I've always had a beef with both the dice method and the "3 rule", as you have it:
The 3 rule's problem is really, really clear. Generally speaking, when abiding by the three rule, there's basically no skill accounted for. The first person to swing will be, three tries later, the first to hit. Always.
As for the dice system, it was originally designed for games with a DM or GM (Dungeon Master or Game Master, respectively). Nearly all genuine "roleplaying games" designed with the dice system account for the presence of the DM/GM, who mediates gameplay and essentially makes sure things stay fair. Without that... You get things like five consecutive 20s in a row between a pacifist noble and Aloria's most skilled swordsman, and suddenly logic gets projected out the window.
TL;DR the dice system wasn't made for a situation where it's essentially "PVP", per-say. It was designed for GM-moderated PVE.
[/rant]