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.

Setup

Pieces

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).

Rules

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

Notes

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 chessvariants.com:

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):

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

Another link about TessChess, which includes more diagrams:

Last revised by Kevin Pacey.