# Super4*Chess (four dimensional chess)

## Introduction

Here's a 4D game I call Super4*Chess that can be played as if on a 2D plane (it uses sixteen 4x4 (2D) mini-boards). A 16x16 board with appropriate spacing could be used even on a coffee table; it would be about the size of a Scrabble board (it's 15x15 for that). Because it is not so easy to checkmate a K in many 3D or 4D chess variants (maybe including my earlier 4D variant 4*Chess), besides standard 4D pieces, in Super4*Chess I've used 6 new powerful types of Super4*Chess pieces (in fairy chess-speak, all [but 1] are compound pieces that are crowned, i.e. all have movement capability of a K included). All this is with the hope of making the game still viable to play & enjoy. Note that some links are provided in the Notes section, for further reference.

## Setup

## Pieces

In Super4*Chess, some 3D & 4D moving pieces are introduced, & all the pieces may possibly move between the mini-boards when performing a move (note that 'coordinate' in these instructions refers to the rank or file of a square on a mini-board, or refers to the row or column of a mini-board). Note that 8 piece types are borrowed from my earlier 4*Chess (a four dimensional chess variant), while a further 6 specifically Super4*Chess piece types are added, for a total of 14 piece types that are used in Super4*Chess: D=4*Chess Balloon (I'd nickname it Dirigible) - moves like a bishop except changes 4 coordinates as it moves & stays on same square colour (standard 4D fairy chess piece); U=4*Chess Unicorn - moves like a bishop except changes 3 coordinates as it moves (standard 3D fairy chess piece); B=4*Chess Bishop - changes 2 coordinates as it moves, like a bishop (& stays on same coloured squares); R=4*Chess Rook - changes 1 coordinate as it moves, like a rook; Q=4*Chess Queen - moves like a 4*Chess B or 4*Chess R, or a 4*Chess U, or a 4*Chess D; K=4*Chess King - moves like a 4*Chess Q, only 1 square/mini-board at a time (no castling); N=4*Chess Knight (nicknamed Horse) - changes 1 coordinate by 1 square and 1 coordinate by 2 squares, like a knight; T=Super4*Chess Pilot - can move like a 4*Chess D or a 4*Chess K; H=Super4*Chess Shaman - can move like a 4*Chess U or a 4*Chess K; M=Super4*Chess Missionary (based on a piece from Shogi [promoted Bishop, or 'Horse', in that game]) - can move like a 4*Chess B or a 4*Chess K; S=Super4*Chess Sailor (based on a piece from Shogi [promoted Rook, or 'Dragon', in that game]) - can move like a 4*Chess R or a 4*Chess K; J=Super4*Chess Judge (based on a fairy chess piece [Centaur]) - can move like a 4*Chess N or a 4*Chess K; X=Super4*Chess Mann (based on a fairy chess piece [Mann]) - moves like a 4*Chess K; P=4*Chess Pawn - moves like a 4*Chess R (unless capturing) except only moves forward 1 square at a time on a rank, or forward by 1 column or 1 row to another mini-board (but moves to same rank & file there). If it is making a capture it moves like a 4*Chess B, except only moves by 1 square, or by 1 mini-board that's adjacent diagonally or by 1 row or by 1 column, & never retreats by rank or mini-board (i.e. by row or column). 4*Chess P promotions occur on the last rank of the corner mini-board where the enemy 4*Chess K starts the game, & a 4*Chess P may promote to any piece type above (other than 4*Chess K). There is no double step or en passant, & it is possible for a 4*Chess P to early on avoid being captured by an enemy 4*Chess P simply by moving to the last rank of a mini-board (except for the appropriate promotion mini-board).

## Rules

Stalemate is a draw, as in standard chess.

