4D chess: quality of life improvements

4D chess

White to move

W = 0 is the inner cube. W = 1 is the outer cube.

How to play, from 3D to 4D

The goal is still checkmate. White moves first. Select a piece, then a marked square. A solid dot is an empty destination; a ring marks a capture. In computer mode, you play White.

1. Give your 3D board one more coordinate

Think of a 3D chessboard as layers of ordinary boards. X and Y locate a square within a layer; Z chooses the layer. Here, each 3D board has two 4 × 4 layers.

Now make a second copy of that whole 3D board. W chooses which copy you are in. Every square has a corresponding square in the other copy. A move along W changes copies while keeping X, Y, and Z the same.

In the tesseract view, W = 0 is the inner cube and W = 1 is the outer cube. Both represent equally sized spaces. The inner cube looks smaller because of the projection. W is another spatial direction; it does not mean time.

a1 [0,1] means file a, rank 1, Z = 0, W = 1. That is a1 on the top-left board.

2. Compare a move in 3D and 4D

Choose a piece, then play or scrub through its move. These cleared-board examples use this game's rules. Other 3D chess variants may define their pieces differently.

Drag either drawing to rotate both. You can also focus a drawing and use the arrow keys. Home resets the views.

These diagrams illustrate movement. In your game, pieces along a sliding path block it, and every move must keep your king safe.

3. Count the coordinates that change

Judge a move by its coordinates. A W move can look diagonal in the drawing and still count as a straight rook move. Rotating the view changes how a move looks, not whether it is legal.

Any bishop or queen move involving Z or W is at most one step long on this board. Those axes only run from 0 to 1. X and Y each have four positions.

4. Look for threats across W

A king can be in check from a piece in the other cube. For example, a rook at a1 [0,0] attacks a king at a1 [0,1] along W. Distance on the screen gives you no protection.

You may capture the attacker, block a longer sliding attack, or move the king, provided the resulting position is safe. A one-step W attack has no intermediate square to block. Checkmate means your king is attacked and no legal reply escapes it.

Two lines crossing in the projection do not necessarily share a square. A piece blocks a sliding move only when its full X, Y, Z, W position lies on the path. Knights jump.

Your first W move

From the starting position, choose White's rook on a1 in the bottom-left board. Select a1 in the top-left board. The rook goes from a1 [0,0] to a1 [0,1]. Only W changes.

In the tesseract, that is a move from the inner cube to its matching point on the outer cube. The rook is still moving along just one axis.

Each side starts with a king, queen, two rooks, a bishop, a knight, and four pawns. There is no castling, en passant, or opening pawn double move.

The game draws on stalemate, the third occurrence of the same position with the same side to move, 100 turns without a pawn move or capture, or two bare kings. The king is never captured.

Rules

Win by checkmating the opposing king. White moves first. Select one of your pieces, then a marked destination. In computer mode, you play White.

Each side starts with a king, queen, two rooks, bishop, knight, and four pawns. The following movement rules apply equally to X, Y, Z, and W.

Move any distance along exactly one axis. It can travel within a board or to the same square on another board in the same row or column.

Move the same distance along exactly two axes. This includes ordinary diagonals and diagonals that cross between boards.

Move the same distance along any number of axes, from one to all four. Every changed coordinate must change by the same amount.

Move one step along any combination of axes. It may cross both Z and W in a single move, but may never enter an attacked square.

Jump two steps along one axis and one along a different axis. It jumps over pieces. On this board, the two-step part must use X or Y.

Move one empty square along Y. White goes toward rank 4, Black toward rank 1. Capture one Y step forward plus one step along exactly one of X, Z, or W. Reaching the last rank automatically promotes to a queen.

Blocking and check. All pieces except knights are blocked by pieces along their path. You cannot land on a friendly piece or leave your king in check. Checkmate ends the game; the king is never captured.

Pawns have no opening double move. There is no castling or en passant. Stalemate, a third repetition, 100 turns without a pawn move or capture, and two bare kings are draws. Each player's turn counts as one move in the journal.

Keyboard. Tab to a square, then press Enter or Space to select a piece or move. Arrow keys move focus within a board. Alt + arrow keys move focus between boards. Escape clears your selection.

Start a fresh game?

Your current game and move journal will be cleared.

Move history

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