I remember a retired engineer was selling perfectly balanced dice intended for RPG players. RPG players are going to gravitate toward the most unfair dice they perceive in their set. I appreciate his enthusiasm but he’s only going to sell those dice to competitions and maybe GMs.

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.

About the last point- I remember hearing somewhere, though it could be an urban legend, that that's precisely the reason early Dungeons & Dragons (OD&D/AD&D era) had so many variations within different dice roll mechanics for whether or not a high (or low) roll was good or bad (ie high rolls for your attack was good, high rolls for initiative were bad).

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

"20? Your axe cleaves straight through through the orc, decapitating him, and reducing the pillar behind him to rubble!"

"You should probably know that this was a load-bearing pillar."

You reminded me, and I think I have some, or at least some variety of these as a set of 10d6. Metal, and the pips are precisely machined to such depths where they're perfectly balanced. Nice bronzed finish, with black pips.

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.

Seems like the solution to that (from a cheater's perspective) would be to bias the dice toward the mid-range numbers, but I don't know enough about D20 layouts to know if that's feasible.