Strategy

[starlifter]

by Slow Thinker:

bonuses are multiplied IMHO:

1 * 3 (mountains) * 2 (fortress)

i.e. a non-fortified caravan has the defense 6

Thanks for the input, Slow Thinker. However, the defenses are not multiplied, they are summed, calculated on the base value of the unit. Several things lead me to believe addition is used:

1. That is what Microprose and Sid Meier have stated, with no retractions I'm aware of.

2. The general game results I have seen seem to comply with it.

3. This is the approach used for taxes, science, and luxuries.

4. The even/odd factors and rounding method was chosen to emphasize the increase in usefulness of a Cavalry over a Dragoon, for instance.

5. A quick test can be tried with a Mech Infantry on a mountain in a fortress.

6 + 12 + 6 = 24 (addition method)

6 * 3 * 2 = 36 (your suggestion)

The defense factor difference is so large that you will see, even with informal testing, that the correct method is the "Addition Method" (defense factor = 24).


BTW, I read the (very slow-loading) Apolyton thread. To me, they were not clear about how the defense factors were applied. The percentages wre correct, but if they advocated a straight multiplication, then those threads are wrong, unless someone can git a direct confirmation from Brian Reynolds, see the source code (post it <IMG SRC="http://forums.civfanatics.com/ubb/smile.gif" border=0>), or decomplile it and determine the exact function used. Failing that, a large Monte Carlo simulation should confirm the addition method, too.


On june 12, 2000:
"(I think Hasdrubal is correct, modifiers are summed, not multiplied; much like the fact that a library and university combo doubles a city's research (1*[1+.5+.5]), NOT (1*1.5*1.5 = 2.25) times as much research. I'm in the minority on this view.)"

the above was posted by one Apolyton person in the http://www.apolyton.net/forums/Forum3/HTML/001196.html thread.


I see Apolyton has been haggling over this for a long time. Haggling seems silly to me, since there is only one absolute truth. All "official" sources I've ever read explictly state the addition method, and even use such examples.

I won't go jump into Apolyton's debate over this, but I suppose there is a chance that Reynolds used a different (e.g., the multiplier) method but documented and blessed the publication of the "addition" method. Perhaps the publications are wrong, or misprinted, too. <IMG SRC="http://forums.civfanatics.com/ubb/beerchug.gif" border=0>

EDIT: Typos.


[This message has been edited by starlifter (edited July 19, 2001).]

 

[starlifter]

Well, Slow Thinker, it seems the published addition formula does not bear up under scruitiny with several hundred tests!

I've just completed a quick and dirty 500 tests of Legion and Catapult vs. Caravan in a fortress on a mountain. The results tend to confirm that at King and Deity, the caravan is defending with 6, not 4. Barring some unknown or overlooked factor, this tests to support your earlier post of 1*3*2=6, not the published 1+2+1=4.

At this point, because I don't have any more time right now, I'd say you are indeed correct, Slow Thinker!

I conducted tests in groups of 50. Typically the Catapult vs Caravan results were 25-25 +/- 2. All the Legion vs. Caravan tests showed the Legions getting butchered, when the results should have broken even.

So, at the moment, I believe the sources that all quote the addition method are actually incorrect, barring some factor coming into play that I'm not aware of.

So, my corrected statement <IMG SRC="http://forums.civfanatics.com/ubb/smile.gif" border=0> (thanks Slow Thinker!!) is:


On a mountian fortress, the defense value for a non-fortified caravan is:

1 - Base value
x3 - Mountain bonus (triple defense)
x2 - Fortress bonus (double defense)
---
6



I am attaching a set of 3 test .SAVs with the Catapults, Legions, and Caravans... plus Diplomats, Warriors, and Horsemen. The 3 .SAVs are identical, except one is Chieftan, one is King, and the other is Deity. individuals can easily run their own tests and see the results for themselves.

