Board Game Component

Today Lee and I brainstormed some improvements to how roll playing games work. Our biggest beef with D&D these days is that it is entirely focused on battle. And I don’t find that part of the game very compelling. What would be more interesting is a game which promoted roll playing, and discouraged battle. And if a fight must occur, it should be swift and merciless.
Along the way I proposed a widget that might be a useful game mechanic. A quick illustration of it is here:

It provides a way to specify three parameters (here marked kill, retreat and defend) that are linked by an algebraic relationship A + B + C = 0. You specify your choice by placing a marker at the intersection of three lines.
Our idea was that a battle would consist of very few rolls, and that the party would act as a group. To provide the kind of statistical outcome that is favorable, there would be a lookup table to translate the die roll + a reduced number of parameters to battle outcome.
This is all obviously a work in progress.