Combat results

[Vev]

Have anyone seen a combat predictor that returns success probability and possibly says unit's hit points of remaining?

I came up with an experimental algorithm to calculate it. But the problem is getting the raw data of combat results to check if the algorithm isn't too far off. I have enough results of 3:2 combat odds and would love to see approx results of other combat odds.

Although technically it is not a binomial distribution, I simplified it to be one and based the algorithm around it with a few tweaks to the combinatorial factors (gotta love pascal's triangle to see patterns).

[Verrucosus]

Maybe I misunderstood your suggestion, but in what way would a combat predictor be different from the "display odds" message that can be enabled in the advanced preferences menu?´
That message doesn't predict remaining hit points, but it purports to predict the chance of success.

[Vev]

The display odds, gives the raw combat chances on winning a single round of combat but it fails to capture the odds that happens over a period of repeated individual events. 3:2 while suggesting 60% chance of winning in one round happens to be around 80% winning for the whole combat. Very different things. But veteran users would have a 'feel' of what could result in a victory based on combat results. This exercise just gives it a quantitative measure to it rather than a qualitative 'feel'.

[MariOne]

Combat thread (Dec 2000 - Jan 2001)
many wrong things in the beginning, work thru the end of it to find better conclusions.
In the "complication" paragraph of my 1st post I basically supported your above approach.
Alas, my ISP doesn't support free webspace since long anymore, I might have the table stored somewhere in my home PC...
Best advice: Read Sikander's posts.

Combat Modifiers thread (May 2001)
this was a follow up where I briefly and vaguely reported my intervening tests findings.
If I was not mistaken, that meant for instance that a strength of 4 vs 1 gets actually treated as 5 vs1. Or 4.5 vs 3 as 5 vs 3.
IIRC the cumulative battle outcomes were over 95% confidence consistent with that further undocumented modifier to the stronger's strength


_____
Mongoose, if you happen to stumble in this post, I've not forgotten you nor am I ignoring or avoiding you... sorry if I just disappeared without letting you know anything. I'm just a gay twàt beyond any hope of redemption

[Vev]

Thanks, seems like I am on the right track. Now I am writing a simple code to give odds based on attacker's hits, defender's hits and combat ratio. If you have statistical data, feel free to write it here so I can compare my model to actual results.

[MariOne]

I found the old excel tables

The "odds" one contains the tables with the probability theory: only the 3rd tab is correct, but the formulas explanation is in the 1st tab

The "combat test" one reports collected data from 4 different combat situations, 100 runs each.
Here I only pasted the % numbers from the other file, and not the formulas.
It shows how actual outcomes favor even further the stronger unit, more than the probability theory would predict starting from the declared strengths shown in the Combat Display

I hope I inserted enough comments inside the tables to make them understandable.
Should further explanations be needed, see you tomorrow, 2am here now.

Oh, and I hope you can open excel files...

[Vev]

thanks

I have a thing in Java, now trying to figure out how to turn it into a .exe file

[Vev]

I think it is the strange multidamage they implemented which is biased towards stronger attacker that is causing these annoying conflicts.

From brief experience, near equal ratios of 1:1 or 8:7 tends to give I thought, a fairly mixed spread of 1's, 2's and 3's damage. When it starts going to 2:1 then it skews into 80+% 3's damages with the rest being 2's and 1's.

In one case with 225:1 where a lone defender with 1 hit point against a horde of crappy singularity needlejets, in all 15 battles, it was all 3's damage, with maybe just one exception. The defender was unharmed throughout that period.

[MariOne]

BTW, you don't actaully need to tweak and simplify the binomial distributin and combinatorial factors.

