FECK!!! It seems im wrong
Here are the results for the extented test.....
Babylonian Vet Archer/Mongol Vet Archer

Win Green 10 /18
Win Yellow 44/40
Win Red 37/34
Lost Green 0/0
Lost Yellow 1/1
Lost Red 8/7
ok, the win/lost ratio is the same, but there still something, the number of victories with the stamina bar remaining in the green zone for the mongol is higher, really strange, maybe, extended tests for another situation will be needed.....
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quote:
<font size=1>Originally posted by Blaupanzer on 12222000 10:05 AM</font>
Bohlen, both have the same hit points since both are the same type of unit. Barring a terrain anamoly, implication is 50/50 would be normal. A builtin bias toward the defender would not surprise me, actually. Statistically, that part of rixxe's result is much more significant than the national bias supposedly shown in the table.
What I'm saying is that one would usually find that a 50/50 scenario would not be the case in this instance because the AT's firepower is only 1, compared to the AT's hit points of 2. Here, the AT is able to lose a few of the "minibattles" and still survive. If we made the AT's firepower a 2, then I would expect to see about a 50/50 split.
[This message has been edited by Bohlen (edited December 22, 2000).]
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quote:
by Edward
rixxie,
Let me see if I've got it straight.
...
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..
..
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Is this correct?
 Absolutely !!!! Well, now someone understand what ive done, ouf
quote:
by Albert B
I majored in applied mathematics and I do know about statistics and numerical analysis. Now that I understand your tables, I find them intriguing. First, each individual test of only 20 attacks leads me to believe that the “advantage” of the Mongols may well be just an anomaly. Flipping a coin 20 times should result in 10 heads and 10 tails but most of the time this will not be the case. Since the difference in the number of wins is never more than 3, I would say that there is not conclusive evidence that the Mongols have a definite advantage. However, that being said, the fact that all 4 tests resulted in a Mongol victory and even more so that the nonvet tests each resulted in a +1 victory margin while each vet test ended in a +3 differential, it makes me go “hmmmm….”.
 I'll do extanded tests, but only with the fourth case (Vet Archer)....We'll be fixed on it. If the difference increase by 45 times (out of 100 attacks) ill be right, if it still equal, or worst, it reduces, i'll be wrong, what would be a disaster for my notoriety....
quote:
by Albert B
I have a quick question before I go off to test... In your original post about testing, rixxe, you stated that gov's must be the same. Is this just to keep the 'control' group consistent or is there some accepted advantage that a particular government has over another that I don't know about? (other than fanatics for fanaticism and vet spies for communism)
 It's just to be sure that the situations are the same in each cases....
Ok, i have miles of Guinness to drink tonight so i wont have the time to do it before tomorrow, no problemo,....
CU,
Rixxe'O'Rixxe
ps. why am i a settler (ok, because im a newbie), & how do i have a better ranking ?!? strange....:?
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Edward  as I understand it, the number 8 is used as a multiplier to eliminate fractions. So a nonvet alpine has a defense of 5*8 = 40; a vet alpine has a defense of 5*8*1.5 = 60; a vet alpine fortified on a river has a defense of 5*8*1.5*1.5*1.5 = 135. The attacking alpine always has an attack of 40. Each unit rolls a die with a number of side equal to this strength; the attacker wins if his number is higher and the defender wins if his number is higher or it's a tie.
For a single combat round in the simplest, nonvet vs. nonvet case, the odds of the attacker winning are 39/80. While this seems like a pretty slight disadvantage, it becomes significant when you think that the attacker has to win 20 combat rounds before he loses 20.
Note that in the vet vs. nonvet case the singleround odds are not 39/100, as I once thought, but 39/120. If one unit is overstrength compared to the other, its advantage is effectively doubled.
These formulae were developed long ago in
this thread, and I've found them to be dependable in predicting combat results.
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Bohlen, both have the same hit points since both are the same type of unit. Barring a terrain anamoly, implication is 50/50 would be normal. A builtin bias toward the defender would not surprise me, actually. Statistically, that part of rixxe's result is much more significant than the national bias supposedly shown in the table.
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Deity Dude,
As Rufus T. Firefly alluded to, when the attacker and defender have the same combat value, hit points, firepower, etc. the defender will have the advantage.
I'm sure someone less lazy than I can find the thread where this was discussed. Basically an entire battle is broken into mini turns. On each mini turn the computer cranks some random numbers and sees who won. If the attacker wins, the defender losses hitpoints equal to the attacker's firepower. Similarly if the defender wins, the attacker losses hitpoints equal to the defender's firepower. This goes on until one unit has no more hitpoints left.
What are the odds for each mini turn? Each unit is given a combat number. For the attacker it's based on his attack value and his vetness. For the defender it's based on his defense value, vetness, terrain, and a host of fortification modifiers (and there's special unit vs. unit modifiers, etc.). Then each unit rolls a random number and multiplies his roll by his combat number and the unit with the higher result wins.
As you noted, Deity Dude, this should result in an Alpine winning roughly half the time when he attacks another Alpine (5 attack value vs. 5 defense value all other things being equal). The surprise comes from empirical evidence from much hard work by people on this board.
It turns out that the die roll each unit makes is NOT the usual 0 to .99999 a computer programmer would expect. It's actually 0 to 7 with only whole numbers! (0, 1, 2, 3, 4, 5, 6, and 7) And the defender wins ties. This means that a mighty battleship might roll a "0" and a lowly phalanx might roll a "0" too. 0 times anything is 0 so there'd be a tie so the phalanx would win that miniturn! Of course with CIV2's hit point system, the chance of the phalanx winning enough miniturns to win the whole battle is insanely small.
