Dice Roll Probabilities for Board Games Using 2d6
In many board games two six-sided dice (d6) numbered 1-6 are rolled, with the values added. This yields a result ranging from 2-12. Since there's only one way to get a 2 (two ones) or a 12 (two sixes), those are the least common results. There are two ways to get a 3 (a one and a two, or a two and a one), two ways to get an 11, etc. This results in a center-peaked distribution of possible results, as shown by the green histogram below.
When you think about it, 2-12 isn't a very natural range of numbers for moving a game piece, or whatever the result is used for in a particular game. A more natural range would be 1-10. MathArtFun's special red d6, when rolled along with a standard d6, yields a center-peaked distribution ranging from 1-10, as shown by the red histogram.
Another way to give an old game new life would be to punch up the possible results by increasing the range a bit in each direction. MathArtFun's special blue d6, when rolled along with a standard d6, yields a center-peaked distribution ranging from 1-13, as shown by the blue histogram.