If you're looking for a triangle, how can you find it if you haven't defined what the points are?
Imagine a Cartesian grid that is 30 units wide and 30 units tall. How many triangles are there? Do all of them have the same orientation? Are all of them the same size? Are all of them equilateral?
The shape shouldn't have anything to do with the cartesian co-ordinate system. If it did, we would need to define what the units were, and what the axis were, which should define what the points are, but then we'd need to define what the lines are again, and worse, what the distance of the lines are. Unless that's the point you were trying to make...?
Correct. The win/loss ratios would form the edges. However, I'm not looking for min-maxed units, simply a minimum win/loss ratio (a unit should win and still retain a certain % of the group's total health--eg. 10 units vs. 10 units should have 3 units left at full health, or 6 at half, etc. (or better) to conform to a 30% health threshold).
But looking at how your searching for these ~points and how you describe such a triangle as irregular, it seems more like you're creating a circle with the distance from the center as the unit's relative strength, then trying to bend that into a triangle. Or perhaps there are many valid overlapping triangles with points in the general shape of a circle.
There are hundreds of triangles available, yes. All I am looking for is one of them, and not all of the points even reside at the same distance from the center of the "circle." Although the points should form more of a "doughnut" (assuming unit strength could be calculated, as there is not an objective place to stand in order to measure).
Doesn't looking for a single triangle out of a multitude by minimum(?) win/loss ratio preclude procedural unit generation? It's not as though in a balanced triangle any of the other units would fall on the sides of that triangle, since those sides are only win/loss ratios, and those wins and losses do not record how much of a win or loss (since you bring up hit-points).
How are you combining the reaction between points simile with the distance from center simile? If we wished to define an absolute strength for each unit we would need to calculate the shape/distortion of the donut, which could be possible by imaginative use of differentials, which does bring us back to the Cartesian co-ordinate system, but what are our units and axis?
Either need a new shape to describe this, or different definitions for the original shape. I guess it doesn't matter much, as long as you're ignoring this triangle concept, but it would make it easier for me, and hopefully others, to understand what you're doing.
I call it a triangle because the results are three units that have a Rock Paper Scissors relationship and the resulting node-graph of "what beats what" resembles a triangle.
And for Scissors Glue Rock Paper? Or any possible balanced relations that aren't just a triangle? If we have a multitude of possible triangles, then we have a multitude of possible points (units), which means we also have a multitude of other shapes as well.