Under what conditions are the LEGO boardgame dice unfair, and by how much?
Conditions for unfairness:


Different shaped tiles applied to each side resulting in different weight wich maked the dice "biased."


Example:

The maximum difference in weight (when all studs get covered) is one side using a 2x2 tile, and another side is using 4 1x1 tiles. the weight difference in this case is calculated based on using these measurements. To show the difference:

X X X X X X X X X X
X       . .       X
X       . .       X
X       . .       X
X . . . . . . . . X
X . . . . . . . . X
X       . .       X
X       . .       X
X       . .       X
X X X X X X X X X X


X = borders
. = border from the 1x1 tiles that are missing using a 2x2 tile

So there are ~ 28 legounits³ = 44.8 mm³ difference in material used. ABS, the material used for LEGO bricks has a density of between 1.04 and 1.12 g/cm³ so 44.8 mm³ have a maximum height of:

1.12g/cm³ / 1000mm³ * 44.8mm³ = 0.050176g


0.05 g would be way too much for a precision-dice used in a casino, but for a "toy" it's almost nothing (it's less than 1% of the die's total weight - I'd like to calculate that, but I can't find information about its weight), so I won't expect anyone to notice the LEGO-dice is "unfair".

EDIT:
Found the dice on bricklink. weight: 8.02 g, so the 0.05 g are just ~ 0.6 % of the total weight.