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.

  • Adding the moves would make more sense than subtracting them. – yobamamama Dec 27 '19 at 16:56

Sorry for the late answer, but here’s “my” suggestion of a total mobility 215 in a legal configuration. White has 216 total moves, minus away one for Black’s only legal move for total.

[FEN "1Q5R/4Q1K1/B1Q5/B4Q2/N2Q4/pQ4Q1/pn2Q3/krQ4R w - - 0 1"]

This position was originally created by William Shinkman as the record for the most mates in two. This position’s mobility will be very hard to beat, as it has no checkmate/stalemates in one, in addition to how the known maximum for any move is 218 contains so many checkmating/stalemating move that it won’t work here.

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