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Joe Joyce wrote on Mon, Aug 22, 2005 11:25 PM UTC:Good idea about starting a thread about 3D Chess. I apologize to Stephane for clutteringup his page with all the extraneous material and debate. One of the mis-conceptions about planar pieces is that because of their wide range of motion that this somehow diminishes their tactical value. Basically turning a sniper position into a machine gun nest. They definitely make defending the King on an open field(or at least lightly-crowded field) almost impossible. But during the opening portion of the game, they are quite restricted in movement by the presence of other pieces. They get in each others' way. If they are only a small percentage of the ranked pieces on the field, the player would be reluctant to risk them without cause. The linear pieces would then be relegated to the front lines, taking the threats of theopposing planar pieces and blocking their potential moves. There is also the potential that planar pieces could be short-range. For example, their planes could be limited to 4x4. This would still give them quite an influence on the field. On one of the central cells of the 8x8x8 field, they could still command the entire volume. This might actually make for an interesting variant. Hmmmmmmmmm. Another restriction might be that planar pieces make only capture moves. They could then threaten portions of the field and an opponent might actually draw a planar piece into a negative position. Needless to say, the potentials of the planar piece is far from totally defined.
You're welcome Harry !! The debate didn't pollute my page at all, but appeared very thoughtful. I don't feel so much confident now as I become aware of so many other ways to find the 3D 'Graal'. As I took one way (extending linear pieces instead of expanding them) which is not 'forbidden' I will keep on, but I'm impressed by your 'Prince' game which mingles omnipotent planar pieces with extended linear pieces, corresponding to all sort of 3D movements. For my part, I intend to write another 'Cross3D' variant where I will allow a double move of pieces of the same kind, to recover the same influence (and 'feeling') in 3D as in 2D, and checkmate the King more easily.
8x8x8 Interactive 3D Board. Check it out. DOWNLOAD it for FREE. I hope that multiple variants can be played on this board! http://thehinge.net/3dchess any questions or ideas can be sent to [email protected]
Stephane Burkhart's Cross3D Chess is the 8x8x8 variant where this discussion started. I proposed [2005-08-22] a sort of 3D-Shatranj on a 6x6x6 board, with a weakened King (3D Wazir) that moved in only 6 directions.
Index to Ralph Betza's 3D Chess covers multiple approaches to 3D variant rules, with Kings and Commoners on 8x8x8 cells. I forget the details, but I believe there was a lack of 3D symmetry. 3D Chess: Major Topics includes: Three Dimensional Chess Endgames, where he states that King, Queen, and Commoner versus King is quite possibly a draw in the general case. But he considers King and Two Rooks versus King to be a forced win. That is very unusual in 3d chess variants.
The way I understand it, the Ralph Betza Rooks aren't the same as Raumschach Rooks.
Grande Acedrex 3D - Part 1
A century ago Ferdinand Maack invented the 5x5x5 chess variant Raumschach. This new 6x6x6 game uses the currently fashionable square arrays of Pawns, while keeping the number of pieces reasonably small. Rooks, Bishops and Knights move the same way as before, making a 'two-dimensional move' in one particular 6x6 plane. The King is limited to 12 Ferz moves and 6 Wazir moves. The Queen combines the moves of the Rook and Bishop, giving it limitless movement in 18 directions. I have combined the sliding move of Maack's Unicorn with the 12 moves of a Ferz, resulting in a new Unicorn that can visit all 216 cells. Note that this is the only piece can change all three coordinates with one move. Minimum-Maximum number of possibles moves is: K 6-18, N 6-24, U 8-29, B 15-27, R 15-15, Q 30-42.
White Pawns start on level 2. They move a single step to the next higher level, either as a Wazir (noncapturing) or as a Ferz (capturing). Black Pawns start on level 5 and always move to a lower level. Yes, it is legal to have more than 30 Queens on the board. Checkmate is a win and stalemate is a draw. Here is a checkmate position: White King (1c3) and Knight (2c3) and Unicorn (2b2), Black King (1a1). The first coordinate indicates the level and the other two coordinates give the location on that level. Question: What is the longest forced mate with King and Knight and Unicorn versus King?
ALTERNATE SETUP: If 3 Queens result in too much excitement, try keeping a pair of Queens in each army 'on their own color' and replacing the third Queen with a Guard, a nonroyal piece moving like a King.
