You misunderstand; the "1+1+1" is a single attack, and the "*2" indicates two attacks. If both people have aggro stance, a knife deals three damage, and attacks twice, for a potential of six damage. A kopesh or katana does four damage in a similar situation, and makes or breaks all that damage on one roll, where the knife gets two chances at three damage. Also, three damage is equal to a head's HP, so the knife user essentially gets two rolls to instakill their opponent, while their opponent gets only one.
In a defense vs aggro battle, the knife does two one damage attacks per turn, while the opponent does one two damage attack per turn. They have identical potential damage, but the knife user gets two chances at a head hit, stunning their foe if
either attack hits.
Basically, in a normal battle, the knife always has the advantage. Even factoring in special attacks, the knife's got it pretty good; crippling blow grants a permanent *2 to damage on a certain limb (which I think is slightly better than the katana's quick draw). It does have the disadvantage of lower defense due to range, but that's mitigatable (through armor--see below). Only the kopesh's cleave ability is on a similar level, and even then only when the knifer has heavy armor and assuming cleave ignores armor.
Hence why I end up saying the knife shouldn't be nerfed. If it were, the kopesh is the undisputed king. As it is, there's two valid munchkin builds:
((Oro refers to the dickish guy who does Dark Souls PvP by overbuffing a katana, making each slash do over a thousand damage, not this game))
Weapon: Dagger and greatshield
Armor: Medium armor on all limbs and head, heavy armor on torso
Weight is 4+1.5*5+3=14.5, for a -4 to defense. Greatshield raises that up to effectively -2 defense. It could be upgraded to full heavy, but I think that would be more trouble than it's worth, because it'd get -7(-5) to defense. The point is probably moot, as this build will probably want to stay in double aggro at all times, but having the option of defending is nice.
Deck would have 3x crippling blows, and LOTS of attacks. A few feints might be nice, but I don't think they'd be useful against anything aside from another havelmonster. The best strategy would probably be to crippling blow a leg, then just spend every attack on killing the legs. With crippling blow and double aggro, it only takes two hits, for three total. If the opponent goes defensive, havelmonster still has the advantage because its not that easy to hit, and can tank a lot of damage while having the best DPT in the game.
Oh course, kopeshes are a hard counter if Cleave ignores limb armor, which is why I have two builds listed.
Weapon:Kopesh and Greatshield
Armor: Medium armor on head, naked otherwise
Weight is 4+1.5=5.5 for a -1 to defense. Greatshield raises that up to effectively +1 defense. You could use a normal shield instead of a greatshield, but that prevents you from wearing a helmet, and I'm not even sure it would provide any benefit whatsoever. Maybe against Feints and Cleaves, but the former isn't actually that bad (your opponent might trade a turn for one of yours), and the latter is still hard to land. Then again, this build relies upon both those moves, so...
Deck would have 3x Cleave, few attacks, lots of feints, all stances (and plenty of them), and a smattering of other cards for versatility. Generally, the strategy would be to go into aggro stance, then repeatedly feint->cleave a leg. Once a leg is missing, go for an arm. Once both are missing, go defensive and either cleave another limb or just start hitting their torso, according to taste. It shouldn't matter much; with def stance, this build has an effective +2 defense, and if the foe's missing an arm, that's up to an effective +4 (plus they'll find it really hard to hit anything except your torso). They'll basically have to go into aggro to stand a chance of hitting you, so you don't even lose much accuracy.
The only counter I can think of is parrying the feint, and parry is generally pretty crappy otherwise. Also, parry isn't compatible with shields or armor, so I doubt it would get much use if people were being serious.
Against a parry-heavy person, aggro-cleave-defensive-wait-anything might be a good turn order. You can move cleave to three different spots in your turn order without any issue, making it hard to parry, and you only spend 2/5 turns out of defensive stance, which makes you really hard to hit if they stop the parry spam.
Katana should basically never be used. Quickdraw is decent, but is too easy to counter and the katana only beats the dagger in raw damage if the dagger hasn't landed a crippling blow. The katana will quickly run out of quickdraws, while both other weapons only need to land their special once per limb.
Maybe Kopesh and dagger are just OP, though. It's hard to tell when we only have three weapons.
EDIT:
I just considered something. The havelmonster
literally doesn't care if its legs are chopped off, so the leg armor can be completely removed. That gives it +1 defense until it loses a leg, which is nice. By then it'll probably have chopped off your leg, so it balances out.