This file details some considerations to make for a Carth build, and may eventually contain a few Carth builds from different playthroughs. We'll see how far I take it.
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Carth is a Soldier. He starts with higher DEX than STR, and feats that tilt toward ranged combat. As a soldier, he gets a lot of feats, so you could spec him as a high-DEX melee combatant if you like.
In fact, Carth starts with a literally impossible collection of feats based on the Soldier class. The game developers artifically increased his early capabilities, because the main character may need to lean on Carth until more companions are available. This makes him suitable for melee in the very early game, even if you're building him for ranged.
This also gives us an opportunity to splurge on selected feats later in the build. Unfortunately, it doesn't do much good because, no matter what you try do with Carth, by mid-game there's always someone better at it.
You're required to use Carth in the early game. He's optional thereafter, other than one plot-centric part of the game where you're required to take him and Bastila. Completing his companion quest involves taking him for at least part of Korriban, but you can put him back on the ship after that's done if you like.
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Carth Builds:
Melee Carth
Ranged Carth