Warrior, Archer, Spearman Screens using 4roll combat

[DrSpike]

Well some of the initial calculations were wrong not because anyone misunderstood the stats, but because no one was really sure what Jesse meant.

Btw if you can do the calculations for the old model then following Charis's analysis at CFC should be possible. Perhaps I can post some sample calculations later, but he has done very extensive calculations, and packaged them neatly for everyone to see.

I should add a caveat though. I'm not 100% sure the model analysed is the right one. Firaxis have never confirmed (to my knowledge) the way we think old combat worked, though there are some tests that bear out the hypothesis. And for new combat we are just shooting in the dark on what is a reasonable interpretation of what they said.

[Harovan]

Originally posted by vondrack
Could you give me a hint how the probability of c=(a+b)/2 from known probabilities of a & b is calculated?

You can't calculate this without knowing the distribution of the probability in form of a continuous function (i.e. how to calculate the probability of a and b depending on a third parameter). If you know this continuous function, you can calculate the probability of c the normal way (using the function).

An example: How is the probability of getting 1.5 out of a die roll, knowing that both 1 and 2 have a probability of 1/6? Nonsense, obviously, but the correct answer would be 0.

Another example: Imagine a die (cube) with two 1's, one 2 and three 3's. The probability to get a 1 is obviously 1/3, the probability of 3 is 1/2. The probability of 2 (1/6) doesn't lie between.

[vondrack]

Yes, sorry for not putting the question correctly - I assumed it's widely believed the distribution of RNG values in Civ3 is uniform (at least the current combat calcs seem to be based upon that assumption). As in six-sided dice with numbers form 1 to 6.

So, the question should have been asked like this:

How do you compute a probability distribution of c=(a+b)/2, given known (uniform) probability distributions for a and b?

Or am I still missing something?

[DrSpike]

You don't actually need to do that here. Essentially the expected value of a random draw from the uniform distribution is just the center point, or 0.5 if the bounds are 0 and 1. This doesn't change no matter how many draws you take, then average. What changes is the variance of your statistic as the number of draws on which is it based increases. It is this variance decrease that filters through into the probability of winning any 1 round. Then you can just use the same style of binomial calculation from the old combat model just with new adjusted probability of success in any one repitition.

[Harovan]

If the distribution of probability between a and b is linear, then p(c) = (p(a) + p(b))/2 too. If it's a gaussian bell curve or another distribution, not.

Look (gaussian curve):
p(-1) = p(1), but p(0) != p(-1) and p(0) != p(1).

[korn469]

Jeem

nye - I just ran the test myself (3 vet pike in a city attacked by 12 vet archers).

the results were :-

1) 1 dead archer
2) 10 dead archers, last pike on 1 hp (already the flaw in combat should be apparent)
3) 4 dead archers
4) 8 dead archers
5) 7 dead archers
6) 8 dead archers
7) 6 dead archers
8) 4 dead archers
9) 6 dead archers
10 11 dead archers, two pike left on 1hp.

Averaging 6 dead archers. Did you leave the defending player on the romans or some other militaristic nation?

Regardless, any system which allows the variance in results, two combats in a row (like in my first two), cannot be good.

And as far as I can see, rushing 3 pike behind walls with 12 archers is a pretty good idea.

did you fortify the pikemen?

if so what we're looking at is something similar to this

3+ [3*.25 (fortify)] + [3*.1(terrain)] + [3*.5(city)]=
3+.75+.3+1.5=5.55

and since that is only a 2.775 advantage over archers that archers should indeed win some of the time, and although better tech should help ensure victory, as others have mentioned before we have 90 shields worth of defenders going up against 240 shields worth of attackers...run your test again with 4 pikes and see how many times archers ever win

[Jeem]

I did not fortify the pikemen - I went with the 4.8 defence that nye used.

I wasn't even sure if fortifying when inside walls counts - I thought that the walls 50% superceded the fortified 25% instead of being cumalative?

4 Pikemen should indeed do much better because generally speaking you need 4 archers for every pike to make victory a very good bet.

But I'll try it out anyway...

