[RPG] maximum attainable beard thickness


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?

Best Answer

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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