Open King 4*4DChess

Here's a 4D game I call Open King 4*4DChess that can be played as if on a 2D plane (it uses sixteen 4x4 (2D) mini-boards). A 16x16 board with appropriate spacing could be used even on a coffee table; it would be about the size of a Scrabble board (it's 15x15 for that). This variant was inspired by my earlier 4x4x4x4 4D variant, Super4*Chess, as well as by Ben M. Reiniger's TessChess.


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 4*4DChess besides queens I've used just 6 powerful types of pieces (in fairy chess-speak, all [but 1] 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. 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 4*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 6 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 4*4DChess pawn may promote to), for a total of 9 piece types that are used in Open King 4*4DChess:

Q=Open King 4*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;

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

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

M=Open King 4*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 4*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 4*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;

X=Open King 4*4DChess Mann (based on a fairy chess piece [Mann]) - moves like a K;

P=Open King 4*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 4*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 4*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 4*4DChess 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 4*4DChess K = 32 x (max. # cells Open King 4*4DChess K moves to [eighty]) divided by (# of cells in 4*Chess [two hundred and fifty-six]) = 10, which seems in the right ballpark, given an Open King 4*4DChess K's great influence in mid-board.

I'd say an Open King 4*4DChess X = 10 roughly (since it moves like a K as well).

Here are my estimates for the remaining pieces:

Open King 4*4DChess S = 11.9;

Open King 4*4DChess T = 12.1;

Open King 4*4DChess M = 12.3;

Open King 4*4DChess H = 12.3;

Open King 4*4DChess J = 14.4 (just as Q=R+B+P in value, J=N+K+P in value, with a N in my earlier 4*Chess 4D variant estimated to be worth 3.4 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 well);

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 well, though there's no ideal solution);

5. Some chance of early mate or relatively short game (appears excellent);

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 (does not score well, as a K can only legally attack pawns, plus it is otherwise powerful on a 4x4x4x4 board);

9. Pieces (especially N-like ones) may obtain great scope (a 5x5x5x5 board would be better);

Fwiw, in scoring Open King 4*4DChess with these 9 criteria, giving a score of 0-4 for each, I found it had a total score of 18/36 (or 50%), whereas my earliest 4D variant, 4*Chess scores 21/36 (or about 58%). IMHO the game's best attraction may be that it seems to excellently meet criteria #5 (i.e. there's a decent chance for having a relatively short game). 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 Open King 5*4DChess (5x5x5x5 variant inspired partly by Open King 4*4DChess):

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.