However, the fact that the combat is based on 8 discrete numbers (like a die, not a continuum of rational numbers) means that ties happen quite often with equally matched units (1 in 8 chance? someone check my math) so the defender has an empirically noticeable advantage. Also the fact that the "die" has a 0 on it means that units with 0 combat value can sometimes win when the hitpoints are low (and therefore fewer miniturns must be won to win the battle) e.g. that barbarian leader just might survive your warrior's attack.
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Oh, sorry, let's take this example...:
Babylonian Alpine/Mongol Alpine

Win Green.......0/0
Win Yellow......2/1
Win Red .......>3/5
Lost Green......0/0
Lost Yellow.....3/4<
Lost Red........12/10
So this is a babylonian alpine attacking a mongol alpine, for the first row, and the inverse for the second row.
Now, we take the third result of the first row the one with the ">" just b4...: Its the number of situations (out of 20 attacks) where the babylonian alpine won with his stamina bar remaining in the red zone....
Now the fifth result of the second row (with the "<" after). It's the number of situations (out of 20 attacks) where the mongol have lost the combat, with his opponent's stamina bar remaining in the yellow zone....
I hope its ok now cu
PS: Ill do advanced tests but 4 only 1 situation....its not too long to do.....but tomorrow
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Don't forget about Firepower and Hit Points.
Alpine troops have Hit Points=2, Firepower=1.
More Hit Points = Tougher unit to kill.
[This message has been edited by Bohlen (edited December 21, 2000).]
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Thanks for the explanation rixxe.
Forgetting about the variable values theory for now, I find it interesting that when the OFFENSIVE 5 unit attacked the DEFENSIVE 5 unit (Nonvet Alpine vs Nonvet Alpine) it lost 31 out of 40. I thought that its losses would be closer to 50% rather than the 77.5% reported. Does anyone else find this unusual or is defense supposed to have an advantage when all else is equal.
I am assuming that neither had a terrain advantage.
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I have a quick question before I go off to test... In your original post about testing, rixxe, you stated that gov's must be the same. Is this just to keep the 'control' group consistent or is there some accepted advantage that a particular government has over another that I don't know about? (other than fanatics for fanaticism and vet spies for communism)
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As I stated before, I don't think the theory will hold true under more rigorous testing but to say that it would have been too much work to include a bonus/penalty to attack/defense strength is a bit overstated.
You already have the varible included in rules.txt that gives a 1/0/1 score based on the militeristic view of the civ. To include this in a calculation to resolve combat would be fairly simple. However, based on generally accepted theory that the attack score of a unit is a whole number (since veteran gives a 50% bonus rounded down, etc.), it would appear unlikely that this has been done or the benefits would be far more obvious since a unit would have to receive a whole point(s) more.
Anyway, I have the day off work tomorrow with my daughter still going to daycare so I should be able to run some tests on this and hopefully come up with some more conclusive results.
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I’ve got to put my $0.02 in here.
Thanks for the clarification on the testing results table. I get it now.
I’d have to agree with Mr. Firefly in that the sample group is too small. Kudos too you, rixxe, for taking the initiative to do the tests for this theory on civ personality and how it effects combat. Although I think the theory will not pan out, I’d love to see some more tests. Theories are meant to be proven, so go for it!
I can’t see the programmers putting that much time into making sure that each civ personality has an effect on combat results. The personality settings in the rules.txt simply controls, as Edward pointed out, how the AI creates a strategy for a particular civ.
But keep going. It is a very interesting theory that I’m sure we’d all like to see proven or not proven.
I’ve said this before…Where is Dave V when you need him? The more mathematicians who are present, the better.
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I majored in applied mathematics and I do know about statistics and numerical analysis. Now that I understand your tables, I find them intriguing. First, each individual test of only 20 attacks leads me to believe that the “advantage” of the Mongols may well be just an anomaly. Flipping a coin 20 times should result in 10 heads and 10 tails but most of the time this will not be the case. Since the difference in the number of wins is never more than 3, I would say that there is not conclusive evidence that the Mongols have a definite advantage. However, that being said, the fact that all 4 tests resulted in a Mongol victory and even more so that the nonvet tests each resulted in a +1 victory margin while each vet test ended in a +3 differential, it makes me go “hmmmm….”.
I would definitely be interested in seeing the results of the extended tests you plan to do. I may even have to do some of my own. When the idea was first introduced, I was VERY skeptical. I am still skeptical that in the end, this will pan out as a coincidence but my mind has been opened a little to the possibility… This could get very interesting.
Albert B
Ps, I am basing this analysis with the same understanding of the tables that Edward has just posted.
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rixxie,
Let me see if I've got it straight.
Each of your four tables show the results of 40 battles. For a given table, the left and right column of numbers refer to different battles (with similar combatants).
For any table, the first column has the Babylonians on the offense. They attack 20 times (fresh units each time). The second column has the Mongols on the offense in 20 new battles.
For the Babylonian Alpine/Mongol Alpine table in particular:
When a fresh Babylonian Alpine attacked a fresh Mongol Alpine, the Babylonian Alpine won 5 times (twice with yellow left, 3 times with red left). The attacking Babylonian Alpine lost 15 times (3 times with the defending Mongol Alpine still in the yellow, 12 times with the defending Mongol Alpine in the red).
In a separate 20 battles, when a fresh Mongol Alpine attacked a fresh Babylonian Alpine, the Mongol Alpine won 6 times (once with yellow left, 5 times with red left). The Mongol Alpine lost 14 times (4 times with the defending Babylonian Alpine still in the yellow, 10 times with the defending Babylonian Alpine in the red).
Is this correct?
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I'm not understanding the table could you please explain it again. I tlooks like you put a lot of work into it and may be on to something  I'm just ont undeerstanding the table.
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