The Civ IV Combat System

[T_McC]

After all the discussion, I'm not sure whether this has already been pointed out, but ...

There is an error in post #24: Under the heading "Basic chance of success", an example was given for an Archer fighting a Horse Archer, and it was stated that success (winning) for the archer was "the chance that the archer wins at least 7 out of 11 rounds". That is incorrect. The correct condition is that the archer wins 7 rounds before losing 5, which is not the same thing.

In the notation of post #24, the correct summation is:
f(7;11, 0.4) + f(7;10, 0.4) + f(7;9, 0.4) + f(7;8, 0.4) + f(7;7, 0.4)

This would sum to ~14.4% instead of the quoted 9.9%.

[Ellestar]

Ok, i made some additions to my combat calculator. v0.13 of a combat calculator is here http://c4combat.narod.ru/c4c_v0_13.htm
Edit: v0.13 with a bug fix

I still don't know how exactly a number of first strike rolls is calculated :/ We should do some more testing to be sure.

****************************************

Originally posted by T_McC
After all the discussion, I'm not sure whether this has already been pointed out, but ...

There is an error in post #24: Under the heading "Basic chance of success", an example was given for an Archer fighting a Horse Archer, and it was stated that success (winning) for the archer was "the chance that the archer wins at least 7 out of 11 rounds". That is incorrect. The correct condition is that the archer wins 7 rounds before losing 5, which is not the same thing.

In the notation of post #24, the correct summation is:
f(7;11, 0.4) + f(7;10, 0.4) + f(7;9, 0.4) + f(7;8, 0.4) + f(7;7, 0.4)

This would sum to ~14.4% instead of the quoted 9.9%.

Note that there are 11 rounds for a reason. If archer wins at least 7 rounds out of 11, then he loses no more than 11-7=4 rounds.
By the way, don't forget to check your formulas on easy examples. Say, 1 str vs 1 str. By your formula chance to win is 74,6% which is obviously wrong. That's because C(10,7) is partially in C(11,7) etc. so you count the same hit/miss combinations several times.

[MattUGA23]

Can someone please just give a simple breakdown for us about what's best against what. For example, what's best against archers, etc. And then, a few simple rules to keep in mind about upgrading and attacking. I appreciate everyone's efforts, but I'm not going to dust off the TI-85 calculator and solve Trig questions I missed 10 years ago to figure out if my cavalry will beat his Rifleman.

Thanks so much in advance.

[OzzyKP]

Ah! Too much math!

[Theseus]

Excellent work. This will be invaluable as combat calculators are developed, but, more importantly, a basic understanding of the math underlying combat mechanics will provide the foundation for players' 'intuitive' feel for the many permutations of A versus D.

(and it only took me 4 or so read-throughs to get it! )

[DeepO]

Yeah, I'm thinking on reworking the largest post to show both advanced (with formulae), and layman (some rules of thumb) parts. Most of that is already in this thread, somewhere, but I need to find the time to separate it... not tonight, and probably not before the weekend...

DeepO

[BgT]

Ok... so basically...emmm the summary of this post is that those odds that the game gives us (right click over the unit) are useless, right?
I've had one case where I actually loaded the same savegame 4 times (with usual 30 minute load time ) and the outcome was completely the same. So it seems the seed of the randomizer is some game data and is always the same? This specific case was:
damaged tank vs. wounded maceman
I think maceman had 5.6 strength and tank around... hm 9-11. Well, the numbers after right click were showing 10.4 vs 8.5 for the tank. In all 4 cases the maceman won. Can someone explain to me how is this possible? If it's because the wounded unit stuff - why are those numbers there anyway?! 10.4-8.5 I mean. If that would be the odds, than the probability of maceman winning all 4 fights is 0.04 or 4%.

[Skanky Burns]

The random seed is probably saved to prevent cheating, as it was in Civ3.

[DeepO]

Originally posted by BgT
Ok... so basically...emmm the summary of this post is that those odds that the game gives us (right click over the unit) are useless, right?
I've had one case where I actually loaded the same savegame 4 times (with usual 30 minute load time ) and the outcome was completely the same. So it seems the seed of the randomizer is some game data and is always the same? This specific case was:
damaged tank vs. wounded maceman
I think maceman had 5.6 strength and tank around... hm 9-11. Well, the numbers after right click were showing 10.4 vs 8.5 for the tank. In all 4 cases the maceman won. Can someone explain to me how is this possible? If it's because the wounded unit stuff - why are those numbers there anyway?! 10.4-8.5 I mean. If that would be the odds, than the probability of maceman winning all 4 fights is 0.04 or 4%.

