How to design and balance a Rock-Paper-Scissor like mechanism

@larienna

If you like. I could focus entirely on one of your games in progress. That you wish to use this mechanic on.

I could work on an excel sheet that calculates the balance.
Make it more functional as well. So that changing numbers would be easier.

I am thinking of a pre-matrix in which you enter the number of dice used against a target. Then another pre-matrix in which you enter the number of dice used in a counter attack. (2 pre-matrixes since this is simpler to work with)

Heck, I can even throw in an extra column for a basic set of dice.

Edit:
The only issue is that I cannot calculate a winchance. But I could have the excel sheet look it up from a separate tab.

True balance depends on how much you use a certain ammount of dice.

But I have a list of simple weight factors.
Perhaps you can use this one as "damage" value's.
Solely based on a continues system of winning.
Ties are not included.

So, each unit you design, will deal this "damage" value.
And if the unit uses a different ammount of dice. A different "damage" value can be applied. Regardless of the ammount of dice the opponent uses.

3: 1
4: 1.6
5: 2.35
6: 3.26
7: 4.38
8: 5.73
9: 7.38
10: 9.39
11: 11.85
12: 14.86
13: 18.54
14: 23.07

How to use this?

Let's say, you have an unit that can use 6 dice.
There are 24 possible opponents.
To 6 of them, you can use 9 dice.
To 6 of them, you can use 10 dice.
So, to 12 of them, you can use only 6 dice.
The total weight will be; 12x 3.26 + 6x 7.38 + 6x 9.39 = 140.

If you have an unit that can use only 3 dice.
But has the same bonusses.
To 6, it uses 6 dice.
To 6, it uses 7 dice.
And of course, 12 of them, only 3 dice.
The total weight will be; 12x 1 + 6x 3.26 + 6x 4.38 = 58.

If you have some sort of cost. Then you might want to divide the numbers by 20.
You get 3 and 7 for these 2 examples.
It isn't perfect. But it is 100 times faster to calculate.

Perhaps I should see a top tier version of this. 9 dice, again with the same bonusses.
The total weight will be; 12x 7.38 + 6x 14.86 + 6x 18.54 = 289.
14.4, lets say 14.

So, 3, 6 or 9 dice, with those bonusses. Result in the weights of 3, 7 and 14.

Let me know, if this is better.