To make it shorter, let's consider a situation where the Defender begins with only 4HP left.
The Attacker can win:
scoring 4 hits and suffering none
scoring 4 hits and suffering 1
scoring 4 hits and suffering 2
scoring 4 hits and suffering 3
and so on, depending on how many HPs A itself began with.
The number of combinations for each different outcome IS determined exactly with the binomial function.
You only need to think that the last hit must go to the winner, thus it's a given and must not be considered when counting the combinations. For instance, the 4-1 outcome has 4 possible sequences leading to it, and not 5, or the 4-3 outcome has 20 possible sequences (that is, bin(6 3), where 6 comes from 4+3-1 ), and not bin (7 3)=35

In summary, for each "winning unit's remaining HP" the # of occurrences is exactly calculated with the binomial function, and the related chance easily follows.
At this point instead of "coding an algorithm" you just need to "table" those outcomes and rely on excel's instant recalculation.
Input the A and D strengths and HPs, and watch instantly the overall battle % chances, also broken down into the different remaining HPs chances, as you requested in your 1st post

[Vev]

The main point is how the nCr thing is calculated. It was easy once I found how to correlate the n and r values to the hits.

As for coding, it's too late, I've already done it. Also I am not much of an Excel person. Another thing I have found was that if I adjusted the hits to be the equivalent number of times it can sustain damage based on avaeraged biased damage rating, I could skew to odds to be more like actual outcomes. Gotta love fudging models.

[MariOne]

Hey, X-posted and still up...

I find your 2:17 post rather confusing

BEWARE
In my tables, as explained in my comments and in the old threads, I consider the STRENGTHS, that is the values obtained from the weapon or armor value, after the modifiers are applied.
I totally disregard the "ODDS" calculated by the game, as we determined that they are screwed...

Even if the curve of our experimental data is shifted in favor of the stronger unit, its form is compatible with Sikander's model where combat is plainly resolved with a sequence of combat rounds consuming only one hitpoint each, with probability P of the single event fixed during the whole battle and determined only by the *strengths* ratio.

The observations are compatible with the hypothesis that single hits are grouped in "3 damages" tokens for ease and speed of display purposes only, and have no influence on the combat mechanism.

It looks like we'd only need to determine the exact amount of that "hidden bonus combat modifier" to the stronger unit's strength, and then Sikander's model (which is nothing more than what is stated in the manual) would perfectly match the experimental data, with no need of exoteric assumptions

Never forget the principle of economy, i.e. Ockham's razor....

[MariOne]

X-post again...

well, whatever floats your boat...
If I can easily get precise data exactly following the theory, I prefer that over doing hard work to get approximate data from a fudged with model.... But those are just my preferences

happy testing!

[Vev]

I do use the combat strengths, but since everything is turned into fractions, it doesn't matter, as long as you do not use their hitpoint modified combat odds. Their use of hitpoints as a metric is completely oddball and unusable.

I am currently disagree with the hidden combat bonus and at the moment prefer like skewed damage attacks. I could modify my program to set it loop for a range of ratios to get a batch of 'close enough results' and see any patterns.

I am too lazy to sit and watch and count the damage dealt.

Unfortunately I am an engineer so I prefer breaking things apart and come up with wacky things.

[Vev]

Well I did an incremental combat odds increase from 0.001 to 0.999 and matches for three of your test results. Next step is to do a brute force hit points combination
{attacker's hits} X {defender's hits}
and see their results with a fixed combat ratio.

[Verrucosus]

I feel a bit like a Spartan exchange student attending the annual lecture by the winner of the Zakharov Price of Theoretical Smacology. While the Spartans would probably volunteer to do some testing, I can just come up with a somewhat naive question.

I understand that the probability of winning a combat is different from that of winning one round of that combat. Therefore, when the "odds"-display gives 3:2 odds of winning in a standard situation, it must refer to the chance of winning a single round of combat. On that basis, however, I wonder what it means when the message says "taking damage into account". In what way is it possible to take damage into account for determining the probability of winning a single round of combat?

I do not doubt that the odds-message is screwed, I just want to know exactly how it is screwed.

Verrucosus