[level 1] [level 2] - - - [level 5] [level 6] . . . . . . . . . . . . 6 . . . . . . . . . . . . . B Q Q B . . P P P P . 5 . p p p p . . n k q n . . U . . U . . P P P P . 4 . p p p p . . r . . r . . R . . R . . P P P P . 3 . p p p p . . u . . u . . N Q K N . . P P P P . 2 . p p p p . . b q q b . . . . . . . . . . . . . 1 . . . . . . . . . . . . a b c d e f a b c d e f a b c d e f a b c d e f __ All original content __ / o\-- --/o \ \ \/ copyright (c) 2007 \/ / / \ / \ [====] by David Paulowich [====]
Grande Acedrex 3D - Part 2
The object of the game is checkmate, which can be a difficult task, even with the relatively weak 18-move King. So I am adding special promotion rules to create some new 3D chess pieces, powerful enough to trap the lone King. White Rooks, Bishops and Queens have the option of promoting any time they end a move in one of the 4 cells in the Special Promotion Zone: (6c3), (6d3), (6c4), (6d4). The 'Promoted Rook' moves like a Rook or a Gryphon. The 'Promoted Bishop' moves like a Bishop or an Aanca. The 'Promoted Queen' combines the moves of the other two promoted pieces. See Tripunch Chess, by the prolific Ralph Betza, for the 2D version of these pieces.
A White Pawn must be replaced by a Queen or Rook or Bishop of the same color upon entering one of the 36 level 6 cells. If the cell is in the Special Promotion Zone, then the player has the option of choosing the promoted version of the piece. Similar promotion rules for Black. No piece in this game can ever be 'unpromoted'. If you happen to find a 6x6x6 chess board in your attic, this game can be played with two cheap plastic chess sets and some thick red rubber bands to wrap around the promoted pieces. Spare Kings can substitute for Queens and you will have to improvise the four Unicorns from the leftover pieces.
__ All original content __ / o\-- --/o \ \ \/ copyright (c) 2007 \/ / / \ / \ [====] by David Paulowich [====]
Joe Joyce wrote on Thu, Jun 7, 2007 01:37 PM UTC:David, you've posted a radical 3D variant here. I'd love to see how it plays. Why radical? Because the pawns do not fill the 'pawn level' [as the pieces do not extend to the edges of the 'piece level'], allowing pieces to sidestep and bypass all the pawns. This ought to change the opening dynamics quite a bit. You commented in another post [Play this Game!? 6/6/07]: 'But after 100 years have passed, I would expect the Raumschach page to have a brief outline of how to force mate with King and three Rooks. Or is it four Rooks? Who is actually playing 3D chess variants nowadays? Does anyone still read Jim Aikin's page on the 4x4x4x4 game Chesseract?' The key problem in 3D and higher-dimensional chess variants is how to mate the king. The Yahoo CV group had quite an extensive discussion of this problem, with various solutions proposed which can be explained briefly here in a later post. The usual method is to restrict the king in some manner. On 4D chess, my understanding is that Chesseract had some popularity as a Zillions game. The 'slippery king' problem is magnified in 4D. I've [independently] designed a couple of 4D variants, and I admit to having considerable difficulty in reading and understanding Mr. Aikin's post.
Grande Acedrex 3D - Part 3
'The black pawns are shown as 'o' rather than 'p' simply because it's hard to see the difference between 'p' and 'P' at a glance.' - Jim Aikin, in Five Up. This 5x5x5 chess variant has queens (rook + bishop), wizards (unicorn + bishop), and guards (26 moves).
I have decided to change the definition of the king, allowing it to move to all 26 adjacent cells, and use a new setup with each player commanding 16 pawns and 16 other pieces. Every pawn is defended at least twice. Shogi was the original inspiration for my R, B, Q promotion rules. As before, the Special Promotion Zone is (1c3), (1d3), (1c4), (1d4) for Black pieces, which have the option of promoting at the end of any move in which the piece enters or exits one of these 4 cells. Another rule change: a Black pawn must be replaced by a queen of the same color upon entering one of the 36 level 1 cells. It never promotes directly to a 'promoted queen'. If the new queen appears in the Special Promotion Zone, then it has the option of making a later move (as an ordinary queen) and promoting at the end of that move.
Part 1 mentions a K+N+U versus K checkmate, which is still valid after these rule changes (one king now attacks the unicorn and the other king defends it). The question of the longest forced mate (K+N+U versus K) remains - it should be possible to hack some existing Zillions Rules File and change the unicorn's definition. After ninety days of increasing problems, I finally formatted my hard drive. Working on getting my email program up and running - it will be some time before I get around to re-installing Zillions.
[level 1] [level 2] - - - [level 5] [level 6] . . . . . . . . . . . . 6 . . . . . . . . . . . . . R U U R . . P P P P . 5 . o o o o . . r k q r . . B N N B . . P P P P . 4 . o o o o . . b n n b . . B N N B . . P P P P . 3 . o o o o . . b n n b . . R Q K R . . P P P P . 2 . o o o o . . r u u r . . . . . . . . . . . . . 1 . . . . . . . . . . . . a b c d e f a b c d e f a b c d e f a b c d e f __ All original content __ / o\-- --/o \ \ \/ copyright (c) 2007 \/ / / \ / \ [====] by David Paulowich [====]
Grande Acedrex 3D - Part 4
No castling or king's leap rules in this game. Previous Zillions Rules Files for 6x6x6 games include Monster 3D Chess [L. Lynn Smith, 2001-11-24] and Tim's 6x6x6 3D Chess [Tim O'Lena, 2004-03-20]. Tim O'Lena also has armies with 16 Pawns and 16 other pieces - the idea of placing the 4 Knights in the center appears to be unique to my chess variant. As for my Q, R, B promotion proposal, people on the Yahoo! 3-d-chess group were talking about stronger pieces a year ago. Joe Joyce mentioned [#1743] the Magician (Gryphon) from Maxima, but did not join it to a Rook. And L. Lynn Smith posted [#1877] an extremely powerful version of the 3D Rook called the Pulsar.
