d4 d6 chess

d4 d6 chess is a chess variant that can be played with one chess set and two dice.

In d4 d6 chess, when you choose to move a piece, you typically roll a die and move as many steps as the outcome of the die.

Igor Seabra and I created this game together while having fun playing it.

Setup

Material

• a d4 dice (with possible outcomes 1, 2, 3 and 4)
• a d6 dice (with possible outcomes 1, 2, 3, 4, 5 and 6)
• a standard Chess set minus 6 White pawns and 6 Black pawns
• optional: four tiles, each with a size of 2 by 2 squares

Initial configuration

At the start of the game, the board looks like this:

White's army comprises two Ratos on c2 and f2 (represented by Chess bishops), two Cavalos on d2 and e2 (represented by Chess knights), two Formigas on c1 and f1 (represented by Chess rooks), one Gata on d1 (represented by a Chess queen), one Gato on e1 (represented by a Chess king) and two Guardas on a1 and h1 (represented by Chess pawns). Symmetrically, Black's army comprises two Ratos on c7 and f7, two Cavalos on d7 and e7, two Formigas on c8 and f8, one Gata on e8, one Gato on d8 and two Guardas on a8 and h8. Note that the two Gatas are not on the same file, and nor are the two Gatos.

In the initial configuration, the Cavalos's noses are pointing forward. That is, the White Cavalos on d2 and e2 should be facing north and the Black Cavalos on d7 and e7 should be facing south. (The directions of the Cavalos are not represented in the diagram.)

Terminology: areas

The playing area consists of the following 48 squares: c8, d8, e8, f8, c7, d7, e7, f7, the entire sixth, fifth, fourth and third ranks, c2, d2, e2, f2, c1, d1, e1 and f1. The 16 squares outside the playing area form the waiting area. So the waiting area consists of a8, b8, g8, h8, a7, b7, g7, h7, a2, b2, g2, h2, a1, b1, g1 and h1. The waiting area mainly serves as a storage room for a few pieces. (It may be helpful to cover the waiting area with cardboard tiles in order to accentuate the playing area.)

The teleportation area consists of the following 4 squares: a8, h8, a1 and h1.

The promotion area consists of the following 8 squares: a6, h6, a5, h5, a4, h4, a3 and h3.

The border area consists of the following 12 squares: c8, d8, e8, f8, c7, f7, c2, f2, c1, d1, e1 and f1.

White's starting area consists of the following 4 squares: c1, d1, e1 and f1. Symmetrically, Black's starting area consists of c8, d8, e8 and f8.

The following diagram displays the waiting area with red squares, the teleportation area with red markers, the promotion area with yellow squares, the border area with blue squares, White's starting area with white markers and Black's starting area with black markers.

Pieces

A Guarda moves as a Chess king. A Guarda cannot capture anything.

All pieces except Guardas are gambling pieces. Unlike the gambling pieces, a Guarda can live on all 64 squares, freely entering and exiting the playing area and the waiting area. However, we will explain below that the guarding power of a Guarda is only existent when the Guarda is in the playing area.

Moving a gambling piece

We next explain how to make a move with one of your gambling pieces within the playing area. First point at the specific gambling piece within the playing area that you want to move, or name the square that they are currently occupying. Then pick up one die, depending on the type of piece:

• a Rato uses d4;
• a Cavalo uses d4;
• a Gato uses d4;
• a Formiga uses d6;
• each time you move a Gata, you can choose between d4 and d6.

Roll the die. It shows some result n. Then you must make, if possible, exactly n consecutive steps with the piece that you chose. These steps together form one move. The stepping must be done within the playing area. You are allowed to change direction in between the steps. Within one move, you are not allowed to visit any square twice. For a non-capturing move, all squares that you visit need to be empty. For a capturing move, all squares that you visit, except for the final square of the move, need to be empty, and the final square needs to be occupied by an enemy piece, which is then captured. You cannot capture a gambling piece that is orthogonally adjacent to one of your opponents Guardas that is in the playing area. If, under all of these restraints, it is not possible to complete the move in exactly n steps, then you must try to make a non-capturing move with exactly n-1 steps instead. If this is also impossible, try a non-capturing move with exactly n-2 steps. Etc. If you get down to 0, you will make a (non-capturing) move with 0 steps, which means that nothing happens.

The gambling pieces step as follows:

• A Rato makes single diagonal steps.
• A Formiga makes single orthogonal steps.
• A Gata can make both orthogonal and diagonal steps, but cannot combine diagonal and orthogonal steps within one move. When the die result n is 5 or 6, you must make orthogonal steps (even if you are making less than 5 steps.)
• A Cavalo, while it is not capturing, makes single orthogonal steps in the direction it is facing. To make a capturing move with a Cavalo, the final step must be a single diagonal step approximating the same direction. Differently put, a Cavalo makes a capturing move in k steps by going k-1 steps in the direction it is pointing at, and then capturing using a single diagonal step in a direction that has a 45 degree angle with the direction it is facing.
• A Gato step is a Chess knight movement composed of three orthogonal substeps. Thus the difference between the Gato step and the Chess knight move is that the Gato cannot jump over pieces: the Gato visits three squares on each step, all of which have to be in the playing area. The following diagram shows three possible ways for the Gato to step.

Turning a Cavalo

• Whenever one of your Cavalos, facing north or south, visits your sixth rank (this is the sixth rank for a White Cavalo, and the third rank for a Black Cavalo), you must immediately choose to let it face either east or west. (This can happen in the middle of a move, and a Cavalo can in this way make a 90 degree turn within a move.)
• Whenever one of your Cavalos visits the border area, the Cavalo is immediately turned vertically towards your sixth rank. So, for example, a White Cavalo on c7 needs to face south.
• Turning a Cavalo is considered part of the way in which a Cavalo steps, so these rules always have to be respected when moving a Cavalo; even when this prevents you from making exactly n steps as described above under "Moving a gambling piece".