Because I don't have the time for more tests now, I'm kind of extrapolating when I say the multiplication method is probably used in all unit combat resolutions, not just pre-gunpowder. BTW, I have not done any Veteran tests or Walls tests, though it seems likely that these are going to be multiplied, too, given the general algorithm.

Thanks again, Slow Thinker. <IMG SRC="http://forums.civfanatics.com/ubb/goodwork.gif" border=0> After lookin into it today, it seems the faction at Apolyton that supports the multiply theory is correct, and the addition method is indeed wrong (barring of course, other as yet unknown explanations).

EDIT: Add Attachment.

[This message has been edited by starlifter (edited July 19, 2001).]

 

[starlifter]

posted July 18, 2001 02:06 AM by HEIROPHANT:

in caculation you put a carvan on a mountain and it has a fortess that would be 6 defesne 1*2*3
...

BTW, you, too, are correct Heirophant. Earlier, I had stated the defense factor was 4. Based on the testing I've done so far as a result of Slow Thinker's reference, I now think you and Slow Thinker have the correct solution!

 

[SlowThinker]

Starlifter,
<IMG SRC="http://forums.civfanatics.com/ubb/smile.gif" border=0> I see you are hungry for testing. There are some unanswered questions in the <A HREF="http://apolyton.net/forums/showthread.php?s=&threadid=988">Info: Combat (GL)</A> thread. I would come in too...

(I appreciate your approach very much. People usually prefer to talk long time about things that may be solved very quickly. See the debate about the healing for example: http://apolyton.net/forums/showthread.php?s=&threadid=2655 )

BTW, did you get my e-mail (I sent it to starlifter@eudoramail.com) ?

[This message has been edited by SlowThinker (edited July 19, 2001).]

 

[Relegin Bor]

Nice debate Starlifter, Slow Thinker et alia ! I'm still not convinced! I'm sure I have documentation on this matter. Currently I am in transit so upon my return I shall check my own records

I am aware of SMAC and her penalty

I did not pursue a full monte-carlo style simulation to confirm the long-term odds match the theory.

I no nothing of this "SMAC" and "monte-carlo" of which kittenOFchaos and Starlifter speak

!

Please elucidate

!

Cheers,

Relegin Bor

PS: kittenOFchaos - very cool name!

 

[TrailblazingScot]

SMAC = Sid Mier´s Alpha Centauri...a truely excellent game.

In that game non-combat units suffer a 50 percenty vs attack...TO get around this armour them and non-combat units are classed as combat units and the penalty is removed!

Thanks for the compliment about my dogtag!...you are about the 8th person!

 

[Relegin Bor]

<IMG SRC="http://forums.civfanatics.com/ubb/smile.gif" border=0> I’m glad to see that Slow Thinker & Starlifter have agreed on defensive calculations. It is distressing to us mere mortals when the gods of Civ clash! <IMG SRC="http://forums.civfanatics.com/ubb/wink.gif" border=0>

However, IMHO, in this case neither are completely correct. <IMG SRC="http://forums.civfanatics.com/ubb/smile.gif" border=0>

I humbly suggest that defensive bonus is neither “all additive” nor “all multiplicative” but a combination of the two. To wit, defensive bonuses offered by terrain, veteran status and fortifying are described in the rule book and Civilopedia as a “ plus percentage”.

Eg: The Civ II / Civilopedia / Game Concepts describes the effect of the “Fortify” command as:
“The defensive value of fortified units is increased by 50%.”

The Civ II / Civilopedia / Terrain Types describes the unit defence bonus of hills as “+100%”

By contrast, the defensive bonus offered by structures is described as a “doubling” or “tripling” of the defence factor of units.
Eg: The ToT / Civilopedia / City Improvements describes the effect of City Walls
as:
“Units in city are tripled on defence versus ground attacks.”

Add to this the ToT rule book’s reference to the effect of City Walls on page 45:
“Veteran status and terrain bonuses are figured in before this tripling takes effect.”

Therefore, a units total defensive score is its base defence plus percentage modifiers multiplied by structure modifiers. To use the example quoted by Slow Thinker & Starlifter a Caravan in a Mountains Fortress would have a total defensive score of 6.

