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BIND is changing how attacks work, and I can't believe I didn't think of this trick before.
The worst way to perform attacks must be GURPS
That's 1 roll for the Initiative (both roll at the same time), and 4 more rolls, making a total of 5.
That's 3 actions performed. The Initiative may or may not be meaningful (well, it's very meaningful considering the action-point system, but let's ignore that). If Alice misses, then Bob hits, we didn't need to know the Initiative. If both miss, then we've returned to the starting condition - we have gained nothing in terms of narrative, or even in terms of basic mechanical resolution.
Every round where nobody receives a hit is pointless.
If this seems odd, it's probably because all RPG players know combat only through various games. The abstraction seems natural, but we can employ other abstractions, which I'm sure will feel equally natural after a while.
Dodging an attack allows one to hit the opponent without getting hit, and hitting an opponent means one has less reason to dodge, as they reel from an attack. Of course a clash of swords can still occur without any resolution in reality, but the system ignores these events, and simply presents us with the results.
We have gone from 5 rolls, to 3, to 1, and lost nothing. All we need to know is what state both parties end up in by the time they flee, surrender, or die. We need to take into account their stats - Dexterity, Strength, and so on; but nothing here stops that happening. We can still add Strength to Damage, and add Dexterity to the attack roll.
Character's are still represented, and even old D&D tropey-classes can find representation. A dexterous thief might hit opponents a lot while dealing minimal actual damage, while a massive barbarian may destroy creatures with his mighty axe, but have a hard time fighting skilled opponents who know how to duck and parry.
A massive chunk of the system will have to change to accommodate the new paradigm. I've spent a few days on it already, and will undoubtedly spend many more.
It's a lot of work to cut out just 1 roll (Initiative will have to remain, for other reasons), but there's no arguing with results.