Issue 19 - Summer 2020
Games with genuinely three-dimensional boards are relatively rare among abstract games. We do not count here games with a stacking mechanism, such as Avalam Bitaka, on the cover of AG18. An exception is the alignment games, such as Tic Tac Toe, and there have been numerous versions of these in three dimensions—Qubic, for example. Axiom, on the cover of AG16, stands out because it is both genuinely 3D and because there is no 2D original game that was extended into the third dimension. Qua, in this issue, also stands out. Not only is Qua a 3D connection game, in itself a first as far as I know, but in addition it is a connection game for three players, another rarity—but why not, with three pairs of opposite faces in a cube?
Among the genuinely 3D games, however, special attention needs to be given to the chess variants, both because of their long development and because they caught the public imagination through Star Trek 3D Chess. L. Lynn Smith wrote a series of articles on 3D Chess, and in the first of these, in AG10, Lynn demonstrated that the concept of chess in three dimensions goes back at least to the Eighteenth Century. There is much to investigate about this topic, and the series continued for every issue to AG15. Finally, Lynn's article on Quad Level 3D Chess, which should have appeared in the old series, was finally published in AG17.
The topic of the 3D chess article in AG15, in 2003, was the 4x4x4 cube, and Rick Hewson's game Exchequer was discussed. A newer version of Rick's game, now called 3D XYZ Chess, is shown above. Actually, 3D XYZ Chess is almost identical to Exchequer, the only significant change being a two-space initial move for some Pawns. Rick has been developing the game since 1988, so for 32 years! The perfected rule set has been stable at least since 2016.
3D XYZ Chess is played on four levels, with 4x4 spaces each, effectively a 4x4x4 array of cubes. The game thus contains 64 spaces, or cubes, the same number as a regular Chess board. Moreover, each player controls a 16-piece army that is identical to the regular Chess army, albeit with some altered powers. The board is placed with vertical corners (rather than sides) facing each player, and the pieces are positioned initially in these opposite vertical corners.
The Rook moves in a straight line through cubes that are connected via their sides; the Bishop moves in a straight line through cubes that are connected via their edges; the Queen combines the powers of Rook and Bishop. Effectively, these pieces retain their regular Chess moves, with the proviso that they can travel also in vertical planes. The Knight has a different and entirely new move that does not correspond to anything in regular Chess—the Knight moves one cube triagonally, in other words between cubes that are connected at their corners. The King's move is constrained, and the King can move only one square orthogonally, not diagonally, both within his plane and vertically. The Pawns step one space (or two spaces initially) towards the opposite corner, and cannot move vertically. Pawns capture as they move, like the other pieces, and unlike Chess Pawns.
The triagonal move of the Knights is interesting, because a Knight can only reach 16 spaces, one quarter of the board. The Knights of one side together cover only half the board. One could regard this as a flaw, but I do not think it is—there is a pleasing symmetry due to the opening placement of the four Knights of both sides. The two sets of Knights do not cover each other's squares, so opposite-side Knights can never capture each other, and together the Knights of both sides cover all spaces on the board. I am sure this special move of the Knight has interesting strategic implications.
The rules of 3D XYZ Chess are very clean and logical. The decades-long period of development and testing shows. The altered powers of Knight, King, and Pawn are perfectly suited to the 4x4x4 three-dimensional environment. The setup in opposite vertical corners is excellent. This is a game that deserves to be studied to develop principles of good play, from opening to endgame. The set itself is beautiful, and guaranteed to create a stir if you take it into a coffee shop to play, as I have done (in pre-Covid-19 times). In my opinion, 3D XYZ Chess is a brilliant translation of regular Chess into a three-dimensional environment. This game is highly recommended, especially for someone with an interest in 3D games, and 3D chess specifically. In the meantime, you can get a set or just a rules booklet from Rick Hewson. ~ KH
Among the genuinely 3D games, however, special attention needs to be given to the chess variants, both because of their long development and because they caught the public imagination through Star Trek 3D Chess. L. Lynn Smith wrote a series of articles on 3D Chess, and in the first of these, in AG10, Lynn demonstrated that the concept of chess in three dimensions goes back at least to the Eighteenth Century. There is much to investigate about this topic, and the series continued for every issue to AG15. Finally, Lynn's article on Quad Level 3D Chess, which should have appeared in the old series, was finally published in AG17.
The topic of the 3D chess article in AG15, in 2003, was the 4x4x4 cube, and Rick Hewson's game Exchequer was discussed. A newer version of Rick's game, now called 3D XYZ Chess, is shown above. Actually, 3D XYZ Chess is almost identical to Exchequer, the only significant change being a two-space initial move for some Pawns. Rick has been developing the game since 1988, so for 32 years! The perfected rule set has been stable at least since 2016.
3D XYZ Chess is played on four levels, with 4x4 spaces each, effectively a 4x4x4 array of cubes. The game thus contains 64 spaces, or cubes, the same number as a regular Chess board. Moreover, each player controls a 16-piece army that is identical to the regular Chess army, albeit with some altered powers. The board is placed with vertical corners (rather than sides) facing each player, and the pieces are positioned initially in these opposite vertical corners.
The Rook moves in a straight line through cubes that are connected via their sides; the Bishop moves in a straight line through cubes that are connected via their edges; the Queen combines the powers of Rook and Bishop. Effectively, these pieces retain their regular Chess moves, with the proviso that they can travel also in vertical planes. The Knight has a different and entirely new move that does not correspond to anything in regular Chess—the Knight moves one cube triagonally, in other words between cubes that are connected at their corners. The King's move is constrained, and the King can move only one square orthogonally, not diagonally, both within his plane and vertically. The Pawns step one space (or two spaces initially) towards the opposite corner, and cannot move vertically. Pawns capture as they move, like the other pieces, and unlike Chess Pawns.
The triagonal move of the Knights is interesting, because a Knight can only reach 16 spaces, one quarter of the board. The Knights of one side together cover only half the board. One could regard this as a flaw, but I do not think it is—there is a pleasing symmetry due to the opening placement of the four Knights of both sides. The two sets of Knights do not cover each other's squares, so opposite-side Knights can never capture each other, and together the Knights of both sides cover all spaces on the board. I am sure this special move of the Knight has interesting strategic implications.
The rules of 3D XYZ Chess are very clean and logical. The decades-long period of development and testing shows. The altered powers of Knight, King, and Pawn are perfectly suited to the 4x4x4 three-dimensional environment. The setup in opposite vertical corners is excellent. This is a game that deserves to be studied to develop principles of good play, from opening to endgame. The set itself is beautiful, and guaranteed to create a stir if you take it into a coffee shop to play, as I have done (in pre-Covid-19 times). In my opinion, 3D XYZ Chess is a brilliant translation of regular Chess into a three-dimensional environment. This game is highly recommended, especially for someone with an interest in 3D games, and 3D chess specifically. In the meantime, you can get a set or just a rules booklet from Rick Hewson. ~ KH