Maths problem: fatigue vs critical hits

[Pehmyt]

I don't know if you are still interested in this, but I was, as it says "maths problem" in the title For future reference, if nothing else, the actual probability distributions for 1d6oe and 2d6oe (=DRN in the manual) are:


and for the original question,

In all expressions X=5n+r, with 1<=r<=5 (note limits!).

The first one is more or less trivial, the second is proven by induction in n and the third follows from that by straightforward summation.