I consider the mobility score of a board to be the number of legal moves one player could make less the number of legal moves the other player could make.
8/7k/2Q2K2/8/6b1/8/8/8 w - - 0 1
Using the board above, white king has 3 legal moves, white bishop has 9 legal moves, black king has 4 legal moves, and black queen has 11 legal moves. According to white, the mobility score of this board is
(3 + 9) - (4 + 11) = 12 - 15 = -3.
What is the maximum mobility score possible of a board which is not a terminal case (checkmate, stalemate, draw) keeping consideration for a legal number of pieces (ie. maximum of 9 queens, 2 rooks, 2 bishops, 2 knights, 1 king of each color)?
I don't really care if the board configuration is impossible to get to (it's probably possible to have 9 queens on the board and not be a checkmate/stalemate, but not possible to get to that state without a checkmate/stalemate), I only care that the configuration is legal.
I've written a chess engine which uses a heuristic which considers the mobility score of a board. I want to know the maximum possible mobility score so I can better define the value of a checkmate, check, etc. There's no point in setting a checkmate to, say, 200, if the mobility score of a board can exceed this, yet I don't want to define a checkmate as an arbitrary number: it need only be the highest mobility score plus one.