H. G. Muller wrote on Sun, Jul 23, 2017 09:14 AM UTC:
I have a conceptual problem with 'power density'. Piece values are relative to other pieces appearing in the same game. They cannot be equated to the value of the same piece in a different game, in particular not on a board of different size or different piece density, as large boards increase the value of sliders w.r.t. that of leapers.
Often values are expressed in terms of Pawns, but this is actually the least suitable piece to be used as reference. Because its value is near zero, very much dependent on positional aspects (Pawn structure: passers, edge Pawns, doubled Pawns, isolated Pawns, backward Pawns), and possibly for a large part determined by promotion anticipation rather than tactical ability. Queen or Knight would be much better standards.
I suppose it would be fair to use a leaper as a standard, when calculating power density. That means slider values go up with board size, but probably only linearly. So two Queens on a 16x16 board might produce the same power density as a single Queen on 8x8.
I still have a bit of an uneasy feeling about this. Would the Q/N ratio really double on a 16x16 board? If the initial population density of the board is ~50%, it hardly matters in the middle-game how large the board is, as most pieces would never hit the edges because of the obstruction they suffer. And in the late end-game, it doesn't seem to be any easier for a Queen to break down a fortress formed by 3 Knights just because the board is larger. Perhaps the advantage must come from the enhanced probability the Knights are spread out so much that they never get the chance to build such a fortress.
I have a conceptual problem with 'power density'. Piece values are relative to other pieces appearing in the same game. They cannot be equated to the value of the same piece in a different game, in particular not on a board of different size or different piece density, as large boards increase the value of sliders w.r.t. that of leapers.
Often values are expressed in terms of Pawns, but this is actually the least suitable piece to be used as reference. Because its value is near zero, very much dependent on positional aspects (Pawn structure: passers, edge Pawns, doubled Pawns, isolated Pawns, backward Pawns), and possibly for a large part determined by promotion anticipation rather than tactical ability. Queen or Knight would be much better standards.
I suppose it would be fair to use a leaper as a standard, when calculating power density. That means slider values go up with board size, but probably only linearly. So two Queens on a 16x16 board might produce the same power density as a single Queen on 8x8.
I still have a bit of an uneasy feeling about this. Would the Q/N ratio really double on a 16x16 board? If the initial population density of the board is ~50%, it hardly matters in the middle-game how large the board is, as most pieces would never hit the edges because of the obstruction they suffer. And in the late end-game, it doesn't seem to be any easier for a Queen to break down a fortress formed by 3 Knights just because the board is larger. Perhaps the advantage must come from the enhanced probability the Knights are spread out so much that they never get the chance to build such a fortress.