A couple of the entries in the "MSP-Games Micro Game Challenge" competition included a number of unit types, which had some complicated relationships of who beat whom.
It got me thinking of how this might be best represented on the pieces themselves, rather than in an additional table.
You can view a possible solution in this image. You could line up the top edges, and look-up the result.
What do people think? It might be a bit confusing to players at a casual glance, but basically the semi-circles go in the opposite order to the arrows.