2d6 vs 1d12: Greatsword vs Greataxe Probability Showdown
Why two six-sided dice beat one twelve-sided die in almost every combat scenario — and the exact breakpoint where Greataxe wins.
2d6 Damage
1d12 Damage
The Bell Curve vs The Flat Line
Rolling two dice creates a triangular distribution. There are 36 distinct permutations of rolling two six-sided dice:
- Sum of 7: 6 combinations out of 36 (16.67%).
- Sums 6, 7, and 8: 16 combinations out of 36 (44.44% of all rolls fall right in the sweet spot).
- Sums 2 and 12: Only 1 combination each (2.78%).
By contrast, a 1d12 has an equal 8.33% chance of rolling every single number from 1 to 12. That means rolling a pathetic 1 damage happens 8.33% of the time on a Greataxe, while a Greatsword can never roll lower than 2.
The Barbarian Exception: Brutal Critical Math
The only scenario where the Greataxe outperforms the Greatsword is when an optimized Barbarian stacks multiple critical hit bonus dice.
The wording of the 5e Barbarian Brutal Critical feature states: "You can roll one additional weapon damage die when determining the extra damage for a critical hit."
| Scenario | Greatsword (2d6) | Greataxe (1d12) | Winner |
|---|---|---|---|
| Normal Hit | 2d6 (Avg 7.0) | 1d12 (Avg 6.5) | Greatsword (+0.5) |
| Standard Critical Hit | 4d6 (Avg 14.0) | 2d12 (Avg 13.0) | Greatsword (+1.0) |
| Brutal Critical (Level 9) | 5d6 (Avg 17.5) | 3d12 (Avg 19.5) | Greataxe on Crits (+2.0) |
| Half-Orc + Brutal Crit (x2) | 6d6 (Avg 21.0) | 4d12 (Avg 26.0) | Greataxe on Crits (+5.0) |
Verdict: Which Should You Pick?
- Fighters, Paladins, and Rangers: Always choose the Greatsword (or Maul). You hit harder on average and avoid whiffing with low rolls.
- Half-Orc Barbarians: The Greataxe is thematic and deals devastating spikes on critical hits once Brutal Critical unlocks at Level 9.