How do you calculate %xHKO?

Keep in mind that you do not need to calculate if , and max is the highest damage one could do with one attack.

But you still need to calculate the array somehow, and the best and most straightforward approach seems to be to perform the convolution on each P_n in succession. Binary convolution as you mentioned near the end of your pdf still ends up being quadratic because you're working with larger and larger intervals, so it wouldn't be a significant time saving.

Regarding defense, you could use another convolution with a negative interval for that and use that as your base interval.