Warrior, Archer, Spearman Screens using 4roll combat

[Harovan]

I have seen the Anti Tank Spearman in the Minitourney III (AU predecessor). Here is the related tale. I didn't lose the Tank (or more precise: Modern Armor), it retreated, but anyway.

But since my next MA killed him, he is now officially dead. So stop to beat dead horses Anti Tank Spearmen.

[vondrack]

Mmmm... excuse me, gentlemen, but after reading through the 4-roll combat threads for several days, I am still lost when it comes to the principle of it - especially after reading Mike's comment (quote: "I don't know where Jesse got the "rerolling for ties" thing because there are no ties.").

Does anyone know for sure how this averaging is going to work? I can imagine two possibilities:

a) averaging "combat round" results
(this would be close to, but not the same as quadrupling the unit hitpoints)

roll 1 = 0.5900
roll 2 = 0.3571
roll 3 = 0.9710
roll 4 = 0.4839

Assuming the attacker needed ~0.6 to win, he would lose 3 out of 4 sub-rounds and lose the "big" round.

This is what everybody seems to assume - but it is probably not the case, as Mike B. clearly stated there is no way to achieve a "tie" - if this was true, a tie would be very possible with two rounds won by both sides.

b) averaging RNG values directly before using the value to determine the combat round result

roll 1 = 0.5900
roll 2 = 0.3571
roll 3 = 0.9710
roll 4 = 0.4839
===========
total = 2.4020
avrg = 0.6005

Assuming the attacker needed ~0.6 to win, he would win the round, since 0.6005>0.6 (the average of four consecutive RNG rolls would be higher than 0.6, despite only one of the individual rolls being higher than that in itself).

If this is the case (and I am, again because of Mike's comment, inclined to believe it is), then I am lost as far as all the "calculations" here showing how unbalanced the game will become... because there is, IMHO, no way to figure these numbers up using the current combat calculators - all of them operate upon the assumption that each roll is equally probable (which, however, would not be the case here - "averaged" 0.9999 would certainly be much less probable than "averaged" 0.5555, since you would need 4 consecutive "raw" 0.9999s to get one "averaged" 0.9999).

Does anybody know for sure how the averaging would be implemented?

[notyoueither]

Isn't it plain that averaging will benefit the superior value?

If the superior value is defensive (which it is in most of Civ3) doesn't that mean that attacking will be harder?

And what about the resource starved Civ? Chances of surviving, let alone winning, are blown to hell by this change if it is not an option.

[Tiberius]

Originally posted by vondrack
b) averaging RNG values directly before using the value to determine the combat round result

roll 1 = 0.5900
roll 2 = 0.3571
roll 3 = 0.9710
roll 4 = 0.4839
===========
total = 2.4020
avrg = 0.6005

Assuming the attacker needed ~0.6 to win, he would win the round, since 0.6005>0.6 (the average of four consecutive RNG rolls would be higher than 0.6, despite only one of the individual rolls being higher than that in itself).

Does anybody know for sure how the averaging would
be implemented?

If I understand it correctly, the more times you average a result, the closer it will be (statistically) to 0.5, which means that a unit having better chances to win (0.6 in your example) will (amost) always win.
Of course, I'm not sure at all that what I'm talking here is not just pure nonsense

[Jeem]

Originally posted by notyoueither

I just tried it 10 times. 12 archers vs a size 7-12 city on grass (I couldn't get the AI to not sell the walls at size 6 )

6 times the archers won through. It took 11, 4, 9, 11 , and 9 archers attacking in those cases.

Then maybe the problem is when the 4 took it? Does that appear little bit too random?

Let's be clear here - 80 shields worth of archers in no way compensates for 90 shileds worth of Pike, the effort made to get iron, the effort made to get to Fuedalism, the 30 shields for the Settler and 20 for the walls. It's the randomness that is the problem - when you defend with a certain level of defence, you expect to see some good results for it. When the first 4 archers take down 3 Pike, you begin to wonder why you bothered defending and didn't just go all out on attack again.