The numbers are not completely wrong, but you don't take into account how wounded a unit is.

This is an interesting example, so let me try to work it out:

You had a tank, normally at strength 28, at let's say 9 after damage. This means his hp are 9/28 * 100 = 32.

His strength, modified, is the 10.4 you see. So T = 10.4

The maceman was near full health at 5.6. his hp were 5.6/8 * 100 = 70.

His strength, modified is 8.5. So M = 8.5.

Now look at the numbers: the tank deals a little bit more damage, and has a little bit better chance of winning a round. It also is less than half the hp, so in a way only half the strength.

The maceman has little less odds of winning a round, and does a little less damage if it would win, but it only has to eat up 32 hp.

The difference between modified strengths M and T is not large at all: it's only ~10%. And from the looks of it, your tank needs to hit 4 times, before getting hit twice. I'd say the chance of him winning are less than 15%. Which means that the maceman is 6 times more likely to win this battle...

DeepO

[DeepO]

Originally posted by Skanky Burns
The random seed is probably saved to prevent cheating, as it was in Civ3.

It is.

DeepO

[BgT]

I've done some calculations for the numbers above and I didn't find them being so bad for the tank.

It says 60.9 : 39.1 in favour of maceman.

Now comes the interesting part.

If maceman would have 5.3 and modified strength of 8.1 the calculation shows:

38.5 : 61.5 now in favour of tank

If maceman would have 5.8 and modified strength of 8.8:

75.6 : 24.4 in favour of maceman

Why did I write this? Well, someone could double-check these calculations and confirm that my excel sheet returns correct info. The other reason is to show that without a tool like that, we have NO CHANCE to see the outcome of the battle. Tank stays at his 9 / 10.4 and when maceman's strength changes from 5.8 to 5.3 we get this huge difference - from 75.6% to 38.5%

Edit: I see one possible problem. How the game rounds certain data? For instance Hit points, probability of hit and dealt damage.
Hm, I see another. The example that describes first strikes on the first page gives VERY small chance of winning to Archer (when we disregard first strikes)

[maven]

hmmm... if all that is true. . .

Admittedly I skimmed most of this topic . . .

Doesn't anyone else notice. . .
If two units that are fairly close in attack power are fighting, after the first round,
if the unit moves it most likely will die.

eg. So if for instance i have a warrior full health and it's attacked by warrior full health.
say 2 of my warriors die(I lose 2 of my hp), and I'm left with one. . .

if his unit repositions to attack my final one, most likely he's dead, if I reposition then I'm likely going to die. I think the attacker normally repositions first, but it's not always the case.

The question is . . . Does repositioning happen after the calculations or before it?

I realize it could be a coincidence, but if you watch it, I think you'll agree. Maybe tonight I'll start writing down the results of battles.

good discussion btw, I'll have to go back through this when I have some more time.

Maven

[BgT]

Numbers in my last post are wrong, I found the mistake. I think it's correct now. My conclusions are, however, correct. Small changes can lead to big difference.

Tank 9/10.4
Maceman 5.6/8.5
----------------------
25.7% for Tank

Tank 9/10.4
Maceman 5.3/8.1
----------------------
41.1% for Tank

Tank 10/11.6
Maceman 5.6/8.5
----------------------
64.2% for Tank

Tank has 28 max Strength. In this particular case Strength 9 gives him 25.7% chance to win. Only ONE point more, Strength 10, gives him 64.2% chance to win. Is this possible? Seems it is.

Ok, now I only have to implement First strike chances and then le'ts got to war.

[SpencerH]

After skimming the first page I thought I'd interject Schrödinger's wave equation into the mix of calculations but then I thought why bother. In any case, I still lost full strength gunships to knights yesterday and also lost a bunch of mech inf and tanks to grenadiers despite removing the city bonuses, so I guess the spearman v tank isnt quite as fixed as I'd hoped.

[BgT]

Tell us the exact case when that happened and we'll see if you have only been unlucky.