Under what conditions are the LEGO boardgame dice unfair, and by how much? For LEGO's board game line, they have moulded a LEGO die, with a 2x2 stud pattern on each side.



Obviously, weight distribution is going to be thrown off if you use a full studless plate on one side and four 1x1 studless plates on another because of the kerf.

Experimentally (by constructing different dice and rolling hundreds of times) or analytically (by analyzing the weight distribution of different plate configurations), how unfair can this die be assuming all studs are covered by a studless plate? What can be done to minimize the unfairness?
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.