Combat Explained....

[Roland Johansen]

Thank you for this great article. It is very useful for people who understand the mathematics a bit.

I read one part that I didn't get completely:

If the expected attacker bonus that is eventually subtracted from the defender’s bonus is greater than the defender’s bonus, the peculiarity helps the attacker (i.e., when overall value for the defender bonus is negative). So, a lot of bonuses will be more valuable than expected if they overcome defender’s bonus. If you’re attacking fortified units in cities, for example, that don’t have a city defense bonus, the specific promotion for that scenario will be worth a little more than its listed percentage value.

In a earlier part you explained how the negative defense bonuses work:

If the overall value is negative, the defender’s modified strength is found by taking the original defender’s strength divided by (1-overall_value). [Note: That’s the same as dividing by (1+abs(overall_value)) when overall_value is negative, which is how I think of it.]

If I understand this correctly, then if the defender has no defense bonuses then it doesn't really matter if the bonuses from the attacker are added to his strength or the defender's strength is reduced by a relative similar amount.

Attacker strength 10 *1.25 vs defender strength 10 has probabilistically the same outcome as attacker strength 10 vs defender strength 10/1.25.

Of course, you already know this, but the first quoted part of text suggests something else. I do agree with the text that describes the lesser effectiveness of specific bonuses of the attacker if the defender has a defense bonus. And it is of course very useful to know the exact percentages of the jump points.

 

[Arathorn]

I read one part that I didn't get completely:

Re-reading, I'm not quite sure what I meant either. Let me ponder on it for a while over the weekend. I have a major goal of understanding collateral damage and having it written up early next week. This is an article in progress. And I think the part you quoted is ... inaccurate. I've got to sit down a bit more and think about the effects of the not-add-to-attacker but subtract-from-defender method they're using. I think I may have it a bit wrong. Thanks for pointing it out and encouraging me to think on it a bit more.

Arathorn

 

[snepp]

Do you have any information on how XP is assigned? I haven't been able to find any details in the manual. (Not that I've looked very hard. )

I know it's been a couple days, but if you haven't already run across this thread, it should answer most (if not all) of your XP assignment questions.

 

[Roland Johansen]

Re-reading, I'm not quite sure what I meant either. Let me ponder on it for a while over the weekend. I have a major goal of understanding collateral damage and having it written up early next week. This is an article in progress. And I think the part you quoted is ... inaccurate. I've got to sit down a bit more and think about the effects of the not-add-to-attacker but subtract-from-defender method they're using. I think I may have it a bit wrong. Thanks for pointing it out and encouraging me to think on it a bit more.

Arathorn

That's absolutely ok. Civ 4 is just out and you're already writing an article about one of the more difficult game mechanics. Errors will be almost unavoidable.

You described the effects of a first strike. But there are differences in the first strike upgrades. Some mention '1 chance of first strike' and some just mention '1 extra first strike'. Do you know what is exactly the difference (how big is the 'chance' on a first strike)?

I guess that completing the article will require some research, because it's not an easy subject. But the main points have been covered by the present version. Great job so far.

 

[hairylegs]

Put that archer in a forest, though, and you get a -50% defender bonus, so the archer's strength is 3/(1.5) = 2 and you get 2 vs. 2, which is worse for the attacker than the expected case of 4 vs 3.75.

Fortify the archer on a hill in a city, and the defender bonus is 25% (fortification) + 50% (hill for archer) + 50% (archer city bonus) - 100% (quencha bonus) = 25%. The attack is 2 vs. 3.75 or R = .53. The "expected value" is 4 vs. 6.75 or R = .59, so the attacker is again worse off than the way the desciption normally would lead one to believe.

What do you mean by these "expected" vs "actual" cases? For example in game if you mouse over the archer in the first situation with the quencha would the game show the strengths 4 vs 3.75 or 2 vs 2?

 

[anton_z1]

Can anybody give me numbers for 3-6 First Strikes !!!!.

 

[WackenOpenAir]

Nice, and so soon
I have my game since yesterday.

