FASA Games, Inc.

Unarmed Damage is, normally, Strength only ("Most unarmed attacks are considered to be punches or kicks, using the character’s unmodified Strength Step as the Damage Step for a successful Attack Test", p. 261).

Does this mean a Fourth Circle Warrior could apply Karma to Unarmed Damage Tests?

:K

No A Fourth Circle Warrior may spend Karma on Strength-only Attribute Tests. This includes trying to break out of some powers, trying to lift something really heavy, break down a door through sheer strength, etc.
Even if it is just Strength, the character is making a Damage Test, a different kind of test. Same thing with Knockdown Tests even though they are usually Strength for most characters without Wound Balance.
At Seventh Circle, they gain the ability to add Karma to Melee Weapons and Unarmed Combat Damage Tests.

Ah. Attribute-only Tests are Action Tests. And since Damage Tests are Effect Tests....

It boils down to needing the right Karma on the right test type essentially.

Karma on Strength Tests = Karma on any Strength-only Attribute at Fourth Circle for Warrior

Karma on melee weapons and unarmed combat Damage Tests...at Seventh Circle Warrior can spend Karma Points on any close combat Damage Test.

The real dealmaker is Crushing Blow. They get that at Seventh Circle as well. So they get Rank + Str for damage (+weapon) and can spend Karma on it. They also get their Discipline ability (note that this allows them to spend an additional Karma Point on close combat Damage Tests, one for their Discipline ability and one for Crushing Blow, so they can spend two Karma Points on Damage Tests). An obsidiman Ninth Circle Warrior in our Earthdawn Kratas Quest Named Ced Roc has Improved Karma (Named Spell). This gives him an insane nine dice damage (Crushing Blow 9 + 10 Strength + Troll Sword R4= 13 =32 + 2 Karma ( Improve Karma +4 steps, so 8/2D6 x 2). That total damage is 3D12+ D10+D8+4D6.

Keep in mind its your Barsaive though. As long as a character is rolling raw strength for damage or knockdown, feel free to allow Karma if you would like. I did that for years personally.