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Updated version 4.0 of 4*Chess (four dimensional chess)

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Here's a 4 dimensional chess game that can be played as if on a 2D plane. [first update: A 16x16 board with appropriate spacing could be used even on a coffee table; it would be about the size of a Scrabble board (15x15 for that).] Using a computer program for it, a player could check if he is making a legal move, and whether it is mate or stalemate, for example. [second update: I call it 4*Chess, assuming the name is not taken.] It's based on a BASIC computer program I made for it in the 1980's, which took up less than 16K. I played a game of it with a friend, and it didn't take too long after a blunder, as we knew a 4*Chess K and 4*Chess Q vs. 4*Chess K can win very quickly. Here's a sort of diagram for a possible start position of the sixteen 4x4 mini-boards the game is played on (sorry, not sure if the position is the same as I had long ago):

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

[N] [B] [B] [N]  [N] [U] [U] [N]  [R] [D] [D] [R]  [R] [D] [D] [K]  44
[P] [P] [P] [P]  [P] [P] [P] [P]  [P] [P] [P] [P]  [P] [P] [P] [P]  43
    :::     :::  :::     :::          :::     :::      :::     :::  42
:::     :::          :::     :::  :::     :::      :::     :::      41

:::     :::          :::     :::  [U] [D] [D] [U]  [R] [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) (R)  (U) (D) (D) (U)  :::     :::          :::     :::  21

:::     :::          :::     :::  :::     :::          :::     :::  14
    :::     :::  :::     :::          :::     :::  :::     :::      13
(P) (P) (P) (P)  (P) (P) (P) (P)  (P) (P) (P) (P)  (P) (P) (P) (P)  12
(K) (D) (D) (R)  (R) (D) (D) (R)  (N) (U) (U) (N)  (N) (B) (B) (N)  11

In 4*Chess, some 3 and 4 dimensional moving pieces are introduced, and 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 number of a mini-board):
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 (does not change square colour if moving to another mini-board);
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 one 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;
P=4*Chess Pawn - moves like a 4*Chess R (unless capturing) except only moves forward one square at a time on a rank, or forward by one column or one 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 one square, or by one mini-board that's adjacent diagonally or by one row or by one column, and 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, and a 4*Chess P may promote to any 4*Chess piece type (other than 4*Chess K). There is no double step or en passant, and 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.

[third update: 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 (and the number of them) are not large enough to ever allow it (actual max. = 24).]

An example legal first move in 4*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 4*Chess notation as 1. Paa12-aa13 Pdd43-dd42 if a game were to be recorded. Thus, all four coordinates (Column, then file, Row and rank) are given for where a 4*Chess piece or 4*Chess P starts and 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 four 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), 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 one move being available). Notwithstanding that, I conceived of possible mates in one move using any four such other pieces, but with at least two of them not being 4*Chess Ds.

Exceptional cases requiring less than four such pieces where mate in one is possible that I've found include having a 4*Chess R plus two 4*Chess Bs, or plus two 4*Chess Us or plus two 4*Chess Ns (or plus a 4*Chess B and a 4*Chess U), (or plus a 4*Chess N and a 4*Chess U), (or plus a 4*Chess N and a 4*Chess Bi). Mate in one with three 4*Chess Rs is also possible.

Five 4*Chess Ds plus one of any other type of piece may make a mate in one possible, too. I've also conceived of possible checkmate positions with exactly eight 4*Chess Ds (the number one starts the game with).

In all these cases of mate in one (i.e. excluding a 4*Chess Q or a 4*Chess P), 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 4*Chess pieces to be about as follows:

4*Chess P = 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

Note that I didn't wish to put the seemingly humble 4*Chess R below 3, as it seems it could deal with at least 3 passed pawns in endgames at times. Also note that a rather humble 4*Chess D might at times have more mobility than a 4*Chess R (besides perhaps often being on more frequently critical open line[s] than a 4*Chess R). In some perhaps rather uncommon circumstances, a 4*Chess B can restrain 3 passed pawns in an endgame, so that's some justification for valuing a 4*Chess B as worth more than 2 pawns (plus, it seems to be more of value than a 4*Chess R or 4*Chess D). As for the 4*Chess U and 4*Chess N, they are judged to be similar in value to a 4*Chess B, in terms of their mobility at least.

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.

It could be an arduous task to discover all forcible 'basic' 4*Chess mates vs. a lone Black 4*Chess K; I'd be speculating to say that the total value of the pieces involved (excluding 4*Chess Pawns or the White 4*Chess K) should be worth at least 16 points (the value of a 4*Chess Q).

Here's a link to 4D crazyhouse/bughouse variants based on the above:

Here's 5 other links, including 1 for comparing chess variants & other board games of skill:

Here's a link to another discussion of 4*Chess:

Updated 08-26-2016 at 07:27 PM by Kevin Pacey

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Chess variants