If you tossed two dice with each showing a 6 on top and the result of the roll was two 1s (snake eyes ) then could calculate that if the two dice each showed a 5 that the end result would be two 2s.

Lets say you always toss with the two 6s showing and these are the results :
6  3 = 9
2  5 = 7
1  4 = 5
2  2 = 4
6  5 = 11
3  1 = 4

Using the above results, how would one recalculate the existing data to determine which 2 numbers should be showing instead of the two 6s that would have generated a result of 8 on one of the rolls?

Edited....
After posting it dawned on me that you can't really determine this based on the numbers on top of the dice as the numbers showing per each side would matter as well.

Two identical dice always display a bell curve probability of possible throw outcomes.

I'm just going to throw this out for beer and skittles.

Production dice are probably not perfect cubes.  If that is true, the side with the most area would likely land on the bottom more often than any other.

Also, the numbers are indented so the heaviest side would be "1" and the lightest "6".  So 6 would be up more than any other number.

If one were to make a set of dice where side 1 is also the largest and the pips were a bit more deeply drilled than usual those dice would show 6 more than normal, and 1 least often thereby skewing the results of multiple throws toward 12 and away from 2.

Is this right?

While the center of gravity of the die may be biased slightly toward the 1 side due to holes (and only really matters if the dots are drilled into the surface as opposed to printed), it is unlikely that this effect will be enough to be statistically noticeable.  It can also be countered by using a filler in the holes to counter the weight difference if desired.  Of more importance are imperfections in the actual shape of the die.  For example, corners that are more rounded around a single face will decrease the surface area of that face and make it less likely to end up on the bottom (not because of center of gravity, but because less energy is required to be available during the roll to tip it off of that face ).  Also, if the distance between two opposite faces is longer than the others, then those two faces will be less likely to end up on top (or bottom, since one being on the top will make the other the bottom).  This last property was used by cheaters, who would sand or shave faces to alter the distance between opposite sides, and is known as shaving the dice.

Mike

Craps players know it's all a matter of how you talk to the dice.

Actually, the surface the dice are rolled on with all it's imperfections are probably a lot more likely to affect the outcome than the miniscule imperfections and weight differences on the number faces.

And the holes are different depths to compensate for the varying number on each face.