24-01-2001 12:02									#1
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What is the order that they come? I mean, say I have a Vet. Knight in a city w/ city walls on a hill.
Def 2
Vet=*1.5
City walls=*3
Hill=*2, but what order?
If there's any other bonus I've left out feel free to add it in. Thanks.

	24-01-2001 15:06									#2
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It doesn't matter!

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	24-01-2001 18:15									#3
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Correct sir. Since multiplication is associative, 2*1.5*3*2 = 1.5*2*2*3 = 3*2*2*1.5, etc. = 18. I'm so sad I didn't get to it first!

	24-01-2001 18:18									#4
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In case you're worried about integer roundoff (in which case the order would matter), all the numbers are multiplied by 8, so roundoff is to the nearest 1/8.

Edit: so a vet fortified pike, defending on a forested river against a crusader (2*1.5*1.5*1.5*1.5*1.5), would, I think, defend at a rounded-off 15.125 instead of 15.1875.
[This message has been edited by DaveV (edited January 24, 2001).]

	25-01-2001 01:56									#5
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I always thought the knight would have a defense of 9 because you dont multiply the bonuses by each other. The basic defense is 2. for vet status, you add 1. for being on a hill, you multiply the basic defense by two, but you don't include the 1 from vet status, so you get +2 from the hills. Then you get +4 from the city walls, so his total is 2+1+2+4, which is 9.

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	25-01-2001 02:50									#6
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Dave V has it right. All Attack/Defense bonuses are multiplied together, never added. There have been numerous threads and tests on this very topic.

	25-01-2001 06:07									#7
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I agree with SilverDragon. According to Sid Meier's Official Strategy Guide (page 270), the bonuses are added.

	25-01-2001 18:29									#8
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The guide is wrong. As Sieve Too said, this has been tested lots of times. It's easy enough to check for yourself: just crank up a couple units in cheat mode. Take my example above: the vet pike would only be 2+1+1+1+1+1 = 7 if you add numbers. Try attacking him with three vet crusaders (5+2.5=7.5) on the same turn - I'll bet you a doughnut they all lose.

	26-01-2001 10:30									#9
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Um....yeah! I knew that multiplication order doesn't count, but I was interested about stuff like pikemen. I guess my example wasn't very good.
And how do easier difficulty levels affect the combat outcomes?

	26-01-2001 13:30									#10
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I`ve never been able to understand what kind of effect hitpoints and firepower have. How about modern units fighting obsolete ones? Does this affect attack/defense strength or HP/FP?

	26-01-2001 18:06									#12
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Marko Polo - the pike advantage is a 50% bonus against units with one hitpoint and a movement of two. So one of the +1 or *1.5 modifiers accounts for that.

Chainsaw - there's no intrinsic advantage for modern units versus ancient; catapults can kill musketeers although the musketeers are a more modern unit. Hitpoints determine how hard a unit is to kill; firepower determines how much damage a unit does when it hits. A rough approximation in comparing strengths is to compare attack*hp*fp for the attacker against defense*hp*fp for the defender.

	27-01-2001 11:33									#13
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Well, if you guys want to be anal, the pikemen ONLY get defensive advantages for unit numbers 16 to 21, I think. Either that or 22, I've never tried pike vs. Calvalry, but that's the way it goes. Also, many scenario designers have found that special unit "places" have advantages. Yeah, so how does difficulty level (chieftan-deity) affect the chances of winning?

	27-01-2001 16:12									#14
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Subject: hit points and firepower are superfluous

BTW, I think the statement in the subject is valid. Two numbers would suit the purpose.

A,D,H,F are attack, defense, hit points and firepower.
In fact, you need to know A*F*H and D*F*H. You may imagine that
A*F*H replaces A and
D*F*H replaces D and
H, F are set to 1.

H/F lowers accidental behaviour of units only (H lowers it and F raises it).

It is my opinion only, I never discussed it, there may be some mistake in my thoughts.
[This message has been edited by SlowThinker (edited January 29, 2001).]

	29-01-2001 20:06									#15
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ruoxiaohai - barb attack factors are altered based on difficulty level, from 25% at chieftan to 150% at deity. I also have read that city defenders receive a 100% bonus at chieftan level.

SlowThinker - I'm not sure I understand what you're saying. FP does make a difference for defenders, and HP for attackers. I agree that raising FP increases randomness, and raising HP decreases it.

