How to determine the base weapon damage for weapons that exceed the size table (specifically the exceptional case of Butchering Axe)?

Question

So I am playing a barbarian wielding a Butchering Axe. Last night it happened that by some glory magic my human (medium sized) barbarian was being enlarged letting his terrifying weapon become even more devastating.

So we checked the rulebook for what its new base damage would be. But unfortunately, the table ends at medium sized 2d6 becoming 3d6.

But since the Butchering Axe at medium size has already a weapon damage of 3d6, we tried to make out the pattern of the table which at that point was ambiguous (for us at least) we thought it either might be 4d6 following the increase from 2d6 to 3d6, or it might be 3d10 due to the steps at lower base damage weapons.

So the question is:

What is the weapons damage to be rolled here and by which pattern would this be identified for weapons exceeding the books printed table?

Please take note that this is a specific case, that differs from the duplicate, as the comments in the accepted answer mention the Butchering Axe differs from the usual determination, but don't mention in how far this is different. Hence that other post does NOT answer it for the specific case of Butchering Axe.

Answer 1

A large butchering axe is one size larger than a medium butchering axe. That means you use the following clause from the relevant FAQ:

• If the size increases by one step, look up the original damage on the chart and increase the damage by two steps. If the initial size is Small or lower (or is treated as Small or lower) or the initial damage is 1d6 or less, instead increase the damage by one step.

So, looking at the chart:

...
3d6
3d8
4d6
...

We count from 3d6 to 3d8 and that's one step, then we count from 2d8 to 4d6 and that's two steps. The FAQ says we should make it two steps bigger, so that's the number we should have.

But wait! We saw some random people arguing in the comment section and now we are worried! Is the Butcher's Axe an exception to this rule?

No. It is not. Moreover, even if it were, the exception would not apply to your case. Lets first deal with that second part. The comments you refer to say:

I'd just like to point out that the Small versions of the chainsaw and butchering axe contradict the FAQ on this point. – SuperJedi224 Apr 26 '18 at 23:25

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@SuperJedi224 I just looked at both weapons and fail to see an issue with the chart. Could you explain what the issue is? Take the chainsaw, its 3d6 when medium and goes to 1d12 (which the chart would concert to 2d6). Thats two steps lower, which is both because medium and higher than 1d8. Same applies to the axe. – Fering Apr 27 '18 at 1:44

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"If the initial size is Medium or lower (or is treated as Medium or lower) or the initial damage is 1d8 or less, instead decrease the damage by one step." Technically, this means a Small butchering axe should be 2d8. – SuperJedi224 Apr 27 '18 at 1:45

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Then the designers decided to have a weird weapon that does not conform to the chart. – Fering Apr 27 '18 at 2:08

Note that these comments are only discussing whether shrinking a Medium butcher's axe follows the chart. No one is saying anything is unusual in increasing a Medium butcher's axe-- in fact that that is normal is explicitly discussed.

Lastly, even inasmuch as a small butchering axe is weird, it is still not an exception to this FAQ. The comments point out the FAQ is contradicting printed text here for these two weapons' damage when made for small creatures, but that is merely notable in that it doesn't do so more most weapons. The FAQ often-- indeed almost always-- contradicts published text. It is a vehicle by which the designers change the rules, and has higher precedence than printed rules. So, even though a small butchering axe says it does 1d12 damage, the FAQ changed that to 2d8 (which is an increase of 2.5 damage on average). So even if you were trying to do the thing that's weird, the FAQ wouldn't steer you wrong there. The only thing that changes Pathfinder's FAQs are newer FAQs, and there aren't any that affect this topic.

Answer 2

The butchering axe is an exception from the rules only when we consider reducing damage dice (hereafter DD), since reducing DD for a Medium to Small weapon transformation should be done by 1 step, not two. But when increasing DD for Butchering Axe, all rules from FAQ (https://paizo.com/paizo/faq/v5748nruor1fm#v5748eaic9t3f) should come in effect. To be exact, DD of the Butchering Axe at larger sizes should be:
Large: 3d6
Huge: 4d6
Gargantuan: 6d6
Colossal: 8d6
Colossal +1: 12d6
etc.
Colossal +n DD should be double of Colossal +[n-2] DD.