Why I didn't Like the Old Mapping

There were two things about the old mapping that I really didn't like.

The first was that the Bishop's 3D move looked like a Rook move to me. Just because it changes color and changes height, well, yes, the move is diagonal in some sense, and yes a person who is viewing the board from a 90 degree angle will see it as diagonal, nut to me, sitting upright in front of the board, a move that stays on the same file feels like a Rook move. Forget about symmetry; I am always sitting straight up and down, and I want my Bishop moves to feel diagonal.

The second was that the most diagonal move of all wasn't even in the game: the move from 1a1 to 2b2 was neither a Rook move nor a Bishop move; some people who used the old mapping invented a new piece to use this move, but they weren't trying to make a 3D Chess with a capital C.

An additional minor worry was that the pieces in that mapping hadn't gained very much mobility from going into the third dimension.

After devising my new mapping, I realized that the old mapping was also bad because "g5" might be a White square. Every chessplayer knows that g5 is always a black square.

Sweat and Inspiration

Befuddled by this quandary, I wandered in a daze for days. Well, if you want the truth, I put the question aside for a day or two and then the answer just came to me.

If the square above a White square is also a White square, everything is different. Now when a Bishop moves from c1 to d2, it stays on the same color, and when it moves from c1 to the square above d2 it also stays on the same color!

This makes Bishop's move very natural and simple. It is easy for any chessplayer to see this kind of Bishop move: it is diagonal, but may stay on the same level or be rising or descending.

Even better, the combination of the Rook and the Bishop cover all the primary directions. This means that the King's move is now a perfect cube, just the way that the 2D King's move was a perfect square.

One minor quibble is that the Rook's vertical move does not change colors with each step, and so in some sense perhaps this ought to be a Bishop move. However, it's a Rook move.

The other quibble with this mapping is that the Rook's rising/descending move looks like a Bishop move if you're looking at the board from the wrong angle. What can I say except "Don't do that!". With my mapping, the Rook's move looks like a Rook move to the players, and that's what counts the most.


So of course the Pawn move is easy, right? A Rook move, a Bishop capture.

Wrong. If it can slide past another Pawn and run up to promote, it isn't a Chess Pawn. Pawns get blocked, mostly by other Pawns. Blocked Pawns form the "terrain" of an otherwise featureless board. The only way a real Pawn can move is one-dimensional: straight forward.

Now, what about the Pawn capture? In the previous edition of my mapping, I allowed Pawns to capture in 8 directions, basically every forward move except straight ahead. Unfortunately, this meant that you couldn't afford to offer gambits because the gambit Pawn would be too easily defended, and what's worse you couldn't form proper Pawn chains or create Pawn weaknesses or sacrifice a minor piece to clear out a few Pawns, all because each and every square was defended by entirely too many different Pawns.

Making up my old sample game was so much work, I hated to throw it away; but the Pawns were wrong.

After a bit more thought, I decided that there were three possible rules for Pawns, and that all three were interesting and would make good games.

One-dimension Move, Three-dimension Capture

You could rephrase the two-dimensional Pawn's rule of movement to be "one-dimensional move, two-dimensional capture". Then a 3D Pawn would be "1D move, 3D capture". (The so-called "Unicorn" move.)

This would be a very good and very interesting Pawn, but I cannot choose this rule for 3D Chess because this pawn cannot make a normal Pawn capture on its own level! In order to capture, it must go to a different file and a different level.

It takes four of these Pawns to form a proper 3D phalanx, and each square is defended by four Pawns.

Flatland Pawns

A surprisingly good rule would be "Pawns can never change level".

Using 2D Pawns in a 3D game seems odd, but the effect is to add quite a lot of strategic complexity to the game. Instead of worrying about one 3D Pawn formation, you need to worry about 8 different 2D shapes, and how they relate to each other in 3D -- because although the Pawns don't cross levels, the pieces that attack them and defend them and are blocked by them do cross levels!

The other big advantage of this rule is that each square is defended by only two Pawns, and therefore the problem of Pawn weaknesses is as important as in normal 2D FIDE-Chess.

Change Level or File

You could rephrase the 2D Pawn's rule as "change file to capture"; than a 3D Pawn would be "change level or file to capture".

This Pawn makes an ordinary Pawn move or capture on its own level, or changes levels by capturing on the same file: 4e4:5e5 for example.

Two of these make a 3D phalanx, and Pawn chains shaped like mountains work very well.

The only disadvantage is that each square is defended by four Pawns instead of by two.

