More dice? Or more rolls, and more info per die?

The canceling thing could have possibilities if the unit values were made with that in mind. I see how that wouldn't work with A&A using the current values.

I hear what you're saying as far as a given unit using weaponry and tactics appropriate to the target force.
But the A&A scenario deals with a limited number of forces that are failry equal. This, i think, is why the balance works with the given combat system.

However, think of a scenario with a large variety of foces, with a wide range of possible capibilities.
You could end up with a militia force using outdated weaponry being assulted by a modern armor force. Under these circumstances, the milita unit is gong to get clobbered. They simply don't have the weaponry to effectively deal with modern armor.
Now, imagine the same militia defending against an attacking force that is similar to the militia. Here, the odds are more equal.

The point is that the defnding militia should not have the same chance to kill the different types of attackers in these two scenarios.

I'm looking for a system that is both simple, and can account for a wide range of possibilities. (Currently in development is a fantasy game, and a sci-fi game. I'd like to have realistic, and internaly consistant, results given the game environment)

The different sided die idea has merit. But I'll still likely have to number, and use bonus die. As I'll probably need probability granularity below 5% if I want to keep the combat within one primary roll.

Suppose two units are facing each other with such a large disparity that one unit hits 10% of the time and the other hits 90% of the time. To be mathematicaly precice I'd need granularity down to 1% (the chance of the weak unit killing the stronger unit while the stronger misses)
Here's the probability breakdown:
Weak unit miss, strong unit hit - 81%
Weak unit miss, strong unit miss - 9%
Weak unit hit, strong unit hit - 9%
Weak unit hit, stong unit miss - 1%

To do this traditionaly I'd have to make two rolls, one for each unit, or have a very large 100-sided die.

Now I could fudge these percentages a bit so they would be represented on a d12 thus:
10 faces: weak unit miss, strong unit hit - 83%
1 face: weak unit miss, strong unit miss - 8%
1 face: weak unit bonus roll, strong unit hit - 8%

So a 1 in 12 chance for the bonus die to be rolled. If the bonus die hits on 1 in 6, the weaker unit scores a hit 1.3% of the time. (8% x 16%)
If the bonus die hits on 2 in 6, the weaker unit scores a hit 2.7% of the time. (8% x 33%)
(I would have to decide on the bonus die set up, and stick to it.)

Now the different sided die does offer more visual distinction, and lets me use the bonus less often. So, my current line of thought is this:
Color coded, and numbered:
0 - d8
1 - d8
2 - d8
3 - d10
4 - d10
5 - d10
6 - d12
7 - d12
8 - d12
bonus - d6 (prolly 2 in 6 hit)

Anyway, I guess I'll have to put some stickers on some dice and see what happens.

Ok, some background.

First off, I'm hoping this is a resolution system that can be used in a number of different games. However, in my previous example an individual unit represented a collection of men. The number varies somewhat, and is reflected in the overall combat strength, but usually 50-100 men.

I'll also explain how a unit that is good defender, but poor attacker can be represented. Basicaly, you're thinking very small units and more tactical detail than I am.
In this system, engaging in combat is more than one encounter. It represents a series of engagements, possibly over a couple of days, in a general geographic area - so level of detail doesn't specify a deffender is on a specific ridge, but rather, if the area is rough terrain such as hills it is assumed that the defender can use this to his advantage. So perhaps there are a number of ridgelines in the area and the defender is assumed to use them when the tactical situation allows it.

So, a Soldiers unit is a unit who's primary attack mode is troops with melee weapons. Now, this also includes some scouts, possibly a few ranged weapons, supplies, unit command and operations. Basicaly, the infrastructure to run that particular unit.

A turn represents a weeks worth of time. When there is an "attack", it represents the Soldiers unit trying to take control of a map region. Conceptualy, this would occur over a few days. First, scouts are sent to asses the situation. As the main body of the force moves in, the may be engaged in several places. There may be some manuevering as the attacker tries to neutralize the defenders terrain advantage, or minimize their own weaknesses. There will be numberous "attacks" and "deffendings" on both sides of the engagement.

The die roll represents the outcome of all these things.

So, if something deffends better than it attacks, it can be assumed that the commanders are trying to minimise this weakness on offensive opperations. They will try to outmanuever the opponent and get into situations where they can use their deffensive cababilities better. Perhaps they will put more supporting troops in a local situation where it isn't possible to manuever well.

This works in reverse, too. Even if a unit deffends well, there will still be situations where portions of the defender must attack the attacker.

