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Edit: I stand corrected :)
1d12 chance to get a 12 is 1/12
2d6 chance to get a 12 is 1/36.
2d6 will give more consistent damage while 1d12 has an equal chance.
The casino game Craps is based off of the rolling of 2d6 and the payouts are based on the probabilities.
Chance to roll d12 2d6
1 1/12 0
2 1/12 1/36
3 1/12 2/36
4 1/12 3/36
5 1/12 4/36
6 1/12 5/36
7 1/12 6/36
8 1/12 5/36
9 1/12 4/36
10 1/12 3/36
11 1/12 2/36
12 1/12 1/36
THanks a lot
Average damage of 2d6 (7 dmg) is better than 1d12 (6.5 dmg), but if you want to get 12s, your odds are better with the 1-12. You also have a better chance of rolling a 1, than you have of getting a 2 with the 2d6. There are just a number of combinations to get you to those middle numbers of 2-12, so you will mostly likely do closer to your average. e.g. to get to doing average damage, a 7, you could...roll a 4-3, 5-2 or 6-1.
In regular 5e, if you are say...a crit fishing Half Orc Champion Fighter, who crits on a 19 or 20 (18,19 or 20 at higher levels) and you want to see big hits from time to time, you would use a Great Axe imo. Your chances of a really big hit are better with the 1-12, than the 2-12. But...your chances of a low number are also higher! I'm an optimist though, so if I had an Half Orc Champion Fighter, I would only be mentally counting up the 12s, in my head, not seeing all the 1s also! lol :)
To sum up...you have only a 2.777% chance of getting a 12 with 2d6, but an 8.333% chance of getting a 12 with 1d12. But remember, those percentage numbers go the other way too and 1d12 has a chance at a 1, that 2d12 doesn't. So, you have a 16.666% chance of a 1 or 2 with 1d12 vs just a 2.777% chance of a 2 only with 2d6.
I totally agree! I was more thinking of the Savage Attacks half orc racial, but in your example, a half orc with Brutal Critical would get even more weapon die attacks. And yes, it is a singular DIE, not weapon DICE for these racial and class abilities on crits. So Savage Attacks crit only gets you 1-6 extra damage with a 2d6 Greatsword, but an extra 1-12 with a Great Axe!
So...a half orc who is a 10th level barbarian with a greatsword who has a crit, would do 2d6 normal + 2d6 for the crit + 1d6 for Savage Attacks + 1d6 for Brutal Critical. That would be a total of 6d6 or 6-36 (average 21) damage plus modifiers. That same half orc would get 4d12 or 4-48 (average 26 damage) from a Great Axe. For a half orc fighter champion or barbarian, a Great Axe is clearly superior to a Greatsword.
Edit: But keep in mind that while a greataxe might be better, a greatsword is still perfectly viable, so if you like swords...
Edit edit: There's also the great weapon fighting style, which lets you reroll 1 and 2 on damage rolls, which is a bigger bonus for sword than axe.