You should not be rolling the dice together to check for balance. It is the DIE itself that is important. How it rolls without the risk of being influenced by another die is the true test. Let us see the 1000 single rolls and determine balance from there
Yep. When you add two independent random variables the output distribution is the convolution of the individual distributions. In semi-English that means one die's distribution will average/smear/blur out the other die's distribution. (To be clear this isn't anything to do with the physical dice hitting each other or anything, this is just the fundamental mathematics of how random variables add and is true even if you roll the dice separately from each other and then add their values). If all we care about is the sum of the two dice that's not a big deal, but in ASL where we do things like ROF, cowering and so forth we should care about each die's distribution separately.
As an example of this, a pair of MMP dice I just tested to 1000 rolls had the following CHITEST results:
Red - 76%
White - 1%
Sum - 92%
The numbers here mean the probability that the measured values came from the expected ("fair") distribution. So the Red die is very likely "fair", while the White die is almost certainly not fair (to a 99% confidence in this case) and turns up 2 and 5 more frequently than it should. The White die in this case is also measurably misshapen with a much shorter physical dimension from the 2 face to the 5 face (0.465") compared to the other two pairs of faces (0.475" and 0.476") making it more likely to tip over onto the wider 2 and 5 faces. So physical measurements imply the measured "unfair" distribution. Note also that since a six sided die always has opposite sides sum to 7 that this kind of "unfairness" or "imbalance" doesn't actually affect the average of all the rolls which still ends up very close to 3.5 as expected.
The result "Sum" is treating the dice together, that is adding the Red and White values together for each roll (they were rolled together in testing) like one would for using the IFT. The "Sum" distribution is actually quite "fair" despite the fact that one if its components (the White die) is pretty distinctly "not fair". In fact the sum is even more likely to be "fair" than either of its constituents.
So anyway, keep track of each die separately when testing as it makes a very significant difference in detecting any imbalance. And the related take away is that if there is an unbalanced die around it is actually not very likely to make a difference for IFT, TH, TK, TC, MC rolls since summing two dice smooths out imbalance. The impact is going to be more significant for things like ROF, smoke grenades and such that are based on a single die.
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