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'Note that there are not only cells, where it can't move, but also cells, where it will be able to make only one leap further. And these are the whole second hyperrank.' You appear to have omitted the adjective qualifying each instance of 'cells', resulting in two mutually incompatible definitions of cell, both of them subsets of the usual meaning. This is a pity, because a specialist term in particular for a cell from which a piece has no further move would be very useful in whatever number of dimensions, and I would happily make use of such a term. Were you waiting to put the adjectives in until you had devised them, have you now devised them, and if so what are they?
Ben Reiniger wrote on Sun, Nov 27, 2011 05:50 PM UTC:The knight here has of course just two moves in its lifetime. Dropping a knight becomes a tricky subject (although I suppose in my few Shogi games I rarely want to drop a knight). I assume the proposed promotion zone is the last hyperrank? I think I would suggest different diagonal movement in this game. As many of the Shogi pieces see 'forward' differently than 'sideways', it is perhaps better to keep track of the two 'forwards' and the two 'sideways' directions in this 4D board. In particular, I think the moves from center square Bb2ii should probably not include Bb3iii, nor any of the extended diagonal forward&back like Bb1iii. I also think that there's a possibility that king restriction (beyond eliminating tri- and quad-ragonals) is unnecessary. This board is so compact that the dense moves of the generals, the enemy king, and especially an enemy dragon king or dragon horse could force mate. (In fact, if 3- and 4-diagonals were included, a dragon on the center square sees everywhere.) (And Charles, Daniil's sentence is fine with the omission of those commas and replacing 'which' by 'that' (a grammatical technicality not recognized by most). I think such cells will occur infrequently enough to not warrant a universal name; one needs a particularly asymmetric piece to have any such squares.)
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Another one mad idea. I see that it have a few defects, and it may contain other defects i didn't notice, and therefore i created subject to discuss it. Also, i'm afraid, this game may be unplayable at all, and it's just a funny time-waste. Inspiration if from Charles Gilman's 3D Switchback Xiang Qi. Consider 3x3x3x3 board. 3--- --- --- III 2--- --- --- 1--- --- --- 3--- --- --- II 2--- --- --- 1--- --- --- 3--- --- --- I 2--- --- --- 1--- --- --- abc abc abc A B C Lowercase letters to mark files, Arabic numerals for ranks, upercase letters for 'hyperfiles', Roman numerals for 'hyperranks'. To set pieces, look at this scheme as at 2-dimensional board and set pieces as in usual Shogi (and promotion zones are same), but rook must face rook, not bishop. If rook will face bishop, it will be able to capture it on first turn, and in this game rook is weaker. However, rook still can capture another rook (protected, of course), and other pieces can contact with opponent on very first turns, and it's the main defect that scares me. If you are familar with other 4D chess varinats, you probably already understood the way of movement of regular pieces. Here moves of piece 'x' are marked with 'o' if orthogonal and 'd' if diagonal: --- -d- --- -d- dod -d- --- -d- --- -d- dod -d- dod oxo dod -d- dod -d- --- -d- --- -d- dod -d- --- -d- --- There are no triagonal and quadrogonal moves. Question 'What are orthogonally-forward moves here?' is simple (there are two directions, and pawn can't be dropped if same rank AND hyperrank that contains another pawn, or simply rank, if you are watching board as 2-dimensional). Same question about diagonally-forward moves is more complicated. Consider diagonal step as two orthogonal steps. One possible solution is that these orthogonal steps must'nt be both sideways and neither may be 'backward-directed': --- -d- --- -d- dod -d- --- --- --- -d- dod -d- --- -x- --- --- --- --- --- --- --- --- --- --- --- --- --- Another solution is that at least one of these orthogonal steps must be 'forward-directed', it gives two more possible moves: --- -d- --- -d- dod -d- --- -d- --- -d- dod -d- --- -x- --- --- --- --- --- -d- --- --- --- --- --- --- --- In either case, silver general have more moves than gold general, and thus there is no point of promoting silver to gold. Perhaps, thier places in promotion hierarchy should be be swapped, and pawns, lances and horses should promote to silver as well. Horse's leaps are any two steps forward+any one step sideways: --- --- --- --- --- --- -h- h-h -h- --- --- --- --- --- --- --- --- --- -h- h-h -h- --- --- --- --- -x- --- Note that there are not only cells, where it can't move, but also cells, where it will be able to make only one leap further. And these are the whole second hyperrank. Another serious problem is too mobile king. Perhaps, it should be able to move only orthogonally. Or, maybe, replacing kings with two Shogi emperors, that are able to leap to any cells (but in practice, only to cells, protected by friendly pieces) will also help? Another, probably, the most efficient way out is to play it as 'Walkers and Jumpers': some pieces treats board as 2-dimensional. In this case, kings, rooks and bishops (thus, no need for mirror symmetry). Probably, pawns, knights and lances are best as being both 'Walkers' and 'Jumpers'.