hardcoe is separate from difficulty. Its been stated that you can play FO:NV on "Easy" with "hardcoe" active. As I understand it... No, HC mode does not affect damage.
Well this damage-changing would be different from difficulty levels.
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I'll try to put it this way. Let's say:
Easy Difficulty = The player can take high damage. Enemies can take little damage.
Normal Difficulty = The player can take normal damage. Enemies can take normal damage.
Hard Difficulty = The player can take little damage. Enemies can take high damage.
hardcoe Mode = The player can take less damage. Enemies can take less damage.
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Pretty much would hardcoe mode, in relation to the currently used difficulty level, make everyone (including you) a little less resilient to shotgun rounds to the face?
Edit: For clarity.