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Open King 5*4DChess

Here's a 4D game I call Open King 5*4DChess that uses twenty-five 5x5 (2D) mini-boards. It was inspired by my earlier 4x4x4x4 4D variant, Open King 4*4DChess, as well as by Ben M. Reiniger's TessChess and my earlier 5x5x5x5 4D variant, 5*4DChess.

Because it is not so easy to checkmate a K relatively early in many 3D or 4D chess variants (maybe including some of my earlier 4D variants, such as 4*Chess in particular), in Open King 5*4DChess besides queens I've used just 5 powerful types of pieces (in fairy chess-speak, all are compound pieces that are crowned, i.e. all have movement capability of a K included). Not only that, but there are relatively few pieces on the board, with the kings all but wide open to attack. Furthermore, my aim was that on a 5x5x5x5 board, pieces (especially N-like ones) can hope to enjoy greater scope (at the same time, a king's influence is reduced due to the larger 4D board). 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.



In Open King 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). Note that 2 piece types are borrowed from my earlier 4*Chess (a four dimensional chess variant), a further 5 specifically Super4*Chess piece types are added, and TessChess pawn rules (as partially paraphrased by me) are used (except for the types of pieces that an Open King 5*4DChess pawn may promote to), for a total of 8 piece types that are used in Open King 5*4DChess:

Q=Open King 5*4DChess Queen - moves like a 4*Chess R or 4*Chess B, or a 4*Chess U, or a 4*Chess D, that is, the Q can move in one direction by any number of squares (or mini-boards), doing so by changing just 1 co-ordinate like a chess R (or just 2 co-ordinates like a chess B, or just 3 coordinates like a 3D Chess Unicorn (U), or all 4 co-ordinates like a 4D Chess Balloon (D)) as it moves;

K=Open King 5*4DChess King - moves like a Q, only 1 square/mini-board at a time (no castling);

T=Open King 5*4DChess Pilot - can move like a Balloon (D) or a K;

H=Open King 5*4DChess Shaman - can move like a Unicorn (U) or a K;

M=Open King 5*4DChess Missionary (based on a piece from Shogi [promoted Bishop, or 'Horse', in that game]) - can move like a B or a K;

S=Open King 5*4DChess Sailor (based on a piece from Shogi [promoted Rook, or 'Dragon', in that game]) - can move like a R or a K;

J=Open King 5*4DChess Judge (based on a fairy chess piece [Centaur]) - can move like a 4*Chess N (changes 1 coordinate by 1 square and 1 coordinate by 2 squares, like a knight) or can move like a K;

P=Open King 5*4DChess Pawn - moves without capturing one square in either of the two forward directions ("big" [by row] or "little" [by rank]). It captures one square diagonally forward[by row or rank]-sideways[by column or file]; that is, it makes one step in one of the two forward directions, and one step in one of the four non-forward directions (it never actually lands in the intermediate cell). Thus, there are a maximum of 8 directions that a P can capture in. P promotions occur on the last rank of any mini-board on the row where the enemy K starts the game, & an Open King 5*4DChess P may promote to any piece type above (other than K).


Stalemate is a draw, as in standard chess. 3-fold repetition and 50 move rule also are draws.


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

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.

Note that an Open King 5*4*Chess P = P = 1.

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

Here are my estimates for the remaining pieces:

Open King 5*4DChess S = 6.6;

Open King 5*4DChess T = 6.8;

Open King 5*4DChess M = 7;

Open King 5*4DChess H = 7;

Open King 5*4DChess J = 8.6 (just as Q=R+B+P in value, J=N+K+P in value, where, in my earlier 4D variant 5*4DChess, a N is estimated to be worth 3.6 pawns).

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 scores well on this);

2. Low total number of pieces in the setup (the game scores OK);

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 (the game scores fairly well, though there's no ideal solution);

5. Some chance of early mate or relatively short game (the game appears to score well);

6. Variety of viable exchanges of differing piece combinations (scores adequately, though see my comment re: criteria #7);

7. Variety of "major" and "minor" pieces (perhaps scores adequately overall, due to many 'major' pieces in the setup, but there are no truly 'minor' pieces, in the sense of a possible even trade of one for a low number of pawns);

8. K can legally attack opposing pieces/pawns (scores OK overall, as even though a K can only legally attack pawns, at least it is otherwise not as often so hugely influential when on a 5x5x5x5 board);

9. Pieces (especially N-like ones) may obtain great scope (the game's 5x5x5x5 board satisfies this excellently);

Fwiw, in scoring Open King 5*4DChess with these 9 criteria, giving a score of 0-4 for each, I found it had a total score of 20/36 (or about 56%), whereas my earliest 4D variant, 4*Chess scores 21/36 (or about 58%). IMHO the game's best attractions may be that it excellently meets criteria #9, and that there's a fairly decent chance for having a relatively short game (especially sweet since it's a 5x5x5x5 4D variant). Perhaps its main weaknesses (the lack of 'minor' pieces that can be evenly traded for a low number of pawns, as in a pure major piece chess middlegame, and kings that can only legally attack pawns, as in a pure queen chess endgame) might instead be seen as interesting features, even, at least for those who like chess positions involving purely major pieces.

Here's a link to 4*Chess as presented on

Here's a similar link to Super4*Chess (4x4x4x4 variant inspired by 4*Chess):

Here's a similar link to 5*4DChess (5x5x5x5 variant inspired by Super4*Chess):'s a another link, to Open King 4*4DChess (4x4x4x4 variant inspired by Super4*Chess):

A link to TessChess on (unlike the other 4D variants listed above, it's a 4D variant not of my own):

Another link about TessChess, which includes more diagrams:

This 'user submitted' page is a collaboration between the posting user and the Chess Variant Pages. Registered contributors to the Chess Variant Pages have the ability to post their own works, subject to review and editing by the Chess Variant Pages Editorial Staff.

By Kevin Pacey.

Last revised by Kevin Pacey.

Web page created: 2016-02-14. Web page last updated: 2016-02-14