Does the barbarian's 9th-level Brutal Critical feature deal one extra die of damage on a critical hit, or two extra dice?

Question

Does the barbarian deal one more die of damage with the 9th-level Brutal Critical feature, or two?

I had a massive fight with GM over this – him going for the one extra die of damage, me for two.

The barbarian's Brutal Critical feature states:

Beginning at 9th level, you can roll one additional weapon damage die when determining the extra damage for a critical hit with a melee attack.

While the rules for a critical hit state:

When you score a critical hit, you get to roll extra dice for the attack’s damage against the target. Roll all of the attack’s damage dice twice and add them together. Then add any relevant modifiers as normal. To speed up play, you can roll all the damage dice at once.

For example, if you score a critical hit with a dagger, roll 2d4 for the damage, rather than 1d4, and then add your relevant ability modifier. If the attack involves other damage dice, such as from the rogue’s Sneak Attack feature, you roll those dice twice as well.

So it would seem like the barbarian actually rolls 2 more dice.

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What's more, it is curious that some magic weapons, like for example sword of sharpness, say that when you roll a 20 on the attack roll you deal bonus 14 damage, not 4d6. Those features add bonus dice, only their condition is for a critical hit to occur. Am I understanding that correctly, or is my DM right, and why?

The same question can be applied to a vorpal sword dealing additional 12d8 on a critical against a creature that doesn't have or doesn't need a head, etc., while the description of the item states that it deals "an extra 6d8 slashing damage".

Answer 1

The extra die from Brutal Critical is rolled once.

The rules for determining the extra damage for a critical hit state:

you get to roll extra dice for the attack’s damage against the target. Roll all of the attack’s damage dice twice and add them together.

This is what Brutal Critical is referring to when it says "extra damage":

...when determining the extra damage for a critical hit with a melee attack

The "extra damage" is the second roll of the weapon's damage dice. So when Brutal Critical says:

roll one additional weapon damage die

It only applies to the "extra damage", not the weapon's base damage, since the features tells you to roll one additional die when determining the extra damage, not when determining the base damage.

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The Sage Advice Compendium also confirms this (versions before 2.0):

If you have the barbarian’s Brutal Critical feature and score a critical hit with a melee weapon attack, you get to roll one additional damage die when rolling the weapon’s damage. It’s one die, no matter what weapon you’re using. For example, if the weapon normally deals 1d8 damage, you roll 3d8 (1 for the weapon, 1 for the critical hit, and 1 for Brutal Critical). If the weapon normally deals 2d6 damage, you roll 5d6 (2 for the weapon, 2 for the critical hit, and 1 for Brutal Critical).

Answer 2

The way I read it is as follows:

Your barbarian attacks with their greataxe (1d12 damage die + modifier). You roll a Natural 20 on your Attack Roll, and thus score a critical hit. You double the damage roll dice for a total of 2d12 damage (+ modifier). Additionally, Brutal Critical adds another damage die to the pool, for a total of 3d12 (+ modifier) damage.

If instead your barbarian used a maul, your normal damage would be 2d6 (+ modifier), a critical hit would be 4d6, and a Brutal Critical would add just one d6 for a grand total of 5d6 (+ modifier)

This makes the greataxe better in terms of maximum damage potential (36 damage vs 30 damage) and average crit damage (3×6.5 = 19.5 vs the mauls 5×3.5 = 17.5), but not for minimum crit damage (3 for the greataxe vs 5 for the maul).

Note that this specific calculation applies to Brutal Criticals (or half-orc Savage Attacks) with one extra damage die. At higher levels when you get more extra dice, a 1d12 weapon pulls farther ahead for average crit damage.

A 1d12 weapon is still slightly lower non-crit damage (6.5) than 2d6 (7), and more swingy (more often roll really low and maybe don't finish off a low-HP target). And without Brutal Critical, has no real advantages even for a lvl 8 or lower barbarian.

Whether the overall average damage per hit (or per attack) favors a greataxe depends on how often you crit (out of hits; a high target AC will eliminate some non-crit hits), and how many extra dice you get. But that's a separate question from how Brutal Critical works when you do crit.