Kevin Pacey wrote on Thu, Feb 2, 2017 09:33 AM UTC:
I'm up way too late, but I was thinking about the 'held' rule once again. It occurred to me that an interesting version (or possible extension) of it might be that a king is permanently confined (or 'held', in a way) to the 2D board (or alternatively, rank & file coordinates) upon which it is located (by defender's choice, as is indicated by his next king move) if and when it is 'bared'. That would allow for all sorts of basic mates (including K+Q vs.K for starters), or permit K+just 1 Pawn vs. K to win quite often, yet still allow for possible draws due to insufficient mating material. I thought of extending this to similarly permanently confining a king if its last pawn was captured (to allow e.g. K+Q+P vs.K+B to be an easy win, presumably), but that seemed too drastic, and might harm the chances of an otherwise superior side winning at times, e.g. with K+Q (no pawns) vs. K+P.
My idea of a Hexagonal version of Hyperchess4 is still looking problematical at the moment, but at least thinking about it led to my latest thoughts on the 'held' rule. [edit: It appears that on the 4D Hexagonal board I have in mind, there's no good setup that doesn't allow a knight to attack something way too fast.]
[edit: I corrected my value estimate for a bishop & a queen in Hyperchess4 (they were wrong due to math errors). I now have them as B=3.2 and Q=3.5. Note that a B's 'average' number of moves (14) is fairly close to a R's (always 12, regardless of its location on an empty 4D board), and I didn't wish to put a R below =3 (since it can cope at times with 3 passed pawns on an empty board in my 4*Chess variant, given its pawn movement rules). Unless I'm wrong, the minimum number of cells a queen can reach in Hyperchess4 is actually 18, so a Q can reach 20 cells if averaging min. & max. (as compared to a knight's 'average' 18 cells). Note a B (like a R, and the other piece types) seems usually unable to eventually win a single passed pawn on an empty board in Hyperchess4, if I understand how these move right. As is evident, I'm not making much of a numerical distinction between a minor piece and a major one with my estimated piece values for Hyperchess4, which might be justified in one abstract way by the preceding sentence. Also, more vitally perhaps, bear in mind that the only major piece in my 4*Chess variant is the Q, which has an average of about 65 moves on an empty board in that game (there I value it = 16, giving a king a fighting value = 10 with it reaching about 47 cells on average), compared to a Q's reaching 20 cells on average in Hyperchess4; this all might be something of a case of comparing apples to oranges, though.]
I'm up way too late, but I was thinking about the 'held' rule once again. It occurred to me that an interesting version (or possible extension) of it might be that a king is permanently confined (or 'held', in a way) to the 2D board (or alternatively, rank & file coordinates) upon which it is located (by defender's choice, as is indicated by his next king move) if and when it is 'bared'. That would allow for all sorts of basic mates (including K+Q vs.K for starters), or permit K+just 1 Pawn vs. K to win quite often, yet still allow for possible draws due to insufficient mating material. I thought of extending this to similarly permanently confining a king if its last pawn was captured (to allow e.g. K+Q+P vs.K+B to be an easy win, presumably), but that seemed too drastic, and might harm the chances of an otherwise superior side winning at times, e.g. with K+Q (no pawns) vs. K+P.
My idea of a Hexagonal version of Hyperchess4 is still looking problematical at the moment, but at least thinking about it led to my latest thoughts on the 'held' rule. [edit: It appears that on the 4D Hexagonal board I have in mind, there's no good setup that doesn't allow a knight to attack something way too fast.]
[edit: I corrected my value estimate for a bishop & a queen in Hyperchess4 (they were wrong due to math errors). I now have them as B=3.2 and Q=3.5. Note that a B's 'average' number of moves (14) is fairly close to a R's (always 12, regardless of its location on an empty 4D board), and I didn't wish to put a R below =3 (since it can cope at times with 3 passed pawns on an empty board in my 4*Chess variant, given its pawn movement rules). Unless I'm wrong, the minimum number of cells a queen can reach in Hyperchess4 is actually 18, so a Q can reach 20 cells if averaging min. & max. (as compared to a knight's 'average' 18 cells). Note a B (like a R, and the other piece types) seems usually unable to eventually win a single passed pawn on an empty board in Hyperchess4, if I understand how these move right. As is evident, I'm not making much of a numerical distinction between a minor piece and a major one with my estimated piece values for Hyperchess4, which might be justified in one abstract way by the preceding sentence. Also, more vitally perhaps, bear in mind that the only major piece in my 4*Chess variant is the Q, which has an average of about 65 moves on an empty board in that game (there I value it = 16, giving a king a fighting value = 10 with it reaching about 47 cells on average), compared to a Q's reaching 20 cells on average in Hyperchess4; this all might be something of a case of comparing apples to oranges, though.]