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This other question asks if attuning to a Belt of Dwarvenkind grants the following benefit (and literally nothing else):

you have a 50 percent chance each day at dawn of growing a full beard if you're capable of growing one, or a visibly thicker beard if you already have one.

My question is about the latter part of that bonus (marked in bold). Say you attune to the belt and then wear it for a prolonged period of time. You never shave, so every other day (on average) your beard becomes "visibly thicker".

Are there any mechanics governing how this works? Like, is there a maximum attainable beard thickness? Could a player reasonably argue that their beard has become so thick and dense that it acts as natural armor and grants them an AC boost or damage resistance?

Would it eventually become an impediment, or even a hazard to the bearded character? For instance, does it become so dense that it's effectively solid and while possibly granting a defensive boost it also impedes movement and makes it difficult to breathe? Do the ever-thickening beard fibers ultimately become so dense that they form a singularity and the character dies? Or does it just do the boring thing, and fizzle out somewhere along the way?

This may all be GM fiat. However the rules as written seem to imply that the beard gets perceptibly thicker every other day without end. If you have a beard, it gets thicker. Each day at dawn (more or less).

If a player demands a strict interpretation, how far do (or can) you take it? What makes sense from a fairness standpoint if the player has gone to the effort of attuning an item just for this one particular benefit?

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    \$\begingroup\$ I rolled my eyes at this question at first, but I've upvoted it now because it raises a surprisingly legitimate point. And it's funny, which is always positive. \$\endgroup\$ – Gandalfmeansme Jul 23 '18 at 15:57
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    \$\begingroup\$ Can Moradin grow a beard so thick that even he can't groom it? \$\endgroup\$ – Pyrotechnical Jul 23 '18 at 17:08
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    \$\begingroup\$ @guildsbounty Careful with the image links. That album also contained images that RPG.se should not have links to. \$\endgroup\$ – SevenSidedDie Jul 25 '18 at 5:39
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    \$\begingroup\$ I would have thought the "if you already have one" would refer to beard before you attuned to the belt, and if your beard is thickened by the belt, it's just in relation to that. So, once it's thick, it's thick (idempotent). \$\endgroup\$ – David Conrad Jul 25 '18 at 23:08
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It's asymptotic.

There's a finite amount of mass available for the beard (based on how much the wearer eats, the weight their neck can support, etc.). Since the beard must continuously get thicker, it has to approach a limit, perhaps something like $$b(t) = b_{max}(1-e^{-t/\tau})$$

where t starts at the time one starts growing a beard (so, for a dwarf, at birth).

What's really interesting is that the beard must not just grow thicker, but grow visibly thicker. This implies that dwarves, at least, can perceive infinitesimal differences in beard thickness, which means they can actually see everyone's facial hair growing all the time. Science!

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    \$\begingroup\$ It's the most common form for a physical process where some quantity approaches a limit. \$\endgroup\$ – Mark Wells Jul 23 '18 at 17:27
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    \$\begingroup\$ While I would agree that it would have to be asymptotic (otherwise it would grow without bound and thus at some point surpass the mass of the rest of the universe combined) a convergent series would contradict the "visibly thicker" portion. At some point the incremental gain would simply not be visible. \$\endgroup\$ – nurdyguy Jul 23 '18 at 22:20
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    \$\begingroup\$ Not visible to you, maybe. Dwarves have darkvision; apparently they also have beardvision. \$\endgroup\$ – Mark Wells Jul 23 '18 at 23:18
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    \$\begingroup\$ Are beards not quantized in the D&D universe? \$\endgroup\$ – Acccumulation Jul 23 '18 at 23:25
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    \$\begingroup\$ If your magic items aren't willing to break their users neck by overweighting them with a collossal beard made out of matter produced from nothing, are they really magic items? \$\endgroup\$ – Yakk Jul 24 '18 at 19:25
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As you already guessed yourself, RAW this would be a GM fiat.

If I apply some kind of logic (and a bit of humor) in this magic item concept, the beard will grow as thick as the thickest dwarven beard in the multiverse because the Belt of Dwarvenkind should never betray its people giving a non-dwarf the thickest beard there is; Moradin wouldn't approve that.

In the case of a Dwarf user, the belt would elevate his beard to the glorious thickness of Moradin's beard; a great honor for every dwarf.

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Since man, dwarves, orcs and other various species are mortal, then the thickness of the beard will be limited by the lifetime of the creature. This circumvents the "infinitesimal beard visibility" paradox. It would follow that long-lived creatures could grow thicker beards than short-lived creatures, so very old dwarves, attuned to the belt, might have sea-otter-esque beards. This would be especially problematic for elves, but, IIRC elves are incapable of beard growth.

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    \$\begingroup\$ An elf with a belt of dwarvenkind isn’t incapable of beard growth. Nor are any variety of immortal creatures. This might side-step the issue for many expected wearers, but we can always find someone that still causes a problem. \$\endgroup\$ – KRyan Jul 25 '18 at 14:54
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Seems to me that the beard thickness must wane during the day. Perhaps beard thickness is related to testosterone levels that peak about 8am. Assume there is a maximum attainable bead. If morning beard growth is proportional to the remaining growth required to reach max beard. With a nightly decline proportional to the beard size at daily apogee, a regime of visible morning size change with maximum beard size converging to a limit. It is not just dwarves who have to perceive the change in beard thickness after all.

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