Hello, this is my first post, so please go easy on me

Due to the controversy surrounding attack and defense, I'm attempting to write a c++ program with the goal of ultimately figuring out a fleet's probability for victory (and probable hp of ships that survived). However this is somewhat of a big undertaking. I've made some progress, but ran into a wall due to a lack of solid information. So far I've done a damage probability calculator, given an attack value and a defense value (the defense is assumed to be ideal, ie shields against beam weapons). However, I've run into a wall for multiple weapon/armor ships. Does anyone have any idea how that is exactly calculated? Searching the forums, I found mostly confusion and a few speculative ideas. One of them is listed below:

"So, say a ship with 20 beam attack and 10 mass driver attack shoots at a ship with 12 shields, 8 armor, and 4 point defense. Roll 1 to 20 for beam damage. The defense against beams is 12 + sqrt(8+4). So roll 0 to 15 for beam defense (the sqrt rounds down). The difference between the attack and defense rolls is the damage. For mass driver attack, roll 1 to 10 for attack, roll 0 to 8+sqrt(12+4) = 12 for defense. Then add the damage done in the beam attack to the damage done in the mass driver attack, and that's the damage displayed in the combat viewer. "

I don't know if this is correct, or if indeed everything is one roll (and in such a case, how are non-congruent offenses and defenses calculated?)

I have, however, begun to progress into single ship vs ship combat survivability, assuming again only ideal defenses.
I will attempt to make the exe, source code, and mathematical anyalsis (ie how I determined the formulas for the probability) avaiable on a website soon.

Here's a few sample outputs from the damage probability part of my calculator:

maximum attack strenght: 3
maximum defense strength: 3

RESULTS:
Damage Probability Exact
0 62.5% 10/16
1 18.75% 3/16
2 12.5% 2/16
3 6.25% 1/16
notes: this shows that shields are usually above 50% effective, assuming the hp of the ships are considerably less than the attack (negating "lucky rolls")

maximum attack strenght: 2
maximum defense strength: 1

RESULTS:
Damage Probability Exact
0 50% 3/6
1 33.33% 2/6
2 16.67% 1/6
notes: again, shields are still effective, with relatively low numbers.

maximum attack strenght: 1
maximum defense strength: 3

RESULTS:
Damage Probability Exact
0 87.5% 7/8
1 12.5% 1/8
notes: outshielding can be effective, if you can afford it.

maximum attack strenght: 20
maximum defense strength: 20

RESULTS:
Damage Probability Exact
0 52.38% 231/441
1 4.535% 20/441
2 4.308% 19/441
3 4.082% 18/441
4 3.855% 17/441
5 3.628% 16/441
6 3.401% 15/441
7 3.175% 14/441
8 2.948% 13/441
9 2.721% 12/441
10 2.494% 11/441
11 2.268% 10/441
12 2.041% 9/441
13 1.814% 8/441
14 1.587% 7/441
15 1.361% 6/441
16 1.134% 5/441
17 0.907% 4/441
18 0.6803% 3/441
19 0.4535% 2/441
20 0.2268% 1/441
notes: if the defending ship is a small fighter with no bonuses (10hp), despite the 20 shields, it has a probability of being destroyed in one hit of about 15%. Not so hot, especially when considering that 20 shields on a fighter is not really realistic either.

If you think there is a problem with the calculator, please post a response highlighting the mistake my probability algorithm. Like I said earlier, I will attempt to place the formulas used, source code, and exe on a website in the near future, as well as work on the optimal ship-survivability part of the calculator. It will be hard to progress with non-optimal defenses unless I know exactly how each case works.