Thad:  And will our maths experts please tell me the new average # of backgammon pips per roll if one die has been changed from a 2 to a 5; and if both dies have been changed from 2's to 5's?  I haven't had enough of my morning coffee to contemplate the new permutations.

As we know, the average for a normal pair at backgammon is 8 1/6...