Base (1) + Mountains (+200% or 2) * Fortress (double)
1+2*2=6

You will note that in this example the result is the same as if we had simply multiplied the modifiers. Hence the obfuscation <IMG SRC="http://forums.civfanatics.com/ubb/wink.gif" border=0>. The disparity becomes clearer in more complicated situations, such as a Fortified Veteran Warrior in a Hills Fortress on a River, which I have set out below.

Additive Method
Base Defence 1
Veteran + 50% (0.5)
River + 50% (0.5)
Hills + 100% (1)
Fortified + 50% (0.5)
Fortress + 100% (1)
Total 4.5

Multiply Method
Base Defence 1
Veteran *1.5
River *1.5
Hills *2
Fortified *1.5
Fortress *2
Total 13.5

Combined Method
Base Defence 1
Veteran + 50% (0.5)
River + 50% (0.5)
Hills + 100% (1)
Fortified + 50% (0.5)
Fortress Doubled
Total 7


On testing, I needed a veteran catapult (Attack 9) to be able to consistently kill the warrior in the example. A normal catapult occasionally killed the warrior, but it was far more likely to lose the encounter. This suggests the warrior’s defence was more than calculated using the additive method (4.5), much less than calculated using the multiplicative method (13.5) and consistent with the calculation of the combined method (7).

I dare say my testing is by no means as rigorous as that done by Starlifter. I have attached it for what little value it is.

Humbly yours,

Relegin Bor
<IMG SRC="http://forums.civfanatics.com/ubb/rocket.gif" border=0>


[This message has been edited by Relegin Bor (edited July 21, 2001).]

 

[Relegin Bor]

Can some one please tell me how to attach a zip file and to insert a table?

Thanks,

Rele.



[This message has been edited by Relegin Bor (edited July 21, 2001).]

 

[Relegin Bor]

The outcome of combat in Civ is determined by two aspects - the chance “to hit” and the damage done.

Combat is fought round by round until one unit is deceased. Damage to each unit involved is determined each round. The chance of a unit winning a round is determined by adding all attack and defence factors together and then dividing this number into the factor of the unit. Eg: an Archer (attack 3) attacks a Phalanx (defence 2). The chance of the Archer winning the round is 60%

ie: attack/(attack + defence) or 3/(3+2).

Like wise the chance for the Phalanx winning the round is 40%.

If the Phalanx was Veteran (defence 3) the chance would be 50/50.

Damage is calculated by subtracting the winning unit’s Fire Power from the loosing unit’s Hit factor*10 (Hit Points or HP). So in the above example if the Archer (FP 1) won against the Phalanx (HP 10) the Phalanx would lose 1 HP and the combat would continue.

This explains why strong attacking units can take an absolute caning <IMG SRC="http://forums.civfanatics.com/ubb/spanking.gif" border=0> in some contests and why relatively high hit point units (such as Settlers as indicated above by Starlifter) can be hard to kill. The attacker might win more rounds but if the defender has twice as many hit points the attacker might well lose the engagement.

In tests for the example I posted for determining defensive bonus, the Warrior with defence 7 was often killed by Alpine Troops with an attack of 5 as the Alpine Troops have twice as many hit points.

Thus we have the element of chance in any engagement!

Cheers,

Relegin Bor

[This message has been edited by Relegin Bor (edited July 21, 2001).]

 

[Duke of Marlbrough]

I agree Relegin Bor. That is how I have always done my calculations for combat.

The only other thing I remember is that you have to round the additive figures before multipling....?

Thus it would be:

Base Defence 1.0
Veteran + 50% 0.5
River + 50% 0.5
Hills + 100% 1.0
Fortified + 50% 0.5
-----
3.5

Round down 3.0
Fortress Doubles 3.0
-----
Total 6.0

This is how I remember it....

This would also support starlifters tests with the caravans.

Base 1
Mountain +2
--
3

Fortress x2
--
Total 6


On Edit: To attach a zip file you need to use the attachment section when you are replying. It is right under your username and password.