[korn469]

afaik the fortification adds on to other defense bonuses

basically 4 fortified pikemen in a city would be almost uncrackable to 12 archers

[Andydog]

In an effort to understand exactly how the game balance would be affected in the ancient age with the introduction of the 4 roll combat system, we should firstly look at the various scenarios. The probabilities have been obtained from using alexman’s combat calculator, I assume they are correct…

First of all, lets examine a regular archer, attacking a warrior:

Regular archer attacks:
Regular unfortified warrior on grassland: Archer wins 95% of the time.
Veteran unfortified warrior on grassland: Archer wins 91% of the time.
Elite unfortified warrior on grassland: Archer wins 87% of the time.
Regular fortified warrior on grassland: Archer wins 86% of the time.
Veteran fortified warrior on grassland: Archer wins 78% of the time.
Elite fortified warrior on grassland: Archer wins 70% of the time.
Veteran fortified warrior on hills: Archer wins 50% of the time.
Vereran fortified warrior on mountains: Archer wins 22% of the time.
Regular fortified warrior in walled town on grassland: Archer wins 44% of the time.

We can see that the warrior would stand a good chance if fortified on hills or mountains. Walls are now much more valuable to the defender. On the open grassland, expect the archer to loose in only a few circumstances.

Now assume that the regular archer was attacked or bombarded first, and had his hit points reduced.

2 hp archer attacks:
Veteran unfortified warrior on grassland: Archer wins 75% of the time.
Veteran fortified warrior on grassland: Archer wins 57% of the time.
Veteran fortified warrior on hills: Archer wins 30% of the time.
1 hp Archer attacks:
Veteran unfortified warrior on grassland: Archer wins 43% of the time.
Veteran fortified warrior on grassland: Archer wins 27% of the time.
Veteran fortified warrior on hills: Archer wins 11% of the time.

The odds in favour of the archer winning reduce significantly with reduced hit points. Bombardment has become a major defensive tactic and can be used to swing the odds in favour of the defender.

Now lets look at a veteran archer vs spearman:

Veteran archer attacks:
Regular unfortified spearman on grassland: Archer wins 54% of the time.
Veteran unfortified spearman on grassland: Archer wins 39% of the time.
Elite unfortified spearman on grassland: Archer wins 25% of the time.
Veteran fortified spearman on grassland: Archer wins 16% of the time.
Veteran fortified spearman on hill: Archer wins 4% of the time.
Veteran fortified spearman in walled town on grassland: Archer wins 3% of the time.
Veteran fortified spearman in walled town on hill: Archer wins 1% of the time.

So the archer is much less effective against the spearman, especially if the spearman is fortified. City walls make it near impossible. If that spearman has dug himself in on a hill, forget it - either wait until you have a stronger unit, or bombard the puss out of him first:

Vet archer attacks:
2hp fortified spearman on hill: Archer wins 27% of the time.
2hp fortified spearman in walled town on grassland: Archer wins 23% of the time.
2hp fortified spearman in walled town on hill: Archer wins 12% of the time.
1hp fortified spearman on hill: Archer wins 60% of the time.
1hp fortified spearman in walled town on grassland: Archer wins 56% of the time.
1hp fortified spearman in walled town on hill: Archer wins 41% of the time.

So archers are STILL USEFUL, but you need to get mathematics and build lots of catapults, and use them until every defender in the city is down to preferably 1 hp. On defence, look at how secure towns are when they’ve been founded on hills.

Now lets look at swordsmen vs speamen.

Veteran Swordsman attacks:
Regular unfortified spearman on grassland: Swordsman wins 91% of the time.
Veteran unfortified spearman on grassland: Swordsman wins 84% of the time.
Elite unfortified spearman on grassland: Swordsman wins 76% of the time.
Veteran fortified spearman on grassland: Swordsman wins 64% of the time.
Veteran fortified spearman on hill: Swordsman wins 31% of the time.
Veteran fortified spearman in walled town on grassland: Swordsman wins 25% of the time.
Veteran fortified spearman in walled town on hill: Swordsman wins 10% of the time.

