Everyone knows that the greataxe has slightly lower average damage than the greatsword. The axe does 6.5 on average, the sword does 7.0. This is not a big deal, but it bothers me more than it probably should.
Of course, when you add in the GWF style, the disparity grows quite a bit. Rerolling 1s and 2s, the axe does 7.33 hp, the sword does 8.33. That's equivalent to a full die step, and seems legitimately significant.
I've wondered about ways to fix this. Simplest would be to make the greataxe 2d6, but that is a little boring. I'm probably not the first person to realize that there is another option:
Give the greataxe the property that when you roll max damage, you get to roll again one time and add that to the total. So if you roll a 12, you end up doing 12+1d12.
If you work it out, that gives an average damage of 7.04 hp, almost exactly the same as the greatsword. With GWF it improves to 8.03, not exactly equivalent but much closer.
I like this, but I have a question: people tend to key in on the max damage, which increases dramatically in my scheme. Even though they are mathematically balanced, would this make the greataxe seem too good? When you read it, is your first reaction that you would always pick my greataxe over a greatsword?
One point: I would not normally apply this to monsters... their greataxes just wouldn't be quite as good.
Ok answers then comments...
I allow weapon reskinning as a matter of course so since the listed "weapons" are just stat-clusters we dont have an issue as the 1d12 vs 2d6 if seen as "an inferior or low quality" version (and notably cheaper at its 30g vs 50g price.) FYI we price mauls at 50 too if they are of the 2d6 quality, 30 if 1d12.
So the difference in 1d12 v 2d6 does not cause us any problem.
Would your new property make it so appealing to ditch the 2d6? Doubtful. The "lack" is seen as being tied to the unpredictability already and adding in a max roll swing adds more swing just rubs salt into that wound. For my plays crazy dice are just **not a plus**.
For me as a gm, adding new cool stuff that is hinged on dice not character is never going to be a direction i choose. Add new cool stuff that emphasizes or adds to character, choices, options - not the bouncey plastic bits.
If i were going to "fix" anything, i would take great axe stats, remove two-handed, add versatile with 1d10 base and 1d12 if used two handed. That give it a unique place... The HEAVY equivalent of longblade, battleaxe and warhammer with its own names.
So now we have..
Veratile d8/d10s in longblade, warhammer, battle axe cost 15g
Versatile Heavy at d10/d12 in the "Heavy Axe, sword, warhammer" cost 30g
Heavy two-hand at 2d6 in the maul, greatsword and "greataxe" cost 50.
So now we have got more options, more choices for the character to choose between and have removed the niggling math without empowering the die at all.
Of course, if i were going full overhaul, all one-weapons would be one die... And twf would be "weapon type" not bonus action eaters so twf would all be where you got two smaller dice damage from a single to hit roll.