You calculated the probability that a randomly-placed piece will threaten
at least one enemy piece. I suggested you could instead calculate the
average number of enemy pieces it threatens, which is a different number,
because sometimes it will threaten multiple enemy pieces at once.
If a King has probability p of threatening a piece in any one of its 8
directions of movement, then the average number of pieces it threatens is
simply 8*p, whereas the probability that it threatens at least one piece is
1 - (1-p)^8.