Making the Choice


Although I really like the Flatland Pawns, I'm afraid that I must choose the "Change Level or File" rule. In the final analysis, when you want the game to be 3D Chess, the truest possible 3D translation of 2D FIDE-Chess, having 2D Pawns and 3D pieces seems wrong.

However, the "3D chess with Flatland Pawns" chess variant might be even better than 3D Chess!


There are actually 6 choices for the 3D Knight.
  1. The basic Knight move is perhaps "one, two, and over" (0,1,2). This is easy to translate into 3 dimensions, and gives the Knight a mobility of 24 possible moves. I call this the "strict construction" 3D Knight.

  2. A "3D-only 3D Knight" would jump to (1,1,2), up to 24 squares. It cannot go to any of the same places as a strict construction 3D Knight; especially, it cannot make the normal Knight move on its own level.

  3. A new 3D move is (1,2,2), up to 24 squares. This strange direction is hard to visualize.

  4. Maybe the basic Knight move is "wherever a Rook or Bishop can't go". This is the "most permissive" 3D Knight, (0,1,2) plus (1,1,2) plus (1,2,2): a total of 72 squares it can go to!

  5. A "flat 3D Knight" would be any 2D Knight's move, or the square above or below, for a total of 24 possible squares.

  6. My favorite 3D Knight is (0,1,2) plus (1,1,2); this is also the flat 3D Knight rotated in all directions. This one makes a pretty pattern, but even more important, the pattern it makes is very useful in checkmating the enemy King.

    This Knight makes its usual leaping move: two squares in one direction, then it turns, goes one square, and lands. Another way of looking at this is that the Knight goes anywhere next to (and at the same distance from) two squares straight out from its starting square. Both of these descriptions are equally applicable to the standard 3D Knight.

I want to choose the most Chesslike 3D Knight, and I want to choose the one that makes the best game. Which one?

The flat Knight is too flat.

My favorite is too strong. It has four times as many forward moves as in 2D, while the Bishop and Rook each have only three times as many. There are a great many mitigating circumstances that reduce its strength, and I really wanted to choose this Knight. In fact, I did, and I hated it when I had to go around and edit all the files to change it.

The strict construction N seems obvious, and in fact is the choice that must be made. It seems less natural than the flat Knight, but I think it's okay that the 3D Knight should give new 3D players a bit of trouble, just as the 2D Knight torments new 2D players.


No problem, right? One square like a Rook or Bishop, which is also all the squares at the outside of the King's 3x3 cube.

No problem with the King's move itself, not at all; but there are four other problems with the Kings.


The King now moves to 26 squares instead of to 8; will it be too hard to give checkmate?

Elsewhere, I have shown that a King and two Rooks can force checkmate against a lone King. This is a very small percentage of your starting material compared to what you need in FIDE-Chess.

If it is true (and I think it is true) that King plus Queen cannot mate a bare King, King plus Pawn versus King is always a draw. Considering that you start the game with 64 Pawns, I think that the requirement to win by two Pawns isn't unacceptable.

In the middlegame, you have so many more pieces to attack with, and the other guy has so many pieces to get in the way of his own King, that I believe it should be no harder to get a mating attack than it is in FIDE-Chess.

Kings that Aren't Kings

You can only have one King, else it isn't really Chess. But what do you put on e1 on all the other levels?

I have chosen to use the Commoner (moves like a King, but doesn't worry about check), for three main reasons.

  1. The Commoner can be physically represented by a King; if you simply mark the real King in some way, then you can play 8x8x8 3D Chess with no special equipment (except of course that you need 8 sets instead of one).
  2. The Commoner moves like a King, so it's already a familiar piece in FIDE-Chess.
  3. The Commoner is a good piece to have in the late endgame because it is good at helping to give checkmate.

However, perhaps the Commoner is too good a defensive piece, and perhaps its presence makes it too hard to come up with traps leading to mate in the opening. I worry about this a bit, but can neither prove nor disprove the proposition.

In any case, this particular page is about how to move the 3D pieces, not about which pieces are in the game.

Starting Position

The White King starts at 4e1, that is, e1 on the fourth level. Should Black start at 4e8, 4d8, 5e8, or 5d8?

In FIDE-Chess, the exciting opening attacks are possible because the KB and the Q start the game on the same colored square as the enemy King. Goodbye 4d8 and 5d8.

I suspect that it's important to have the Kings directly facing each other because the completely open King-file (when it arises) then endangers both Kings equally.


We must have 3D Castling. However, some details need to be considered.