Capturing a Cavalo

When you capture a Cavalo that is in the playing area, do not remove it from the board. Instead place it on an empty square of choice in the waiting area. You also do this when you promote a Cavalo. (Of course, a Cavalo in the waiting area cannot move, except when using a special move as explained below under "Special move".)

Example

Imagine that the White Cavalo on e5 in the diagram below is facing north.

Suppose White wants to move the Formiga on b6. If they roll a 1, the Formiga can move to a6, capture the Guarda on b5 or capture the Gato on c6. If they roll 2, 3, 4, 5 or 6, they have no choice but to move the Formiga to a6.

Suppose White wants to move the Cavalo on e5. If they roll a 1, they can move the Cavalo to e6 (and face either east or west) or capture the Gata on f6 (also with the choice of facing east or west). If they roll a 2, they can move it to d6 facing west or capture the Rato on f7 and turn south. If they roll a 3, the Cavalo must capture the Rato on c7 and then face south. If they roll a 4, the Cavalo must move to d6 facing west.

Suppose White wants to move the Gata on d8 using the d4-die. Then, whatever number they roll, they will always be able to capture the Rato on c7 if they want to.

Rules

The objective of d4 d6 chess is to capture the opponent's pieces. If ever you have no gambling pieces left in the playing area, you lose the game. When a hundred consecutive gambling moves (fifty per player) occur without any captures, Cavalo steps or intermediate promotions, the game ends in a draw. The game can also end in a draw by mutual agreement.

White starts.

In your turn, you must make a move with one of your gambling pieces and you may make one special move. You are allowed to make a special move before or after performing a move with a gambling piece. When you start your turn by choosing a gambling piece to move and rolling a die, you cannot make a special move before completing the move with the gambling piece.

We described how to move gambling pieces above.

Special move

A special move can be one of four things:

1. Move one of your Guardas.
2. Place one of your Guardas. This can only be done with a Guarda that is currently in the teleportation area. Pick it up and place it on any empty square in the playing area.
3. Promote one of your Cavalos. This can only be done with a Cavalo that is currently in the promotion area. Replace it by any other piece of choice that is of the same color. There is no limit to the amount of pieces of a type: you can have two Gatas or two Gatos of the same color on the board. Note that a White Cavalo that never makes a capturing move can only promote on a6 or h6, and a Black Cavalo that never makes a capturing move can only promote on a3 or h3.
4. Place your "third Cavalo". This is only allowed if both of your Cavalos are in the waiting area and your starting area contains at least one empty square. Remove one of your Cavalos from the board, and place the other Cavalo on any empty square of choice in your starting area.

Notes

Endgame tablebase

I generated a 2-men tablebase for this game. Denoting a sure win for Black by -1 and a sure win for White by +1, the following are some notable results according to my computer's calculations:

• White Gata on a light square VS Black Rato on a dark square, White to move: +1.00
• White Gata on a light square VS Black Rato on a light square, White to move: +0.98 on average (worst-case scenario: White on a6, Black on d3, +0.899)
• White Gata VS Black Gato, White to move: +0.17 on average (worst-case scenario: White on a6, Black on g4, -0.29)
• White Gata VS Black Gato, Black to move: -0.44 on average (best-case scenario: White on a4, Black on a5, -0.10) (worst-case scenario: White on a6, Black on b4, -0.64)
• White Rato on a light square VS Black Rato on a light square, White to move: +0.24 on average
• White Formiga VS Black Formiga, White to move: +0.21 on average
• White Gato VS Black Cavalo, White to move: +0.73 on average (best-case scenario: White on c5, Black on d8 (hence facing south), +0.96)
• White Gata VS Black Cavalo, White to move: +0.71 on average
• White Cavalo VS Black Cavalo, White to move: +0.17 on average
• White Gato on c8 VS Black Gato on f8, White to move: -0.08 (mutual Zugzwang)

(For the Cavalos I included all semi-legal positions. For instance, you can have an absurd White Cavalo on g3 facing west, but you can't have a White Cavalo on g6 facing north as this contradicts the rules for turning a Cavalo.)

Fortress

Imagine the White Cavalo on b6 in the diagram below is facing west.

Black is up in material, but White can force a draw. They can choose the Cavalo on every turn so that all of the three White pieces stay put, while Black has no piece that can attack the White Guarda.

Variant: Rinoceronte

Each player has an additional gambling piece: a Rinoceronte. These can be represented by knights from another Chess set. The nose of a Rinoceronte is always pointing in a diagonal direction. In the starting position, add a White Rinoceronte on g1 and a Black Rinoceronte on b8. For each, use the d4 to randomly determine its initial orientation.

Differently from other gambling pieces, a Rinoceronte is not restricted to the playing area: it can also step in the waiting area. A Rinoceronte uses the d6 die. It can step diagonally in the direction it is facing, but it can also step orthogonally backwards (w.r.t. the direction it is facing). For example, a Rinoceronte on b3 facing northeast can step to c4, a3 and b2. Moreover, a Rinoceronte can combine these three different ways of stepping within one move. Naturally, a Rinoceronte can also capture pieces in the waiting area.

As a special move, you can turn your Rinoceronte by 90 degrees.

A Cavalo in the promotion area can promote to a Rinoceronte facing any diagonal direction of choice.

If a Rinoceronte is your last remaining piece, you may still move it through the waiting area. Naturally, in this case you cannot end your move in the waiting area or you would lose the game (see "Rules" above).

Last revised by Maurice Dekker.