the route they put on CDG and their immortals with very little loss as far as we can tell. Now, as we advance, they pick seemingly odd times to send the horse against the mercs and are 2 for 2 with the odds against them, once heavily. So, I support a complete examination of results and compilation of odds.

btw, Dominae, for you calculations of this last merc... the attacking horse could have had no more than 4 pips

During our turn 90BC, there were 2 horse at Algalord 8 7, an elite at 3/5, and a vet at 4/4. There were no other horse visible from Algalord 8 8 7.

During their 70BC, the elite would recover to 4/5 and they had the vet at 4/4. These are the only two horse available who could attack, win, and get out of sight before our 70BC turn. Unless... they came forward with an elite, attacked, won, and then disbanded the unit. I doubt very much that they would have done that.

During our 70BC, there are no GCA units visible from Algalord 8 8 7. IF a unit other than the two horse we saw last turn had attacked us, they would still be visible or disbanded. Beginning from out of our sight, they would have to move 2 tiles on road, attack, win, and then have only 1/3rd of an MP left; only enough movement to move a single tile, or to do the completely rediculous and disband.

Therefore, the winning horse from GCA turn 70BC had 4 pips. No more.

	10-10-2003 07:07									#11
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I come up with a 6.6451% chance of winning for an elite horse (2 attack) vs a veteran merc on a hill (7.5 defense).

I don't remember how to do the actual statistics calculations, so I wrote up a quick decisions tree based C app to compute the odds based on weighting each branch in the tree with the odds of getting there from its parent node. The branch with the merc losing a pip had a weight of .2105 and the branch with the horse losing a pip had a weight of .789. The program added all branches to the tree until one of the two units died.

I got the final odds by summing the multiplied weights of every path that led to the merc dyIing.

I'll attach the zipped program when I get a chance. (and source so someone can double check me)

	10-10-2003 07:10									#12
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I just want to point out that for NONE of these battles were any of our units fortified, as they had just moved to the place in question before being attacked.

Edited: to eliminate all trace of blatant stupidity

And for the success odds in the thread I started, it seems that the Calculator at CFC I used calculates success odds by summing the odds of each individual path to victory.

Last edited by MrWhereItsAt on 10-10-2003 at 08:07

	10-10-2003 07:19									#13
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Strength would have been 4.5

3 plus 50% terrain bonus.

	10-10-2003 07:21									#14
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There's already an app out there that computes odds, thats good. I also took the path of summing paths to victory, only in our case thats defeat

I won't bother posting my code then, its rather messy/undocumented as I did a quick job on it.


Also, I used 7.5 defense because I was thinking hills was 250% defense not 200%, my mistake.

Just for validaiton though, I'm getting 11.3815% when I use 200% and assume an elite horse vs a merc on a hill (200% instead of 250%), that goes down to 7.0557% if the horse is only a veteran or was an elite at 4 pips remaining.

	10-10-2003 07:24									#15
	Inflate your Upload Space

+50%

3 * (1 + .5) = 4.5

Try 4.5

	10-10-2003 07:28									#16
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It was a 4 pip horse. It could not have been anything else.

	10-10-2003 07:29									#17
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Ok, +50% for hill gives me.
20.8294% elite horse vs vet merc
13.6228% vet horse vs vet merc

EDIT:
Odds of elite horse vs vet merc with no (not even the 10% you get with grassland) bonus: 40.5%

If they did that twice and got the 13.6% victory on the hill and
don't have any losses then the combined odds is down to 2.2%
with just that. I think they've only won the two victories so far though?

I think that actually matches what MrWIA got in the other thread.

I'll go ahead and put the program up:
http://apolyton.net/upload/files/wervdon/OddsCalc.zip

To just run the program go into the debug directory where i've compiled it and run the oddscalc.exe, best done from a dos prompt.

It'll ask you for attackers hp (pips), defenders hp (pips), attacker's attack power, defenders defense power, and the terrain bonus (for 50% that would be a 1.5), then spit out the answer.

If you want to look at the code, then I assume you know how to use visual C projects.....

Last edited by wervdon on 10-10-2003 at 07:44

	10-10-2003 10:56									#18
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quote: Originally posted by MrWhereItsAt And for the success odds in the thread I started, it seems that the Calculator at CFC I used calculates success odds by summing the odds of each individual path to victory.

...which is correct. The total probability of a unit winning a given combat is the sum of probabilities of all possible outcomes that lead to this unit surviving and the other one dying.

	10-10-2003 11:37									#19
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The combat calc on CFC:

http://www.civfanatics.com/civ3combatcalc.html

It doesn't calculate retreat chances and also it isn't updated with the PtW units, but you can always use units with similar stats. (pikeman instaed of num.merc., for ex)

	10-10-2003 12:03									#20
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Another calculator:

http://www.zachriel.com/BattleCivulation.asp

	10-10-2003 18:45									#21
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quote: Another calculator: http://www.zachriel.com/BattleCivulation.asp

Tested with this a 4-hp horse attacking a 4-hp merc on a hill (10k trials). Results: 11.5% horse wins, 53% horse retreats, 35.5% merc wins. 88.5% of the time we would get our GA from it. On average if the merc survived it would have 3 hp, and if the horse survived it would have 1.

	10-10-2003 19:48									#22
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I didn't realize that causing retreat of a unit would fire a golden age.

	10-10-2003 20:33									#23
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Don't 'Cats have free shots when in the defending stack?

	10-10-2003 21:14									#24
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quote: Originally posted by roadcage Don't 'Cats have free shots when in the defending stack?

yeah whose idea was it to bring cats along thats just going to complicate the hell out of everything.

	10-10-2003 23:17									#25
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GCA is a bunch of cheaters who dont deserve to be in this game!
(i know we don't have proof yet)

	11-10-2003 00:03									#26
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If there were to be another ISDG game would Apolyton likely refuse to participate if GCA were involved? I guess CFC and CDG would have a similar attitude?

	11-10-2003 01:30									#27
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quote: Originally posted by notyoueither Unless... they came forward with an elite, attacked, won, and then disbanded the unit. I doubt very much that they would have done that.

Hmmm... not totally unthinkable, even if the chance is very remote... if an elite would have come out of the FoW, and lost 4 pips, I would abandon it instead of leaving it next to NMs which would surely trigger the GA when attacking. The only thing I'm not sure on is if it is possible to abandon a unit with no movement remaining, as otherwise moving it out of the way is of course always better (and possible, I think)

DeepO

	11-10-2003 01:39									#28
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I think you can "disband all" a unit even if it has no movement left.
Maybe they moved all the other units away from the tile (or there was only the elite attacker on the same tile) and then disbanded all. Is it even possible to "disband all" when there's only one unit on a tile? Otherwise, they had to sacrifice a unit - not likely at all, unless they REALLY don't want us to get our GA now.

	11-10-2003 01:59									#29
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A Horseman that retreats does not "lose" the combat, and therefore does not trigger a GA.


Dominae

Last edited by Dominae on 11-10-2003 at 02:36

	11-10-2003 02:11									#30
	Avatar Enlargement: We've got the solution

quote: Originally posted by DeepO Hmmm... not totally unthinkable, even if the chance is very remote... if an elite would have come out of the FoW, and lost 4 pips, I would abandon it instead of leaving it next to NMs which would surely trigger the GA when attacking. The only thing I'm not sure on is if it is possible to abandon a unit with no movement remaining, as otherwise moving it out of the way is of course always better (and possible, I think) DeepO

You cannot disband a unit with no movement left.