Maths problem: fatigue vs critical hits

[lch]

Endoperez said:
What is the probability of getting a number of X or higher with 2 DRNs?

I quickly came up with the formula for one DRN, then noticed that you wrote 2 DRNs.

When one applies basic calculus regarding geometric series to the probabilities you already gave, the result is:

Let X = 6a + b, 0 <= b < 6. Then the probability that a DRN gives X or higher on a roll is (7-b)(1/6)^(a+1).

Now with two dice, I'm not sure but I think it goes like this: You want a combination of two rolls that add up to X, so X = Y+(X-Y) and 0 < Y < X. Your probability is given as follows: For every Y from 1 to X-1, multiply P(Y) and P(X-Y) as given above. Add all of them together, divide by X-1. That's your probability for two rolls. You can simplify it into a closed form, which could be kinda tricky because of the modulo representation for Y and X-Y. Maple helps.