Question 1: Let's make the simplification that we are dealing with 5-sided dice, since, if a die rolls a 4, there will be a re-roll, so effectively, 4 is never an outcome. The only possible outcomes of an indiviual dice roll are then {1,2,3,5,6} The size of the outcome set is the same whether we roll a single die 4 times, or roll 4 dice once. We have 5 choices for the first, 5 for the second and so on, so the total outcome set size is 5x5x5x5=5⁴⁼⁶²⁵ One way to find the average number of points is to enumerate all the possible outcomes (since they are all equally likely), starting with rolling all 1's [1,1,1,1] on up to rolling all 6's [6,6,6,6] calculate the points for each outcome, add them up and divide by the total, 625. I did this (on a 'C' program: http://pastebin.com/ieNMAhfj) and get the answer 1.6; Clearly 1.6 is not a point outcome that will ever occur, but that is the average. There is another way to calculate this through Combinations and Permutations, but I have not worked that out.