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5*4DChess (four dimensional chess)

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Here's a 4D game I call 5*4DChess that has the following start position, with 25 5x5 mini-boards:


Code:
a a a a a  b b b b b  c c c c c  d d d d d  e e e e e
a b c d e  a b c d e  a b c d e  a b c d e  a b c d e  Rr

j n r b x  j n r b x  t n r n t  s d d u h  s d d u k  55
p p p p p  p p p p p  p p p p p  p p p p p  p p p p p  54
:   :   :    :   :    :   :   :    :   :    :   :   :  53
  :   :    :   :   :    :   :    :   :   :    :   :    52
:   :   :    :   :    :   :   :    :   :    :   :   :  51

  :   :    :   :   :    :   :    m d d u h  m d d u q  45
:   :   :    :   :    :   :   :  p p p p p  p p p p p  44
  :   :    :   :   :    :   :    :   :   :    :   :    43
:   :   :    :   :    :   :   :    :   :    :   :   :  42
  :   :    :   :   :    :   :    :   :   :    :   :    41

:   :   :    :   :    :   :   :    :   :    :   :   :  35
  :   :    :   :   :    :   :    :   :   :    :   :    34
:   :   :    :   :    :   :   :    :   :    :   :   :  33
  :   :    :   :   :    :   :    :   :   :    :   :    32
:   :   :    :   :    :   :   :    :   :    :   :   :  31

  :   :    :   :   :    :   :    :   :   :    :   :    25
:   :   :    :   :    :   :   :    :   :    :   :   :  24
  :   :    :   :   :    :   :    :   :   :    :   :    23
P P P P P  P P P P P  :   :   :    :   :    :   :   :  22
Q U D D M  H U D D M    :   :    :   :   :    :   :    21

:   :   :    :   :    :   :   :    :   :    :   :   :  15
  :   :    :   :   :    :   :    :   :   :    :   :    14
:   :   :    :   :    :   :   :    :   :    :   :   :  13
P P P P P  P P P P P  P P P P P  P P P P P  P P P P P  12
K U D D S  H U D D S  T N R N T  X B R N J  X B R N J  11

In 5*4DChess 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).
A total of 14 piece types are used, 13 borrowed from my earlier 4*Chess & Super4*Chess 4D chess variants:
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=5*4DChess Pawn (a unit specific to this game that moves differently than a 4*Chess P) - moves like a 4*Chess R (unless capturing), but generally moves forward by only 1 square at a time on a rank, or forward by 1 row to another mini-board (but moves to same rank & file there). It may make an initial double step like a 4*Chess R moving forward two squares (i.e. not jumping over anything on a R move's path), that is either by rank, or by moving to another mini-board two rows forward on the same column (landing on same rank & file there). If it is making a capture it can do so like a 4*Chess B that moves 1 rank forward on the same mini-board, or it can do so like a 4*Chess B that moves to a mini-board that's adjacent to (but not behind) it, i.e. it must always advance by rank or row, & never retreat by rank or row. Capturing a 5*4DChess P that has taken a double step by en passant capture is allowed, with the side doing the capturing placing his pawn making such a capture on the square the enemy pawn would have gone to if it had taken only a single step in the same direction that it took the double step on the previous turn. 5*4DChess P promotions occur on the last rank of any mini-board that's on the same row where the enemy K starts the game, & a 5*4D*Chess Pawn may promote to any 4*Chess or Super4*Chess piece type above (other than 4*Chess K). It is possible for a 5*4DChess P to early on avoid being captured by an enemy 5*4DChess P simply by moving to the last rank of a 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. (can be true in 5*4DChess)

If a game were to be recorded, all 4 coordinates (Column, then file, Row & rank) are given for where a 5*4DChess piece or 4*Chess P starts & finishes its move. If a 5*4DChess P promotes, this is recorded by tacking on the letter of the 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 5*4DChess Ps or 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.

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 added the 6 powerful types of Super4*Chess pieces above in the hope of making checkmating a king during a game easier, with that game (or 5*4DChess) still possibly being viable to play & enjoy. My original inspiration behind 5*4DChess was to give pieces (especially a 4*Chess N) chances for even greater scope than on 16 4x4 mini-boards, possible on many of the added & larger mini-boards. It also inspired me that mann-like pieces would have somewhat less strength.

I'd guess the relative values of 5*4DChess pieces to be about as follows:

5*4DChess P = 1
4*Chess R (for within 5*4DChess, this piece for example could be called a 5*4DChess D instead, if one prefers) = 3
4*Chess D = 3.2
4*Chess B = 3.4
4*Chess U = 3.4
5*4DChess N = 3.6 (stronger than a 4*Chess N on its 4x4x4x4 board)

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 5*4DChess K = 32 x (max. # cells 4*Chess K moves to [eighty])
divided by
(# of cells in 4*Chess [six hundred and twenty-five])
= 4 approx.

Thus, a 5*4DChess X = 4 (since it moves like a K as well).

Here are my estimates for the remaining pieces:

5*4DChess S = 6.5;
5*4DChess T = 6.6;
5*4DChess M = 6.7;
5*4D*Chess H = 6.7;
5*4DChess J = 8.6 (just as Q=R+B+P in value, J=N+K+P in value).

Here's are links to my blog entries discussing 4*Chess & Super4*Chess:

http://www.chesscanada.info/forum/en...nsional-chess)

http://www.chesscanada.info/forum/en...nsional-chess)

Here's a link to 4D crazyhouse/bughouse variants based on 4*Chess (similar variants could be made arising from 5*4DChess instead):

http://www.chesscanada.info/forum/en...chess-variants

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

http://www.chessvariants.com/index/m...4chessfourdime

A 2nd link re: 5*4DChess:

http://www.chessvariants.com/index/m...54dchessfourdi

A link to a variant inspired by 5*4DChess:

http://www.chessvariants.com/index/m...openking54dche


http://www.chesscanada.info/forum/en...Chess-variant)

http://www.chesscanada.info/forum/en...in-fairy-chess

Updated 08-03-2016 at 06:32 PM by Kevin Pacey

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