So again, it’s still tough for the swordsman against a fortified spearman. Lets hit the spearmen with a few catapults:

Veteran Swordsman attacks:
2hp fortified spearman on hill: Swordsman wins 68% of the time.
2hp fortified spearman in walled town on grassland: Swordsman wins 62% of the time.
2hp fortified spearman in walled town on hill: Swordsman wins 42% of the time.
1hp fortified spearman on hill: Swordsman wins 88% of the time.
1hp fortified spearman in walled town on grassland: Swordsman wins 85% of the time.
1hp fortified spearman in walled town on hill: Swordsman wins 72% of the time.

What can we conclude from all this?

Under the 4-roll combat system, the attacking ‘warmonger’ player would need to attack with a variety of units. They need to administer significant bombardment, need to defend their attacking units against return bombardment, and need to recognise that targets fortified on hills, on mountains, and behind walls to be much more difficult and will required lots more bombardment and/or lots more attacking units. The militaristic trait will become more valuable for the warmonger as they can build cheap barracks and produce veteran attacking units that will be promoted quickly, and we've seen how an extra hp now goes a long way. Those civs with strong attacking UUs in the ancient age will become more valuable (Iroquis mounted warriors, Persian immortals). Tech-wise they will now need to place a higher priority on Mathematics for catapults, but Warrior Code for archers, Bronze Working for spearmen, and Iron Working for swordsmen remain priorities as before.

The defensive ‘builder’ player is now able to defend their cities effectively in a variety of ways - Walls are now much more effective (as are fortresses), and cities built on hills are a tough target for the aggressor. Masonry becomes more of a priority (for Walls). The defence bonuses of terrain are much more significant.

Ultimately I think the strategy of war will become much more pronounced. With more certain results comes more careful planning, and this can only be a good thing in my book. I think in general it will be harder for the warmonger, but as things currently stand, I believe that this is also a good thing. IMHO war is too dominating in the current game. It is much harder for the ‘builder’ player to build AND fight off a warmonger, especially early on, and therefore I see the current game as being unbalanced toward the warmongers. With the 4-roll combat system the warmongers are going to have to carefully plan and be certain of their war strategy before attacking a builder.

The only real problem I can see with the introduction of this 4-roll combat system is with the AI not being able to use bombardment. An AI has never attacked me using catapults, cannons etc, and so I could see that they’d just carry on hurling loads of attacking troops at you but would now suffer huge losses. The AI’s need to prioritise bombardment like the human player would, and I’m not sure how much extra work this would involve for the programmers.

[Jeem]

12 veteran archers attacking 4 veteran, fortified pike in a size 7 city.

1) 9 dead archers, 3 dead pike (last pike has 1hp)
2) 9 dead archers, 3 dead pike (last pike has 1hp)
3) 10 dead archers, 2 dead pike (1 on 2hp, 1 on 1hp - and a great leader!)
4) 6 dead archers, 4 dead pike
5) 11 dead archers, 1 dead pike (all 3 remaining pike on 1hp)
6) 6 dead archers, 4 dead pike
7) 11 dead archers, 1 dead pike (and great leader)
8) 10 dead archers, 2 dead pike
9) 8 dead archers, 4 dead pike
10) 9 dead archers, 3 dead pike (last pike has 1hp)

No real surprises looking at my previous run with 3 pikemen. There is still the problem of streaky results though. I've gone from killing 11 archers and getting a great leader to losing the city for only 6 dead archers.

This is a very small example, and the results are far too varied. It's not the final result per-se, but the fact that far too often, a combat you would expect to win fairly comfortably will go to crap.

By rolling 4 times and averaging, the unit with the best value will win more often. However, as Jesse mentioned in his first post - there might be a problem with experience gains. I agreed with that, and having seen this I still do. ALL my Pike finished at Elites, every combat. That is the main reason why the archers struggled more here - those times when the pike survived on 1hp would not have happened if not for the automatic experience gain from winning 2 fights same turn.

That is why I said 2-rolls with 3-victory experience gain, or 3-rolls with 4-victory experience gain would get Firaxis closer to what they are looking for. The better unit will win each round more often, but will not gain experience so often. This will give the lesser units a better chance of whittling them down and it'll all probably end up looking fairly balanced.

