Can you count numbers on a $6\times 6$ grid to calculate the probability one pair of dice when rolled has a sum greater than another fair pair of dice?
You can calculate the number of grid spots for every place on the grid where the spot's sum exceeds that of the selected grid value and count that number and divide by $6^4$, but is that the probability one pair of dice exceeds another identical pair of dice?
I know the sample space is $6^4$
if the first roll is a (1,1) the number of spots on a 6x6 greater than that is 35/36.
If the first roll is a (1,2), the number of spots on a 6x6 grid greater than (1,2) is 33/36.
Continue until you hit 36 spots and summed the corresponding spots with a sum greater than that
I imagine this probability is (35+33+...)/6^4