Kevin Pacey wrote on Wed, Feb 1, 2017 08:33 PM UTC:
Regarding piece values for Hyperchess4, the rook & knight move the same way as in my 4*Chess game, where I gave R=3 and N=3.4. For now I'll give P=1, still (though they move very differently in the two games). In Hyperchess4 after my own calculations I'd tentatively estimate a K's fighting value=2, with B=3.2 and Q=3.5. An abstract way I can try to justify have a Q ranked slightly more than a N is that a Q moves to slightly more cells on average on an empty board, with a Q's relative long-range movement capability, on such a 4D board, roughly offsetting the N's leaping ability.
[edit: If I understand Pawn movement rules correctly, upon further reflection it's plain a P is worth more than 1 in Hyperchess4, if, say, a R=3 as I estimate. It's not yet clear to me how to evaluate fairly closely what a P is worth in this game, except it seems a R can normally (at best) only keep a single passed pawn from promoting on an empty board, and is never able to win it (the side with the P could try to repeat the position, eventually, if no other pieces are ever in the picture). So, for now I'd guess a P would be worth between 1 and 3 pawns, with a rook still being worth more due to its greater mobility, in my eyes. Perhaps P=1.5 would not be too bad an estimate, unlike my initial P=1 assumption.]
At the moment I'm playing around with the idea of a Hexagonal version of Hyperchess4. It might never be at all popular, but maybe someone could later make use of the board diagram for it if I ever made a preset for such a game. One thing that's difficult is deciding on the pawn rules, assuming such a variant could ever be feasible.
Regarding piece values for Hyperchess4, the rook & knight move the same way as in my 4*Chess game, where I gave R=3 and N=3.4. For now I'll give P=1, still (though they move very differently in the two games). In Hyperchess4 after my own calculations I'd tentatively estimate a K's fighting value=2, with B=3.2 and Q=3.5. An abstract way I can try to justify have a Q ranked slightly more than a N is that a Q moves to slightly more cells on average on an empty board, with a Q's relative long-range movement capability, on such a 4D board, roughly offsetting the N's leaping ability.
[edit: If I understand Pawn movement rules correctly, upon further reflection it's plain a P is worth more than 1 in Hyperchess4, if, say, a R=3 as I estimate. It's not yet clear to me how to evaluate fairly closely what a P is worth in this game, except it seems a R can normally (at best) only keep a single passed pawn from promoting on an empty board, and is never able to win it (the side with the P could try to repeat the position, eventually, if no other pieces are ever in the picture). So, for now I'd guess a P would be worth between 1 and 3 pawns, with a rook still being worth more due to its greater mobility, in my eyes. Perhaps P=1.5 would not be too bad an estimate, unlike my initial P=1 assumption.]At the moment I'm playing around with the idea of a Hexagonal version of Hyperchess4. It might never be at all popular, but maybe someone could later make use of the board diagram for it if I ever made a preset for such a game. One thing that's difficult is deciding on the pawn rules, assuming such a variant could ever be feasible.