A doubt strucked me.
The 1, 2, 3, 4 squares range is a absolute value (no matter the size of
the board) or a n/2 range (where n=8)?
Looks silly to ask that, but, in a 8x8 board the piece crosses 1/2 board
in a move, but in a 12x12 it just crosses 1/3, while a n/2 piece would
still crossing 1/2 board.
In a rectangular board the things could be worse, after all wich number
should be used to get the number of squres crossed, or in a odd shaped
one?
Well, regarding the 1st question I don't really know an answer.
About the 2nd, the lowest number should be used in the equation (round
down), and in a odd shape is a case by base situation, but, as a rule of
thumb treat the board as square or rectangular (which fits best) and do
the math.