Dynamic Clustering - How many matches do you look for?

Right now Diamond's main gun uses max(1, min(225, numDataPoints / 9)). So it scales linearly from 1 at start of round 1 to 225 data points at about 2000 ticks (~3rd round). I've many times evolved these settings from scratch with genetic algorithms and gotten max-k values from 150 to 350 and divisor from 9 to 14 without much change in performance.

It's important to note that I (and I think most of us) also weight the data points by distance when doing kernel density to decide on an actual firing angle, which is why the actual choice of k (er, N in your post) doesn't matter so much.

Btw if you're spending a lot of time in the gun lab, you might like WaveSim.