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Check out Janggi (Korean Chess), our featured variant for December, 2024.
Check out Janggi (Korean Chess), our featured variant for December, 2024.
I don't believe the relative importance of captures andnon-captures for the piece value has much to do with the ratio empty squares - occupied squares. Both have a factor 2, but in opposite directions: there are only half as much capture targets, yet the captures are twice as important. Furthermore, tests of end-game values, on a much emptier board, usually give very similar conclusions as for opening values, for 'normal' pieces. (Pieces where the moves depend on 'spectator pieces', such as Pao / Vao,or lame leapers are exceptions.) I guess that even when there is ot much to capture, capture moves represent much of the value of the piece, as they can be used to cast a mate net around the enemy King.
The value of a piece in Chess is much dominated by its end-game value anyway, as sooner or later the board will get empty. This would be very different in games with drops, such as Shogi or Crazyhouse. There the pieces tend to relocate by drops much more than by board moves, so that differences in (non-capture) mobility are much less important.
Most of my piecevalue determinations were done on 8x8 or 10x8 boards, and even from that it seemed the size of the board can have a significant effect on the value of sliders versus leapers. E.g.on 8x8 a lone Bishop or Knight are approximately equal, but on 10x8 the Bishop was half a Pawn stronger. (Wide boards favor diagonal sliders, as the chance that both their forward moves hit the enemy gets larger.In Cylinder Chess the difference etween Bishop and Rook is even smaller than on 10x8.) The latest version of Fairy-Max can handle boards up to 14x12, but I have not used that in systematic piece-value testing yet.