I believe combat is rigged in this game and it ruins it for me

[TheHateMale]

If you round out the results of battles you can use a binomial distribution, but this will be highly inaccurate. You would have to, at the very least, divide the significance result/multiply the probability you get to compensate for being able to get the same amounts of wins and losses from highly different combat results.

The binomial does indeed model completetly what you say it models, but what you are modelling isn't Civ4 combat when you start ignoring sections of it.

[DrSpike]

Can't you see that the combat model is irrelevant to determining the probability of winning in a completely even fight? If you can't see this you will never get it I'm afraid. Reread my example above.

Everything I have said is perfectly true, and their are no flaws in the procedures I have described. It's very basic statistics.

I tire of this. Others can continue to try to explain if they want.

[Hauptman]

In response to something a few posts back, by someone I cant remeber...

The civ 4 combat system is much more capable of making fights less random, that is, adding much more probability average to the combat itself.

In civ1, a knight vs spearman combat was resolved by adding the two units str together and rolling 100 based on the percentage of a units total, thus 4 + 2 = 6. 4 is 66% of 6, giving the knight a win on a roll of 1 - 66, and the spear a win on 67 - 100. Simple? Yes, too simple. Now even though my battle ship with 12 str seems like it should be invincible against spearmen, its based on 1 simple roll.

In civ3, they tried to make that less likey by adding "hit points". Now, with that same combat system, one single "lucky" hit will not be enough, now you have to get lucky 3, 4, or 5 times. Still possible, but much LESS likely.

Now with civ 4, we have 100 hit points, and damage is based on unit str. So we have so many fights in any given combat, that the chance of a weaker unit getting lucky, is so much LESS likely. Now if an axe does 10 dmg per fight (damn, what is the actual damage/str formula?) and a knight does 20, we add in the fact that an axe would need to win twice as many times at half the chance to actually win a fight, thus reducing its chances even further of getting lucky.

So begs the question, why are we seeing such streaky fights? Why would i loose 9 times out of 11 when the odds were in my favor (always above 50-50). I still stand by my earlier statement, something is not working as intended. because seeing as how I got lucky last night ( ) my luck isnt really that bad. So I blame the RNG.

[Hauptman]

Ok I'm at work, so I had time to run a test...

I did not run any 50 - 50 tests, as others have already done that, these are "real" fights with unfair unit matches.

Unit vs Unit - showed % - test 1 - test 2 - test3

axe vs spear 98.8 100 100 100
axe vs sword 74.9 80 100 80
spear vs axe 1.2 0 0 0
sword vs axe 24.9 30 30 30
pike vs knight 72.8 40 60 70
knight vs pike 27.0 40 40 10


"porcupine" stacks, when attacking you should loose all fights, as you attack your counter unit. units include Knight pike xbow and maceman

Test 1 -- 2 units killed both by knights
test 2 -- 1 unit killed by knight
test 3 -- 3 units killed, 2 knight 1 mace.

Everything except Knights vs pikemen went as expected, The knight vs pike % falls into the "soft spot" that people have been complaining about. So maybe, there is a small bug at that 72% mark?

[Tuberski]

I'm willing to bet that, in the OP, the AI civ had the Aggressive trait and he didn't.

It gives the auto-upgrade and doesn't count towards xp.

ACK!

[Mergle]

Originally posted by Hauptman
Ok I'm at work, so I had time to run a test...

I did not run any 50 - 50 tests, as others have already done that, these are "real" fights with unfair unit matches.

Unit vs Unit - showed % - test 1 - test 2 - test3

axe vs spear 98.8 100 100 100
axe vs sword 74.9 80 100 80
spear vs axe 1.2 0 0 0
sword vs axe 24.9 30 30 30
pike vs knight 72.8 40 60 70
knight vs pike 27.0 40 40 10

[snip]

Everything except Knights vs pikemen went as expected, The knight vs pike % falls into the "soft spot" that people have been complaining about. So maybe, there is a small bug at that 72% mark?

Sorry, not quite clear to me - how many times did you run the test? Are those % times you got a victory?

[Mergle]

Originally posted by Tuberski
I'm willing to bet that, in the OP, the AI civ had the Aggressive trait and he didn't.

It gives the auto-upgrade and doesn't count towards xp.

ACK!

You know, I think you may have nailed it.

