How do you calculate %xHKO?

The problem with your approach is that it's not dynamic at all. After three hits, that square looks horribly disfigured. And after 100 hits, even though it looks a lot like a bell curve, it's still not exactly a bell curve. It's just a square wearing the bell curve over itself and you'll still be able to see the corners, if only slightly. So your approach should be a shape that can transform with by using the x hits variable, not a static one.

As x goes towards infinity, the curve goes towards a bell curve. Therefore, shouri is correct by stating that after n hits, where n is a positive integer, one can use the bell curve for an approximation which will yield an approximation as good as needed. (I'll not go into epsilon delta, unless someone want me to do so)

That's what I thought was a good way of doing it, but I'm pretty confident that there's an exact way of calculating this in less than O(log N) time.

Noah