	30-01-2001 10:33									#18
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SlowThinker - I used to think exactly the same thing, but I've been convinced by others' testing (and my own) that there are differences between the various numbers. The combat odds are based on each side rolling an n-sided die, which results in a bonus to the stronger unit. So, to reconsider your example:

With the default numbers: the odds of mech. infantry winning each round are 11/12 (6 + 5 bonus vs. 1). Mech infantry needs to win 20 rounds, so will probably take 2 hits = 4 hitpoints.

With "unified" numbers: the odds of mech. infantry winning a round are 8/9 ( 18 + 14 bonus vs. 4). Mech infantry needs to win 10 rounds, so will probably take 1 hit = 1 hitpoint.

	30-01-2001 00:31									#19
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I am not sure if I have understood:

Mech. Inf. has 0,1,2...6 on his die (7 sides).
Artillery has 0,1 on his die (2 sides).

Is it OK?
(I thought there is just one 7-sided die, 6 sides own Mech. Inf., 1 side Artil.)

	30-01-2001 01:26									#20
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As I understand it, the Mech. Infantry has a 48-sided die (0,1,...,47), while the artillery has an 8-sided die (0,1,...,7).

Here is a link to a thread detailing some calculations and experiments: http://apolyton.net/forums/Archives...4-1-000624.html

	30-01-2001 02:01									#21
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... and in the event of a draw the defender wins - thus a zero defence unit such as a barb king or diplo can (very) occasionally defeat an attacker.

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Scouse Git[1]

"CARTAGO DELENDA EST" - Cato the Censor
"The Great Library must be built!"
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were it not so it would be 'the way'." - Paul Craven

	30-01-2001 05:03									#22
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I have read that thread quickly.

I hope I have understood it:

On defender's die	Nr. of attacker's wins	Nr. of defender's wins
0	47	1
1	46	2
2	45	3
...	...
6	41	7
7	40	8
Total:	(40+47)*8/2	(1+8)*8/2

Generally:
Suppose m=max(a,d), n=min(a,d). Then wins are distributed among both units following way:  

	Attacker's wins (AW)	Defender's wins (DW)	Total number of attacks
a>=d	m-n/2-1/16	n/2+1/16	m
a<=d	n/2-1/16	m-n/2+1/16	m

 

In our example:  Artillery wins 1/2+1/16, Mech. Inf. wins 5 1/2-1/16.

(Edited: DaveV multiply these numbers by two: it looks more functional:
Artillery wins 1+1/8, Mech. Inf. wins 11-1/8;
11=6+5, 5 is the "bonus" for the stronger unit)

quote: Originally posted by DaveV on 01-29-2001 12:33 PM With the default numbers: the odds of mech. infantry winning each round are 11/12 (6 + 5 bonus vs. 1).

	30-01-2001 15:56									#23
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Sorry, my last post is indigested. I am rebuilding it now.

	30-01-2001 18:12									#24
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I have rebuilt the post now.

	30-01-2001 19:12									#26
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This bad explanation lies somewhere on Apolyton:

quote: "FIRE!" Making War in Civilization II by Marc Fisher The actual equation used to resolve each combat round is: __a__ (a+d) where: a = attacker's attack rating d = defender's defense rating The result is a fractional number (percentage). A random number is generated, and if the result is less than the percentage, the defender loses hit points equal to the attacker's firepower rating. The reverse happens if the random number is higher - the defender's firepower rating is subtracted from the attacker's hit point rating

	30-01-2001 19:28									#27
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Oops, after further thought I have to disagree with your "expected result" calculation. The question is, how much damage do we expect the mech infantry to sustain while destroying the artillery? I think the answer is a straight ratio of the combat strengths:

mech infantry damage/artillery damage = 16.31/2.25

artillery damage = 100%; mech infantry damage = 2.25 / 16.31 = 14%; so I expect the mech infantry to survive with 86% of hitpoints. A small difference, I know...

	30-01-2001 20:43									#28
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Of course, it was my mistake. A big difference in a general case.
I corrected it, somebody may consider that post useful.

Note:
If we disregard sixteenths, then weaker unit makes 1/(2*m/n-1) of damage.
For large ratio m/n, weaker unit looses a half of his power ("-1" in the expression looses his significance).

	31-01-2001 00:09									#29
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I have a presentiment that attacker has a 50% chance to get vet status, defender has a 100% chance.

Is it OK?

	31-01-2001 04:37									#30
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SlowThinker - I concur tests I have made would tend to suggest that the attacker will win vet status (without Sun Tzu) 50% of the time - I do not have any stats for the defender


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Scouse Git[1]

"CARTAGO DELENDA EST" - Cato the Censor
"The Great Library must be built!"
"A short cut has to be challenging,
were it not so it would be 'the way'." - Paul Craven