[Mergle]

Originally posted by TheHateMale
If you round out the results of battles you can use a binomial distribution, but this will be highly inaccurate. You would have to, at the very least, divide the significance result/multiply the probability you get to compensate for being able to get the same amounts of wins and losses from highly different combat results.

The binomial does indeed model completetly what you say it models, but what you are modelling isn't Civ4 combat when you start ignoring sections of it.

Yes and more importantly no. Using the Binomial is not an approximation or "rounding out". It is precisely the distribution.

The binomial model, as Dr Spike has said, is a perfect model for whether or not you win or lose. There are two possible outcomes of a battle - you win or you lose. Over a number of trials, This is perfectly modeled by a binomial distribution. Thankls to DeepO, Civ4 now gives you your real % chance of winning - the theoretical value of p. Any tests conducted should see if there is a statistically significant deviation from this value over a meaningful sample.

It is perfectly true that the chance of winning one round is not equal to the chance of winning the combat except (as is pointed out upthread) for p=0, 0.5, or 1. However, this is irrelevant - you just have to make sure you're using the value of p relating to winning the whole combat (which in the examples given in the OP of equal combats, is 0.5). It is then a Binomial distribution using this p.

Where you have a point is that determining no change to the win-ratio does not eliminate the possibility of bias. For example, it could be that the human is always badly damaged and the AI unscathed after a win, despite no bias in who actually wins. But this is not what has been alleged, and is not what we're testing in this thread.


[If you want to know why destroyer v destroyer is truely 0.5 win despite the variable number of rounds consider this: For every sequence of rolls that gives the human a win, the inverse sequence (100-number rolled) gives the AI a win. It's totally symmetrical.]

[Tuberski]

Originally posted by Mergle


You know, I think you may have nailed it.

I have my moments.

ACK!

[sabrewolf]

mergle:
for the knight vs pike, one other thing must be considered: the knight can withdraw. that puts his chances of losing lower that the official mathematical values.

and i would also like to know how big your sample sizes were for your stats...

[Mergle]

Originally posted by sabrewolf
mergle:
for the knight vs pike, one other thing must be considered: the knight can withdraw. that puts his chances of losing lower that the official mathematical values.

A knight withdraws if otherwise he would have lost - it's actually a "loss", but the last bit of damage isn't applied and so you don't lose the unit. So it doesn't affect the distribution. But you're right in that one needs to be careful in reporting test results to count this as a loss.

and i would also like to know how big your sample sizes were for your stats...

Presumably you mean for Hauptman's stats?

[Hauptman]

Knights donot start with a withdrawl chance.


My test, I included the save, were stacks of 10, very simplistic, reloaded 3 times, and tried in different orders (to bypass seeding) with 3 of the porcupine stacks per test. load it up try it out, but it seems knights would beat a pikeman way too easily, much closer to 50/50, especially on my porcupine stacks. when 2 out of 3 knights won on two different tests.

[Hauptman]

ran it again, and again, the knights vs pikemen stand out.


5 for 5 on that middle stack, where the one below is more true to odds.


wanted to add that the sword vs axe is also similar odds, yet those happen as expected. both of those stacks are 3 to 7.

[xxFlukexx]

Blake if that is the best you can do, you seriously need to leave this thread, winning two battles where you have a 50% and 40% chance to win respectively? And what is so great about your infantry creaming an enemy SAM infantry, it had ~12% chance to win and it lost, is that supposed to be ground breaking?

I'll run a 100 vs 100 pikeman vs knights test tommorrow and post it here.

A good point about a difference between winning easily and winning with few hp left. In my test I lost more units but hp wise didn't lose as badly and I had a much larger number of units winning easily than expected. I hit end turn and my remaining army still got creamed though, from a 100 vs 100 battle I think the AI had around 10-20 troops left. And besides it's really all about winning or losing, winning with 1 hp left means you can possibly go back and heal.

[Blake]

It was the same infantry which won all 3 battles in succession, unfortunately that couldn't be indicated in the screenshot of the combat log.

I can't be arsed trying to calculate the exact probability of winning 2 even and 1 uneven fights with 50% hitpoints remaining, but can estimate. The first fight was 1/32 chance anyway. The second probably about 1/15, the final battle was about 1/6 (winning fairly convincinly with poor odds). Overall the odds of winning that sequence about that well is somewhere around 1 in 3000. Not quite lotto winner odds but unsual enough to be noteworthy .