[This message has been edited by Duke of Marlbrough (edited July 21, 2001).]

 

[SlowThinker]

Relegin Bor,
There is an "Attachment:" field under the "Post reply" page.
Do you want to insert a html table directly into you text?
<hr>

<font size=1>Originally posted by Relegin Bor </font>
Multiply Method
Base Defence 1
Veteran *1.5
River *1.5
Hills *2
Fortified *1.5
Fortress *2
Total 13.5

To be Fortified is not cumulative with fortress, only Fortress applies.

But there is something wrong in my presumptions: At least, river with hills is cumulated in some different manner than I thought! (I tested with hit points set to 10=100 in rules.txt so that the fortuity is low)

<font size=1>Originally posted by Relegin Bor </font>
Combat is fought round by round until one unit is deceased. Damage to each unit involved is determined each round. The chance of a unit winning a round is determined by adding all attack and defence factors together and then dividing this number into the factor of the unit. Eg: an Archer (attack 3) attacks a Phalanx (defence 2). The chance of the Archer winning the round is 60%

ie: attack/(attack + defence) or 3/(3+2).

No, the chance of the Archer winning the round is (3+1)(bonus for the stronger unit)/(3+2), i.e. 80%
Read <A HREF="http://apolyton.net/forums/showthread.php?s=&threadid=988">Info: Combat (GL)</A> thread.


[This message has been edited by SlowThinker (edited July 21, 2001).]

 

[SlowThinker]

I tested it extensively and this is my result:
Everything is multiplicative but the river is additive! The terrain forms a unified multiplier that may include a river adjustment (i.e. a rivered mountain multiplies the defense strength by 3.5(=3+0.5), not 4.5(=3*1.5) )

An example of testing (see the attached file and the situation on east of map: there are vet warriors on rivered mountain in a fortress attacked by chariots.
(I tested with hit points set to 10=100 in rules.txt so that the fortuity is low.)
warrior's defense is 4 <FONT SIZE="1">(base defense)</FONT>*1.5<FONT SIZE="1">(veteran)</FONT>*2<FONT SIZE="1">(fortress)</FONT>*(3+0.5)<FONT SIZE="1">(rivered mountain)</FONT>) = 42
Therefore I set chariot's attack to 42:

Warriors, Feu, 0, 1.,0, 1a,4d, 10h,1f, 1,0, 1, nil, 000000000000000
Chariot, PT, 0, 2.,0, 42a,1d, 10h,1f, 3,0, 0, Whe, 000000000000000

Outcomes were even.


[This message has been edited by SlowThinker (edited July 22, 2001).]

[This message has been edited by SlowThinker (edited July 22, 2001).]

 

[SlowThinker]

ignore

[This message has been edited by SlowThinker (edited July 21, 2001).]

 

[SlowThinker]

Originally posted by Duke of Marlbrough:
The only other thing I remember is that you have to round the additive figures before multipling....?

AFAIK the attack and defense numbers are rounded to 1/8, i.e. to 1.125, 1.250, 1.375 etc., but after the multiplying.
See <A HREF="http://apolyton.net/forums/showthread.php?s=&threadid=988">Info: Combat (GL)</A> thread.

 

[Duke of Marlbrough]

No offense, but just because it is listed on Apolyton doesn't make it fact for me. They have it listed that the power graph and power rating take into account military units, which it doesn't, so.....

And as starlifter said, it seems to go against everything I remember from the game and have seen published in the hint/strategy books. But I am always open to new tests.

 

[SlowThinker]

Originally posted by Duke of Marlbrough:
No offense, but just because it is listed on Apolyton doesn't make it fact for me.<IMG SRC="http://forums.civfanatics.com/ubb/smile.gif" border=0>

I don't believe it 100%, but 95%: not because it is listed on Apolyton but because i read threads where they found it out: it seems it was tested very thoroughly: see http://apolyton.net/forums/Archives/Archive-000008/HTML/20000504-1-000624.html

Originally posted by Duke of Marlbrough:
But I am always open to new tests.<IMG SRC="http://forums.civfanatics.com/ubb/smile.gif" border=0>

Go on! Verify it.