At any rate, the unit will have to do more "work" to neutralize its weaknesses and so it may have a lower overall combat effectiveness then its attack ability would suggest. Or perhaps it might have a higher build cost as it may represent a larger number of troops to get a same overall combat effectiveness.

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Now then, as far as how combat would work, the attacker would declare what units he is moving to attack an area. Then the defender would say which units he is moving to intercept and block the attacking units.
After seeing which units are squareing off against which, you compare combat scores and roll the appropriate die. One die is rolled for each pair of units.
Now, the defender could block a single attacking unit with more than one defender. In this case, the attacker would only get to direct its firepower agains one of the defenders, while the defender gets two roll against the attacker. In this way it is possible for weaker units to overwhelm a stronger unit with numbers.
Any attacking unit that the deffender neglected to block, then gets to decide where to direct their attack (possibly teaming up on a defender)

In cases where one unit has used up its attack and is getting engaged again, you would still compare scores and roll the die, but you would just ignore any hits from the beseiged unit.

That's the basics, and there ae some other nuances, especialy in regards to ranged units, but they are out of scope for this discussin, I think.

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I still have to so some testing, but after analyzing the odds and how to create the die faces, my current idea is this:

<br />
# Die Color   -   +   | Hm  HH  mm  mH  Faces<br />
0 d8  Yellow 50% 50%  | 25% 25% 25% 25% 2  2  2  2<br />
1 d10 Yellow 45% 55%  | --unfinished--<br />
2 d12 Yellow 42% 58%  | 17% 25% 25% 33% 2  3  3  4<br />
3 d8  Orange 38% 63%  | 13% 25% 25% 38% 1  2  2  3<br />
4 d10 Orange 30% 70%  | 10% 20% 20% 50% 1  2  2  5<br />
5 d12 Orange 25% 75%  |  8% 17% 17% 58% 1  2  2  7<br />
6 d6  Red    20% 84%  |  3% 17% 13% 67% 0  1  1* 4<br />
7 d8  Red    15% 88%  |  2% 13% 11% 75% 0  1  1* 6<br />
8 d10 Red  11.5% 90% |1.5% 10%  9% 80% 0  1  1* 8</p>
<p>Bonus  d6  Green  17% hit    1 hits, 5 misses</p>
<p>I listed the actual percentage chance the Weaker (-) and Stronger (+) unit have of hitting the enemy (regardles of the enemy result) Ideally, these would change by 5% going down the list. It's not perfect, but close enough, I think.</p>
<p>Next, I've broken down the odds.<br />
The battle results are grouped weak unit then strong unit with a Hit (H) or a Miss (m) and the percentage of the time that result will occur. So, MH means that the weaker unit misses while the stronger unit hits. The number in this coulmn is how often that will happen</p>
<p>Finaly, I have listed the number of die faces that have a particular battle result, in the same order as the battle result columns.</p>
<p>The * indacates that the weaker unit misses, unless a hit is rolled on the bonus die.<br />

(If the table looks messy and wraps lines, you may have to adjust your browser font size - the preview result was not the same as the post result)

As you can see, the die shapes progress from lesser to greater number of faces, and get more red as the score disparity gets greater. Because each category is unique in shape and color, it should be easy to quickly identify the correct die (though they will be labled as well)

The battle result can be shown with helpfull little icons. I think that d20 will have too little space on it, and this is why it isn't used.

The bonus die is rarley used so far. Only in the last category and then only on a single die face each.

Now the unfinished row is problamatic. I have the hit percentage here is only the target numbers. I should use a d10 to keep it consistant, but it doesn't divide into the target percentages very well. I can get the odds close with liberal use of the bonus die, but this seems like a messy kludge. I'll have to work on it.

Edit:
Ok, I think I have a possible solution for score difference 1.

<br />
# Die Color   -   +   Hm  HH  mm  mH   Faces<br />
1 d10 Yellow 44% 54%  24% 21% 21% 34%  2  2  3* 3</p>
<p>The * appears in every position on these 3 faces; indicating a miss unless the bonus is rolled.</p>
<p>My math here is on shakey ground for this one though.... it might be wrong.<br />

You need the chart to see what a percentile roll means.

Ok, so you roll a 30 and a 2, making 32. But what does 32 mean? That's where the chart is needed. You would have to look it up in the correct score disparity column and find what battle result 32 comes under.

The way I'm trying to get this system to work, is that the chart is kind of "built-in" to the dice themselves.

I'm sacrificing a little bit of odds precision for resolution speed and simplicity.

Now, maybe you're suggesting a completly different mechanic?