Super4*Chess (four dimensional chess)

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. 3-fold repetition and 50 move rule also are draws.

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:

Here's a similar link to 4D crazyhouse/bughouse variants based on 4*Chess (similar variants could be made arising from Super4*Chess instead):

Here's a link to 4*Chess as presented on chessvariants.com:

Here's a similar link to 5*4DChess (5x5x5x5 variant inspired by Super4*Chess):

A similar link to Open King 4*4DChess (4x4x4x4 variant that uses 48 pieces, inspired partly by Super4*Chess):

Last revised by Kevin Pacey.