 

[Arathorn]

Issues I'm trying to work on right now/have planned to resolve:
- Correcting the article because hps ARE tracked and kept, so that a 5.0/6.0 unit (e.g., a wounded longbow) is weaker than a 5/5 unit (e.g., unwounded axeman). I had pulled the information on full hps at the start of battle from the Solver/DeepO article, but it's incorrect.
- Collateral damage. I've got most of this figured out, I think. A few more details to really work on nailing down, but I should have that part up early this week.
- XPs. As snepp mentioned, we got that figured out in another thread and I need to write it up.
- x-y first strikes. The "chance of first strike" thing. I'm not even sure how I'm going to test that at this point. It's probably important, but I don't even have a plan of attack.
- Air combat. Another major area, but it's going to have to wait a bit.
- A full-bore combat calculator to do stack combat and recommend best order for combat given the conditions. One-on-one is easy (and I'm sure the linked one will be corrected soon for the hp "problem"), but a stacked combat is much harder. I'm working on it, but even if I do it, I can't design a reasonable GUI to save my life.

If anyody knows of these (or wants to figure them out), I'd love to incorporate them into the article. I'm leveraging a LOT of people's work here, not just mine. Thanks to all who have contributed (snepp, especially, has helped a TON). And I'd love to get some more...

Arathorn

 

[snepp]

- Correcting the article because hps ARE tracked and kept, so that a 5.0/6.0 unit (e.g., a wounded longbow) is weaker than a 5/5 unit (e.g., unwounded axeman). I had pulled the information on full hps at the start of battle from the Solver/DeepO article, but it's incorrect.

I looked at this the other day after reading a post somewhere, as all of my testing had been done on full-strength units. I was surprised to see that when attacking with a 5.5/10 knight that I didn't start at 100 HP as I expected, but at 55 HP.

So as you mentioned, this means that a knight with strength 6/10 is weaker than a longbowman at a full 6/6, not equally matched as I was assuming. The odds to win in each round of combat are equal (50/50), as is the damage that they will deal per round win (20). But with the knight starting at 60 HP compared to the longbow's 100 HP, the odds lean heavily towards the longbow.

Side note: If you haven't been making use of collateral damage in warfare, this is a very significant reason why you should.

- Collateral damage. I've got most of this figured out, I think. A few more details to really work on nailing down, but I should have that part up early this week.

Excellent, I haven't looked much at collateral numbers other than the basic values assigned to cata/cannon/artillery.

- XPs. As snepp mentioned, we got that figured out in another thread and I need to write it up.

Git'er done!

- x-y first strikes. The "chance of first strike" thing. I'm not even sure how I'm going to test that at this point. It's probably important, but I don't even have a plan of attack.
- Air combat. Another major area, but it's going to have to wait a bit.

When you've got a plan of attack give me a shout, I love testing.

I'm leveraging a LOT of people's work here, not just mine. Thanks to all who have contributed (snepp, especially, has helped a TON). And I'd love to get some more...

I....I think I'm starting to tear up a bit. Now if you fix my name in the first post I'll be all set.

 

[WuphonsReach]

Aye, collateral damage is key in Civ4 warfare. Especially against stacks-of-doom where your units would have to go up against the strongest defender in the stack.

At the start of a turn, I might be looking at 30 vs 60 odds (not very good for me) for attacking a heavily entrenched defender. But after a few bombing runs and a few suicide runs by artillery / heavy armor, those odds change over to 30 vs 15. Which lets me mop up the enemy stack with almost zero losses.

 

[KrikkitTwo]

I looked at this the other day after reading a post somewhere, as all of my testing had been done on full-strength units. I was surprised to see that when attacking with a 5.5/10 knight that I didn't start at 100 HP as I expected, but at 55 HP.

So as you mentioned, this means that a knight with strength 6/10 is weaker than a longbowman at a full 6/6, not equally matched as I was assuming. The odds to win in each round of combat are equal (50/50), as is the damage that they will deal per round win (20). But with the knight starting at 60 HP compared to the longbow's 100 HP, the odds lean heavily towards the longbow.

