[Anthony]

I'm confused by the exploding mechanism; I would expect a second explosion to be 1d+6 (minimum 9).

For the simple exploding die with a minimum value of 3, the average value A is equal to (3 + 3 + 3 + 4 + 5 + (A+3))/6, or 3.5 + A/6, or 5/6A = 3.5, or A = 4.2. As the first die does not have a minimum of 1, its actual average is (1 + 2 + 3 + 4 + 5 + (A+3))/6, or 3 + A/6, or 3.7.

If exploding dice go up by 6 instead of 3, A becomes 4.8 and the final average is 3.8