'First off, it is quite interesting to instead of picking a magic number
as
the chance of a square being empty, calculate the value for everything
between 32 pieces on the board and 3 pieces on the board. Currently I'm
then just averaging all the numbers,'
I've done that, too. The problem is, if the only reason you accept the
results is because they are similar to the results given by the
magic number, then the results have no special validity, they mean
nothing more than the magic results. So why add the extra computational
burden?
If, on the other hand, you had a sound and convincing theory of why
averaging the results was correct, that would be a different story.
'This concept seems to be directly related to distance.' Actually, I
think
I'd call it 'speed'. I'm pretty sure that I've played with those numbers
but gave up because I couldn't figure out what to do with them.
Maybe you can; I encourage you to try.