[vondrack]

Originally posted by notyoueither
Isn't it plain that averaging will benefit the superior value?

My feeling is the correct statement would be "it will benefit significantly superior units" - as in, say, "twice as...". The "streak" defeating (very) bad odds will need to be longer (but admittedly not so "dense").

If you ask me... I believe that a warrior should VERY seldom (almost never) win over a spearman - his A rating is half the spear D rating! That sounds like an overwhelming advantage. The warrior guy has a funny hammer only, while the spear guy has a shield and a long sharp stick... j/k

I would consider it ok if I needed an archer to have even chances against a spear (A2 vs. D2).

What I am questioning is all those impressive numbers, not the fact that the change may be unbalancing. I do not know how all those numbers were determined (especially if it was using 'modified' combat cals we use these days). It's been some time I left the uni, so I need someone to help me out with my maths...

Can someone explain to me how the odds of a, say, vet knight attacking a fortified vet spear on a hill were calculated (under the new 4-roll system)?

Originally posted by Tiberius
If I understand it correctly, the more times you average a result, the closer it will be (statistically) to 0.5, which means that a unit having better chances to win (0.6 in your example) will (amost) always win.

This would be true, but only speaking about large data sets (averaged). An average of 4 consecutive RNG rolls may adjust the distribution curve only moderately, cutting the number of "outrageous" combat results (like MIs on offense losing to longbows on defense... ).

Again... I am honestly asking the question: how do you compute the odds of a knight killing a fortified spear on a hill under the new 4-roll combat system? I admit I'm no longer a math freak, I am making my living reselling software and that does not need any fancy math...

As for "why 4?" - that's another thing that leads me to believe the change may be at least worth trying... The guys at Firaxis/BA are not idiots and have undoubtedly playtested this system... I would assume that averaging 4 rolls was giving the "most acceptable" combat results (as in "they felt most acceptable").

[DrSpike]

I have done the calculations for a few special cases.........enough to make me concerned. If you are really interested a guy called Charis at CFC has done extensive calculations on the way we now believe the averaging is implemented. Quick conclusion: 4 times is just too many times for intra-era balance.

And Jeem, though Catt has defended himself perfectly well, I too have to respond to say its not about being scared of learning new strategies. I'm perfectly prepared to play a game with averaging 4 times, and adapt to it. However, it is not *this* game, which is balanced around the combat model as it is now. Do we have any reason to believe that balance will transfer to the new situation with a radical change to the combat model? I, and the vast majority of experienced players, think not.

[Rommel2D]

Originally posted by Jeem:
The whole reason the combat rolls are not being changed, but are being done 4-times and averaged, is because they don't want to change the code.

How are they doing this without changing code? How are they going to present an option to the player of what combat system to use without changing code? My concern here is that alexman has a sizable list of things to fix that are alot more aggravating to deal with than losing some combats to 'excessive randomness'. Of course- since this is such a huge change- if they are set on doing it, the sooner they start testing, the better the end result.

Just to throw something out there- If hit points were modded to 8 (conscript), 12, 16, and 20(elite), (assuming promotions could be granted in 4 point chunks), would this achieve the single-case stability of the 4 roll system, while allowing streaks and lightweight units to still make a dent? It might be a pain to sit through big battles, but the graphics could be sped up (or shut off?) pretty easily.

[DrSpike]

Well you are right you can achieve the same effect for a single battle by increasing hitpoints, as I was at pains to point out in another thread. However, using the averaging model for units with A/D values that are quite far apart would require very large increases in hitpoints as a corollary. Also, the distribution of damage done is not the same in the 2 models.

Personally I think everyone would be happy if they found a way to retain intra-era balance which has been painstakingly created, but reduce flaky results for inter-era combats. Spencer suggested averaging only for inter-era battles........it's a reasonable suggestion, but I get the impression Firaxis don't want to do something so fiddly.

[vondrack]

That's a lot of graphs by Charis... I guess trying it out is the only way for me. Implementing it as a configurable INI setting would probably be the way to go - one could set how many rolls to average. 1 would be the current system, but could be upped to 2, 3, 4... I know I would love to try that.