Are you sure of those last 2 facts? (equal chance to hit and damage per round) After all, if the number of hp reflect the 'max strength' of the unit might not the chance to hit or damage calculations Also use the knight's 10 instead of its 6?

 

[snepp]

Are you sure of those last 2 facts? (equal chance to hit and damage per round) After all, if the number of hp reflect the 'max strength' of the unit might not the chance to hit or damage calculations Also use the knight's 10 instead of its 6?

Absolutely certain. It's tough to setup the ideal testing situation I described with a 6/10 vs 6/6, but here are a couple examples that are close. The numbers in () are what the damage dealt would have been if units were at full strength.

Swordsman 1.7/6 vs Warrior 2.0
Swordsman starting HP: 28
Damage dealt per round win: Swordsman 18 (33) vs Warrior 21 (12)
Swordsman died in 2 hits

Swordsman 5.2/6 vs Jaguar 5.0
Swordsman starting HP: 86
Damage dealt per round win: Swordsman 19 (21) vs Jaguar 20 (18)
Swordsman died in 5 hits

Swordsman 4.3/6 vs Skirmisher 4.0
Swordsman starting HP: 72
Damage dealt per round win: Swordsman 20 (24) vs Skirmisher 19 (16)
Swordsman died in 4 hits

 

[KrikkitTwo]

Well I guess that explains damage, are the odds also althered (bes one I can think of is the swordsman/warrior battle, did the swordsman only get in one or two hits...hm actually that's not the best way to ask the question.) the odds would be a bit harder to test.

 

[snepp]

Well I guess that explains damage, are the odds also althered (bes one I can think of is the swordsman/warrior battle, did the swordsman only get in one or two hits...hm actually that's not the best way to ask the question.) the odds would be a bit harder to test.

I can't provide specific numbers for rounds won (should have kept a save), but the ratio was pretty close to 1:1, leaving the victorious unit significantly damaged.

 

[Arkalius]

Both the attacker and the defender always begin with 100 hps, regardless of whether they are injured or not at the start of combat.

You know this for sure... I always thought units started with the hp they had...

Unfortunately it's hard for me to test this... there's no easy way to damage a unit in the worldbuilder.

 

[snepp]

You know this for sure... I always thought units started with the hp they had...

Unfortunately it's hard for me to test this... there's no easy way to damage a unit in the worldbuilder.

Read the handful of posts directly above yours.

 

[Arkalius]

Oh... perhaps I should pay attention, eh?

 

[KrikkitTwo]

what this actually means is that numbers are much more valuable, a 'wave' of troops can easily take out a more advanced one, because as each one damages it, they do more damage. (they already did, but this increases it)
reworked 'zergling' numbers
# units strength 10 attacking; strength of unit they can on average take out (based on this average number of X units required to destroy a tank)

1; 10 (tank to beat tank)
2; 17 (2 Infantry/Marines to beat tank)
3; 24 (3 Cavalry/Riflemen to beat tank)
4; 29 (4 knights to beat tank)
5; 34 (5 macemen/elephants/Muskets to beat tank)
6; 38
7; 42
8; 46 (8 swordsmen/longbowmen/horsearchers to beat tank)
9; 50
10; 54
(11 axemen to beat tank)
12; 61
15; 71 (~15 spearmen/chariots to beat tank)
20; 87
25; 101 (~25 archers to beat tank)
30; 115
40; 142 (~40 warriors can take on a tank/Panzer)
50; 168

 

[Arkalius]

I've developed a command-line Java app that calculates the odds of a unit winning given both it's health status and it's strength values. It also supports first strikes but only a single amount, it doesn't consider a range of first strikes (ie 1-2 first strikes). This is because I'm not sure how the game determines how many first strikes a unit will get in a particular situation. I'd be happy to send the app to anyone who knows how to work such things. I'm not terribly interested in making a "how to run a java app" tutorial and troubleshooting

 

[snepp]

Oh... perhaps I should pay attention, eh?

Just a friendly heads up is all.