Games, analysis and discussion

Super4*Chess (four dimensional chess)

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Here's a 4D game Super4*Chess - can be played as if on a 2D plane. A 16x16 board with appropriate spacing could be used even on a coffee table; it'd be about size of Scrabble board (15x15 for that). The following is start position for the 16 4x4 mini-boards game is played on:

Col =a= and file Col =b= and file Col =c= and file Col =d= and file Row and rank
 aa  ab  ac  ad   ba  bb  bc  bd   ca  cb  cc  cd   da  db  dc  dd  Rr

[X] [B] [B] [R]  [T] [U] [U] [R]  [N] [D] [D] [S]  [J] [D] [D] [K]  44
[P] [P] [P] [P]  [P] [P] [P] [P]  [P] [P] [P] [P]  [P] [P] [P] [P]  43
    :::     :::  :::     :::          :::     :::      :::     :::  42
:::     :::          :::     :::  :::     :::      :::     :::      41

:::     :::          :::     :::  [N] [D] [D] [H]  [M] [D] [D] [Q]  34
    :::     :::  :::     :::      [P] [P] [P] [P]  [P] [P] [P] [P]  33
:::     :::          :::     :::      :::     :::  :::     :::      32
    :::     :::  :::     :::      :::     :::          :::     :::  31

    :::     :::  :::     :::          :::     :::  :::     :::      24
:::     :::          :::     :::  :::     :::          :::     :::  23
(P) (P) (P) (P)  (P) (P) (P) (P)      :::     :::  :::     :::      22
(Q) (D) (D) (M)  (H) (D) (D) (N)  :::     :::          :::     :::  21

:::     :::          :::     :::  :::     :::          :::     :::  14
    :::     :::  :::     :::          :::     :::  :::     :::      13
(P) (P) (P) (P)  (P) (P) (P) (P)  (P) (P) (P) (P)  (P) (P) (P) (P)  12
(K) (D) (D) (J)  (S) (D) (D) (N)  (R) (U) (U) (T)  (R) (B) (B) (X)  11

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 'coordinate' in 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 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 (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);
Stalemate is a draw, as in standard chess.

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. Because it is not so easy to checkmate a K in many 3D or 4D chess variants (maybe including 4*Chess), besides standard 4D pieces, in Super4*Chess I've used the 6 new powerful types of Super4*Chess pieces (in fairy chess-speak, they are compound pieces that are crowned, i.e. all have movement capability of a K included) in the hope of making checkmating a K during a game easier, with the game still possibly being viable to play & enjoy.

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 R = 3
4*Chess D = 3.2
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 = ((4*Chess R + 4*Chess B + 4*Chess P) + 4*Chess D + 4*Chess P) + 4*Chess U + 4*Chess P = 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.

Thus, a Super4*Chess X = 10 (since it moves like a K as well).

Here are my estimates for the remaining pieces:

Super4*Chess S = 12;
Super4*Chess T = 12.1;
Super4*Chess M = 12.2;
Super4*Chess H = 12.2;
Super4*Chess J = 14.4 (just as Q=R+B+P in value, J=N+K+P in value).

Here's a link to my blog entry discussing 4*Chess:

Here's a 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 another discussion of 4*Chess:

A 2nd link re: Super4*Chess:

A link to a variant inspired by Super4*Chess:

A link to a 8x8x2x2 4D variant inspired by (3D) Alice Chess:

Updated 11-26-2016 at 05:09 AM by Kevin Pacey

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Chess variants