 

[EyesOfNight]

And knowing this helps you how?

 

[Relegin Bor]

Originally posted by Duke of Marlbrough:
The only other thing I remember is that you have to round the additive figures before multipling....?

I went back and tested Regular & Veteran Catapults versus Veteran Fortified Warriors in a Hill Fortress on a River (henceforce known as “Vet Warriors”).

In a hundred combats versus the Vet Warriors, Regular Catapults won 15 combats and lost 85.

In a hundred combats versus the Vet Warriors, Veteran Catapults won 81 combats and lost 19.

Regular Catapults attack at 6 and Veteran Catapults attack at 9. So if the Vet Warriors were defending at 6 then there should be a 50/50 result versus Regular Catapults. Likewise if the Vet Warriors were defending at 9 there should be a 50/50 result versus Veteran Catapults. As the defence of the Vet Warriors in this scenario is clearly superior to the Regular Catapults attack and clearly inferior to the Veteran Catapults attack I suggest that there defence bonus was between 6 & 9. As the results slightly favoured the Veteran Catapults I would suggest that the defence factor for the Vet Warriors in this scenario is 7. This would support my proposed Combined Method of determining defence and also suggest that the rounding down does not occur before the structural defence multipliers.

I took extra data during the combats, specifically the colour of the Hit Point bar of the winners. I thought I might be able determine the exact defence factor by analysing the number of combat rounds that were won and lost. My attempts at analysis only confused me! My skills at probability and statistics are way too rusty to make sense of the data. Perhaps someone else could look at it (please).

Cheers,

Relegin Bor

 

[Relegin Bor]

OK! So, I did some more tests and found a consistant slight advantage to the defender. So, thinking my method flawed, I went back to basics and just had a regular Warrior versus a regular Warrior. No fortifying, non-veteran, un-modified grassland . 200 combats me attacking the AI, 200 combats the AI attacking me. The results:

Me vs AI 66 to 134 - ie: a 2 to 1 advantage to the defender.

AI vs Me 61 to 139 - ie: again a 2 to 1 advantage to the defender.

What’s going on here?

I tried Horseman AI versus my Phalanx, again no modifiers. Roughly the same result - 76 to 123 advantage defender.

Slow Thinker’s bonus to the stronger unit (which I have heard of but coudn’t find in the literature) doesn’t appear to work in this case unless the bonus is to the defender if the attacking factor = defending factor.
I don’t believe that no one has noticed this before so hopefully someone can enlighten me!

Cheers,

Relegin Bor

PS: Slow Thinker, the example I quoted for determining combat comes from the ToT rule book (Hey, I didn’t claim originallity!

).
Do you suspect we are deliberately being misled?

Or am I justing getting more paranoid?
Rele

PPS: Slow Thinker, I couldn’t download your file (404 error).
Rele.

 

[Relegin Bor]

Originally posted by SlowThinker:
Everything is multiplicative but the river is additive! The terrain forms a unified multiplier that may include a river

Slow Thinker, I agree with your "Unified Terrain Theory"

I recalculated my previous example:

Unified Terrain Theory
Base Defence 1
Veteran *1.5
Hills with River *2.5
Fortress *2
Total 7.5

Combined Method
Base Defence 1
Veteran + 50% (0.5)
River + 50% (0.5)
Hills + 100% (1)
Fortress Doubled
Total 6 (apologies to Duke of Marlborough)

And the results given by the Unified Terrain Theory fit the results of my testing. Ah, the wonders of scientific method.

Originally posted by SlowThinker:
To be Fortified is not cumulative with fortress, only Fortress applies.

DOH!

"Well I'll be a henpecked chicken in a hog patch!"

I've only been playing for five years and this fact eluded me! Is it the same for fortifying behind City Walls?

Cheers,

Relegin Bor