I guess if this really matters, you could come up with some set-up rules to swap some 3s with 11s, 4s with 10s, etc, so that biases towards 1-2-3 are less impactful. But that would be painstaking and annoying. I absolutely wouldn't care to do that, unless we track ELO and have an evenly matched group, which is a bit absurd in a casual game. And as in any strategy game FFA, everyone will still gang up against the current leader (even with imperfect information).
I think that’s one of the reasons GMs sometimes make a high roll from the player into a punishment. Especially by asking for the roll first and telling what they were looking for after. It’s a way to balance out the consequences of unintentionally loaded dice.
If the player used the same dice for all rolls, a balance check against biased or loaded die was therefore built directly into the game, with the perk of making it very obvious if a player was using specific dice for specific rolls
"You should probably know that this was a load-bearing pillar."
Also, if someone is obviously cheating with a loaded die at an RPG game, they're not the kind of player that should be invited back. Most characters have ways of increasing their modifiers to rolls that matter most to them (My current ranger is 1d20 +16 for Perception), and having high-enough base numbers can mean that anything other than a natural 1 is usually some kind of success.
- How dense is the wood?
- How much wood does each pip remove?
- How much water does the wood absorb per unit of volume?
- Are any capillary effects at play transferring absorbed water into the rest of the die?
- Is it better to soak the 6 side to take advantage of more surface area? Or the 1 side to take advantage of more soakable volume?
- Is the wood even uniformly dense to begin with?
A naïvely constructed die - i.e. a perfect cube, but with pips dug out for each face - will already bias in favor of 6 rolls and away from 1 rolls simply because six pips require removing more material (and therefore mass) than one pip. Likewise with 5/2 and 4/3. The "precision" dice used in e.g. casinos address this by filling in the pips with material exactly as dense as the die's base material; the injection-molded dice in most board games (let alone wooden dice) obviously ain't constructed with that level of care.
This is also part of the reason why some dice games - particularly those typically played with cheap dice - deem 1 to be more valuable than 6 (example: Farkle) or require at least one 1 roll to win (example: 1-4-24). Or they'll require some number of high dice to make the game ever-so-slightly less brutal (example: Ship-Captain-Crew).