H. G. Muller wrote on Fri, Apr 28, 2023 08:02 AM UTC:
I was running out of ideas for adding other rook-class pieces. Leapers with 12 move targets can play that role, but I dislike having pieces that just add 4 moves to a piece that already participates. This is what you automatically get when you use an oblique atom in them, as these already have 8 moves, and the pure N, C and Z already participate. As an exeption I do allow the Omega-Chess Wizard (FC), because it is a well-known and popular piece, while the Omega-Chess Champion (WAD) is acceptable despite its overlap with WA and WD because the latter two in the variant I am contemplating would have the special ability to block flying captures, which makes them very different even from a normal piece that would move exactly the same. Since all combinations of pairs of W, F, D, A already do occur as minors, the non-inclusion requirement would limit sufficiently non-overlapping 12-target leapers to compounds that contain both G and H. This leads to unattractive and difficult-to-master move patterns.
But then it occurred to me that pieces can also be weakened by making them lame, rather than reducing the number of move targets. A lame 16-target leaper might have a value similar to a true 12-target leaper. And lame leaps are not counter-intuitive. (In fact every distant slider move is one, and we understand sliding.) In particular, the following pieces seem nice:
A (lame) Squirrel (nAnDnN, where the non-jumping N move is the multi-path Moo.
The nHnGnCnZ ('Snake'), where the nCnZ part is George Duke's multi-path Falcon.
The heuristic of the interactive Diagram guestimates Champion, Wizard, Cannon and Bishop on 18x18 around 500 (where the 8-target leapers and Vao are around 300), the Squirrel at 600, the Rook at 650, and the Snake and Dragon Horse (BW) around 750. For comparison, Queen is valued 1350, Marshall (RN) 1100, Griffon and Lion around 1200.
Thus this Squirrel and Snake fit well in the set of pieces that can be traded 2-1 for a super-piece (plus Pawn). Or together with a minor for one of the weaker super-pieces.
I was running out of ideas for adding other rook-class pieces. Leapers with 12 move targets can play that role, but I dislike having pieces that just add 4 moves to a piece that already participates. This is what you automatically get when you use an oblique atom in them, as these already have 8 moves, and the pure N, C and Z already participate. As an exeption I do allow the Omega-Chess Wizard (FC), because it is a well-known and popular piece, while the Omega-Chess Champion (WAD) is acceptable despite its overlap with WA and WD because the latter two in the variant I am contemplating would have the special ability to block flying captures, which makes them very different even from a normal piece that would move exactly the same. Since all combinations of pairs of W, F, D, A already do occur as minors, the non-inclusion requirement would limit sufficiently non-overlapping 12-target leapers to compounds that contain both G and H. This leads to unattractive and difficult-to-master move patterns.
But then it occurred to me that pieces can also be weakened by making them lame, rather than reducing the number of move targets. A lame 16-target leaper might have a value similar to a true 12-target leaper. And lame leaps are not counter-intuitive. (In fact every distant slider move is one, and we understand sliding.) In particular, the following pieces seem nice:
The heuristic of the interactive Diagram guestimates Champion, Wizard, Cannon and Bishop on 18x18 around 500 (where the 8-target leapers and Vao are around 300), the Squirrel at 600, the Rook at 650, and the Snake and Dragon Horse (BW) around 750. For comparison, Queen is valued 1350, Marshall (RN) 1100, Griffon and Lion around 1200.
Thus this Squirrel and Snake fit well in the set of pieces that can be traded 2-1 for a super-piece (plus Pawn). Or together with a minor for one of the weaker super-pieces.