I can live with the current combat system, but I know I'd welcome a tad less "unpredictable" results, especially in PBEM games, facing human opponents. Bad luck you can easily fix by superior human intelligence in SP is much more significant in human vs. human games.

[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.

[DrSpike]

Originally posted by vondrack


That's a lot of graphs by Charis... I guess trying it out is the only way for me. Implementing it as a configurable INI setting would probably be the way to go - one could set how many rolls to average. 1 would be the current system, but could be upped to 2, 3, 4... I know I would love to try that.

If you want a quick and easy way chuck some numbers into the old and new versions of the combat calculator, the new one being posted by Alexman in the patch thread. The new one does not work exactly correctly (due to some miscommunication) but should give you a flavour of the changes for the battles you want to calculate.

[vondrack]

Originally posted by DrSpike
If you want a quick and easy way chuck some numbers into the old and new versions of the combat calculator, the new one being posted by Alexman in the patch thread. The new one does not work exactly correctly (due to some miscommunication) but should give you a flavour of the changes for the battles you want to calculate.

Thanks, but I would rather do my own calcs than use someone's 'blackbox'. Could you give me a hint how the probability of c=(a+b)/2 from known probabilities of a & b is calculated?

My secondary school math was enough for the old combat system (elementary combinatorics), but once this averaging thing kicks in, I am pretty much lost...

Thanks.

EDIT: Do I suspect correctly that integrals will have to be used?

[DrSpike]

Well what you are familiar with is I suspect the probability of a unit winning one round of combat, reducing the opponent by one hitpoint.

To carry that forward to working out the probability of an overall victory it's easiest to use a form of the binomial distribution, though you can calculate longhand.

The averaging makes things a little trickier. Essentially you need to know what distribution the 'random' part comes from (some have plausibly analysed the uniform distribution), then look at the effect on the variance of your statistic as the number of draws increases. This variance reduction increases the chance of the most advanced unit winning.

To do all this correctly is not really that difficult, but some knowledge of statistical methods is necessary not to make errors. The worst part is posters misunderstanding the analysis of clever people over at CFC and then joining here just to mistakenly correct clever people here. But lets not go into that.

[vondrack]

Originally posted by DrSpike
Well what you are familiar with is I suspect the probability of a unit winning one round of combat, reducing the opponent by one hitpoint.

To carry that forward to working out the probability of an overall victory it's easiest to use a form of the binomial distribution, though you can calculate longhand.

Ah, no, not really - I perfectly understand and am able to mathematically calculate the probability of the whole battle (the whole math underneath the current combat calcs is perfectly known to me - it's widely assumed that the distribution of the RNG rolls is generally uniform, right? as in the probability of every number within the RNG value interval is the same?).

Originally posted by DrSpike
The averaging makes things a little trickier. Essentially you need to know what distribution the 'random' part comes from (some have plausibly analysed the uniform distribution), then look at the effect on the variance of your statistic as the number of draws increases. This variance reduction increases the chance of the most advanced unit winning.

To do all this correctly is not really that difficult, but some knowledge of statistical methods is necessary not to make errors. The worst part is posters misunderstanding the analysis of clever people over at CFC and then joining here just to mistakenly correct clever people here. But lets not go into that.

Well, yes, I intuitively understand that averaging makes things more tricky - that's why I am asking about how to compute the probability of the average of two numbers, given their own probabilities/distributions... is there a mathematical formula?

If I had more time, I would be less lazy and use a piece of paper and some of my brains (it still works, just the boot-up time increases and often, the thing just refuses to work completely... but when it fires up, it's still got some decent potential... ).

Anyway... I do not think I will have time enough for this until the end of the year, so just forget it - I only felt many posters misunderstood the implementation of the averaging (and the thread over at CFC demonstrated that quite well - even over there, the understanding in the beginning was wrong).

The averaging as I understand it from Mike's post is NOT "you need 3 wins out of 4". It's just that you roll four dices and do your fight with the average of the rolled numbers, which is something different.