## Notes

An implication of the above is that the following pieces have certain max. number of directions that they can move along in making a move: 4*Chess R: 8 directions max. (including the 4 if it stays on the same mini-board as it starts) 4*Chess D: 16 directions max. 4*Chess B: 24 directions max. (including the 4 if it stays on the same mini-board as it starts) 4*Chess U: 32 directions max. 4*Chess Q (or 4*Chess K): 80 directions max. (the sum of the above pieces' max. directions) 4*Chess N: 8 plus 8 plus 4x4 plus 4x4 = 48 directions max. in theory, but less than that since the mini-boards (& the number of them) are not large enough to ever allow it (actual max. = 24). An example legal first move in Super4*Chess would be to move White's 4*Chess P in front of his 4*Chess K one square forward (staying in the same mini-board). Then, Black could reply the same way. These first moves can be written in Super4*Chess notation as 1. Paa12-aa13 Pdd43-dd42 if a game were to be recorded. Thus, all 4 coordinates (Column, then file, Row & rank) are given for where a Super4*Chess piece or 4*Chess P starts & finishes its move. If a 4*Chess P promotes, this is recorded by tacking on the letter of the 4*Chess piece type selected after the promotion square's 4 coordinates. Similarly, a capture, check or mate can be indicated as in standard chess notation. Beyond easily checkmating a lone 4*Chess K with just a 4*Chess Q, I've imagined checkmates of a lone 4*Chess K with other 4*Chess pieces (excluding 4*Chess Ps or new pieces specific just to Super4*Chess), though these might not be even close to being generally forcible 'basic' mates if the starting point is not totally favourable (i.e. beyond mate in 1 move being available). Notwithstanding that, I conceived of possible mates in 1 move using any 4 such other 4*Chess pieces, but with at least 2 of them not being 4*Chess Ds. Exceptional cases requiring less than 4 such 4*Chess pieces where mate in 1 is possible that I've found include having a 4*Chess R plus 2 4*Chess Bs, or plus 2 4*Chess Us or plus 2 4*Chess Ns (or plus a 4*Chess B & a 4*Chess U), (or plus a 4*Chess N & a 4*Chess U), (or plus a 4*Chess N & a 4*Chess B). Mate in 1 with 3 4*Chess Rs is also possible. Five 4*Chess Ds plus 1 of any other type of 4*Chess piece may make a mate in 1 possible, too. I've also conceived of possible checkmate positions with exactly 8 4*Chess Ds (the number one starts the game with). In all these cases of mate in 1 (i.e. excluding a 4*Chess Q or a 4*Chess P[or any piece specific to Super4*Chess]), the lone 4*Chess K was in an extreme corner square, with the opposing 4*Chess K very close. I'd guess the relative values of the Super4*Chess pieces to be about as follows: 4*Chess P (for within Super4*Chess, this piece for example could be called a Super4*Chess P instead, if one prefers) = 1 4*Chess D = 1.2 4*Chess R = 3 4*Chess B = 3.4 4*Chess U = 3.4 4*Chess N = 3.4 Just as a chess Q = R+B+P in value, 4*Chess Q tentatively = ((4*Chess R + 4*Chess B + 4*Chess P) + 4*Chess D + 4*Chess P) + 4*Chess U + 4*Chess P = 14, but actually I penalized a 4*Chess D by two pawns worth for its additional forms of binding, so I think the value of a 4*Chess Q = 14 + 2 = 16. A chess K has a fighting value of 4 (even though it cannot be exchanged); this value in my view might be rather oddly expressed (for lack of a known formula) as chess K = 32 x (max. # cells chess K moves to [eight]) divided by (# of cells on a chess board [sixty-four]) = 4, and similarly, the fighting value of a 4*Chess K = 32 x (max. # cells 4*Chess K moves to [eighty]) divided by (# of cells in 4*Chess [two hundred and fifty-six]) = 10, which seems in the right ballpark, given a 4*Chess K's great influence in mid-board. I'd say a Super4*Chess X = 10 roughly (since it moves like a K as well). Here are my estimates for the remaining pieces: Super4*Chess S = 11.9; Super4*Chess T = 12.1; Super4*Chess M = 12.3; Super4*Chess H = 12.3; Super4*Chess J = 14.4 (just as Q=R+B+P in value, J=N+K+P in value). How would I try to assess the strengths & weaknesses of this 4D variant? In attempting to invent a number of 4D variants, I came up with 9 equally weighted (sometimes slightly conflicting) criteria, to try to compare these variant ideas with each other: 1. Low total number of piece types (the game is perhaps barely OK on this); 2. Low total number of pieces in the setup (the game scores well); 3. The pieces (other than pawns) are "natural" or "pure" to 4D Chess (no, not the Mann-like ones); 4. Good rules (& setup) for pawns (I like them; there's no ideal solution); 5. Some chance of early mate or relatively short game (scores well); 6. Variety of viable exchanges of differing piece combinations (excellent); 7. Variety of "major" and "minor" pieces (excellent); 8. K can legally attack opposing pieces/pawns (good score, but powerful K); 9. Pieces (especially N-like) may obtain great scope (a 5x5x5x5 board would be better); Fwiw, in scoring Super4*Chess with these 9 criteria, giving a score of 0-4 for each, I found it had a total score of 21/36 (or a little over 58%), the same as for my earlier 4D variant, 4*Chess. To break the tie, IMHO Super4*Chess did just slightly better in satisfying the 9 criteria, if scoring them only 0-2 for each. IMHO the game's best attraction may be that it nicely meets criteria #5-7. Here's a link to my Chess Federation of Canada website blog entry discussing 4*Chess: http://www.chesscanada.info/forum/entry.php?31-Updated-version-4-0-of-4*Chess-(four-dimensional-chess) Here's a similar link to 4D crazyhouse/bughouse variants based on 4*Chess (similar variants could be made arising from Super4*Chess instead): http://www.chesscanada.info/forum/entry.php?86-Updated-version-2-0-of-four-dimensional-crazyhouse-bughouse-chess-variants Here's a link to 4*Chess as presented on chessvariants.com: http://www.chessvariants.com/index/msdisplay.php?itemid=MS4chessfourdime Here's a similar link to 5*4DChess (5x5x5x5 variant inspired by Super4*Chess): http://www.chessvariants.com/index/msdisplay.php?itemid=MS54dchessfourdi A similar link to Open King 4*4DChess (4x4x4x4 variant that uses 48 pieces, inspired partly by Super4*Chess): http://www.chessvariants.com/index/msdisplay.php?itemid=MSopenking44dche

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By Kevin Pacey.

Web page created: 2016-01-06. Web page last updated: 2016-01-06