[Jeem]

Originally posted by korn469
basically 4 fortified pikemen in a city would be almost uncrackable to 12 archers

I would also have assumed so, and I think many players would. However, the small test I just ran shows the archers winning 3/10, and in another 3 the last pikeman held on with 1hp so I wouldn't call that 'almost uncrackable'

Thats 4 Pikes fortified and behind walls and they are still pretty open to being overrun by a unit that many races start with.

[Aeson]

I think any changes to the combat system should be aimed at making all units useful in some context. If a unit isn't worth building, it shouldn't be in the game in the first place.

Currently, most units can be effective used correctly. Even most the 'useless' units are worth building if soley for upgrade purposes. Games can be won both with agressive warmongering (from a technical or numerical superiority), turtling, or something inbetween. There are situations where a certain playstyle is a must, but not due to the combat system. I don't think it needs fixing.

The difference I see this change making to the game is that conquest becomes slower in a broad scope, and quicker is a more narrow scope. This isn't a problem in and of itself, but it changes the entire feel of the game dramatically and reduces viable style of play. There will be certain very small windows of opportunity to dominate offensively. To play warmonger well the player will have to play in a manner to take advantage of those. Beelines and rushes (in a literal sense) will only become more important.

Numerical superiority will be largely irrelevant, only technical superiority matters. This may appeal to some players, but how it is now, both are balance reasonably well. I enjoy playing both ways, and either route can be taken and the game still played effectively.

As for 'luck'. By reducing luck in individual combat this way, luck will be an even bigger factor in the overall scope of the game. A military leader for an Army will be the end all be all of warfare. Get it at the right time and you've basically won the game if you wish to apply your advantage. It's already that way to some extent, but this will just exacerbate the problem even further.

[vmxa1]

Originally posted by Jeem
nye - I just ran the test myself (3 vet pike in a city attacked by 12 vet archers).

the results were :-

1) 1 dead archer
2) 10 dead archers, last pike on 1 hp (already the flaw in combat should be apparent)
3) 4 dead archers
4) 8 dead archers
5) 7 dead archers
6) 8 dead archers
7) 6 dead archers
8) 4 dead archers
9) 6 dead archers
10 11 dead archers, two pike left on 1hp.

Averaging 6 dead archers. Did you leave the defending player on the romans or some other militaristic nation?

Regardless, any system which allows the variance in results, two combats in a row (like in my first two), cannot be good.

And as far as I can see, rushing 3 pike behind walls with 12 archers is a pretty good idea.

I think the first two results are the reason that people complain and the reason they are tinkering with the combat system.

Results 4-7 are close enought to each other to be acceptable. Anntenuating the rng to some narrow range is what I would like to see, no more wild swings.

[notyoueither]

Originally posted by Jeem
I did not fortify the pikemen - I went with the 4.8 defence that nye used.

I wasn't even sure if fortifying when inside walls counts - I thought that the walls 50% superceded the fortified 25% instead of being cumalative?

4 Pikemen should indeed do much better because generally speaking you need 4 archers for every pike to make victory a very good bet.

But I'll try it out anyway...

Damn, I was being a bit careless last night. They were forted so they were 5.55D.

Here is the save so that people can play with it if they wish.

[Catt]

Originally posted by Andydog
In an effort to understand exactly how the game balance would be affected in the ancient age with the introduction of the 4 roll combat system, we should firstly look at the various scenarios. [. . . .]

Nice post. One of the first from the "the change makes sense" view that strikes me as really taking the "balance" issue head-on. Also highlights, I think, that the 4-roll-combat proposal could very well deserve a different analysis depending on MP or SP play. I don't play MP and can't comment on whether I think 4-roll-combat would be an improvement or degradation of play, though I feel pretty confident that for SP it would be a degradation.

@Jeem - your examples of archers versus pikes are interesting. And they make an interesting case that current combat is too random. I don't believe that it is, but clearly the optimal spot on the scale between absolutely random and absolutely determinative is subject to widespread debate and opinion.

But even assuming that one could conclude that the current implementation is too random, how does decreasing the degree of randomness via 4-roll-combat add to game balance? Does it strengthen balance or just reduce the frequency of variable outcomes?

Catt