Joshua Randall
Legend
From the 3.5 SRD:
Round 0: Bbn1 flies into rage -> Con 18 (+4), hp 14. Rage will last 3 + 4 = 7 rounds.
Round 1: Ogre clubs Bbn1 for 23 points of damage. Bbn's hp are 14 - 23 = -9.
Round 2: Bbn is unconscious and dying. (He's also still raging!*) At the end of this round, he makes a stabilization check (10%). If this check fails, he loses another hp, dropping to -10: he's dead.
Rounds 3-7: Assuming the Bbn stabilized in round 2, he is at -9 hp for each of these rounds.
Round 8: The Bbn's rage ends. His temporary hp go away. If he was still at -9 hp (because he stabilized in round 2 and no one has cured him above that), he now drops to -11 hp and dies.
* That is, he's still raging as long as we use the 3.0 rules Sage Advice on this subject. Otherwise, it's up the DM to decide what happens to a raging barbarian who falls unconscious.
Edit: added note about Sage Advice.
In your example, an assumed Bbn1 with Con 14 and hp 12:... The increase in Constitution increases the barbarian’s hit points by 2 points per level, but these hit points go away at the end of the rage when his Constitution score drops back to normal. ... A fit of rage lasts for a number of rounds equal to 3 + the character’s (newly improved) Constitution modifier. A barbarian may prematurely end his rage. At the end of the rage, the barbarian loses the rage modifiers and restrictions and becomes fatigued ...
Round 0: Bbn1 flies into rage -> Con 18 (+4), hp 14. Rage will last 3 + 4 = 7 rounds.
Round 1: Ogre clubs Bbn1 for 23 points of damage. Bbn's hp are 14 - 23 = -9.
Round 2: Bbn is unconscious and dying. (He's also still raging!*) At the end of this round, he makes a stabilization check (10%). If this check fails, he loses another hp, dropping to -10: he's dead.
Rounds 3-7: Assuming the Bbn stabilized in round 2, he is at -9 hp for each of these rounds.
Round 8: The Bbn's rage ends. His temporary hp go away. If he was still at -9 hp (because he stabilized in round 2 and no one has cured him above that), he now drops to -11 hp and dies.
* That is, he's still raging as long as we use the 3.0 rules Sage Advice on this subject. Otherwise, it's up the DM to decide what happens to a raging barbarian who falls unconscious.
Edit: added note about Sage Advice.
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