[EDIT: Decided to stay with my original coordinate system. Tim O'Lena marches his Pawns 'sideways', while mine move 'up' and 'down'.] I believe that my Promoted Rook (with 3D Gryphon moves) has 63 possible moves from the cell (b2B), consisting of 18 one-step moves and 15 lines (each 3 cells long) extending out toward the faces of this 6x6x6 board. I hope that King and Promoted Rook can force a lone King into a mating position. Time will tell.
1a- 1b- 1c- 1d- 1e- 1f- * 2a- 2b- 2c- 2d- 2e- 2f- * (etc.) and 1 2 3 4 5 6 are the coordinates required for six boards on a preset. Note that the Raumschach preset starts the Black pieces on 'level A'. [2008 EDIT] I have created a Grande Acedrex 2007 preset - I do not intend to play this variant, but this preset can be adapted for other 6x6x6 games. Try moving 'N 1c3-2b1' to see BLACK's upside down view of the board. This move has the benefit of freeing up a square for the King to later retreat to.
On November 4, 2001, David Moeser made posts #976 and #977 in Yahoo chessvariants, suggesting that the Unicorn in Raumschach be replaced by a Ferzicorn. That is the first mention of the piece I am calling a Unicorn in my game. Here is an endgame position, with all four pieces on dark cells (empty dark cells are marked *). White: King (3b2) and Knight (3d4) and Unicorn (1c3), Black: King (1aA).
level 1 - level 2 - level 3 * * * | * * * | * * * 6 * * * | * * * | * * * 5 * * * | * * * | * N * 4 * U * | * * * | * * * 3 * * * | * * * | K * * 2 k * * | * * * | * * * 1 a b c d e f - a b c d e f - a b c d e f 1. Unicorn-2b2 check, King-1b2 2. Knight-2d2 mate. level 1 - level 2 - level 3 * * * | * * * | * * * 6 * * * | * * * | * * * 5 * * * | * * * | * * * 4 * * * | * * * | * * * 3 k * * | * U * N * | K * * 2 * * * | * * * | * * * 1 a b c d e f - a b c d e f - a b c d e f __ All original content __ / o\-- --/o \ \ \/ copyright (c) 2007 \/ / / \ / \ [====] by David Paulowich [====]
Piece Values on 6x6x6 I am calling the original triagonal mover in Raumschach an Alicorn and the (Alicorn + Ferz) compound a Unicorn. After looking over the ZRF for Tim's 6x6x6 3D Chess, I decided to set the Knight equal to 30 points and use Zillions to calculate some numbers. NOTE: I had to estimate the Alicorn value by subtracting the Rook and Bishop values from the Queen, which is a (R+B+A) compound in both 3D variants. That approach is consistent with Zillions behavior I have observed in other games.
P=6.4, A=13, R=23.8, N=30, B=30, Q=66.8
Now I am going try a very simple pencil and paper system. Set the Pawn value at an abitrary 10 points. Start estimating the other piece values by adding their minimum possible moves (from one of the 8 corners) to their maximum possible moves (from one of the 8 central cells).
Alicorn 5+17=22 Rook 15+15=30 Knight 6+24=30 Guard 7+26=33 Bishop 15+27=42 Unicorn 8+29=37 Queen 35+59=94
I am mostly interested in 3D variants using weaker pieces than this 26-directions Queen, so I have little knowledge of it. Perhaps its true value is somewhere between 80 and 100 points. The (New! Improved!) Unicorn can visit all 216 cells, which suggests that it is actually worth 3.7 Pawns. I would multiply the (limited to 108 cells) Bishop by 0.8, resulting in a value of 33.6 points, and the (limited to 54 cells) Alicorn by 0.6, resulting in a value of 13.2 points. The Rook can reach any cell on an empty 3D board in three moves, which often turns out to be one move too late. Setting it equal to the Knight seems reasonable. All in all, this 'pencil and paper' system seems to give surprisingly good results. But one thing I have learned from playing chess all these years is not to push my luck too far. I do not trust Zillions, nor my little system, to cope with the subtle behavior of the 5x5x5 Raumschach board, where (my) Unicorn still attacks 28 cells from the unique central cell.
[2008 EDIT] I added the Guard moving like a nonroyal King. Worth 33 points, its value almost equals the adjusted 33.6 points of a Bishop. There are legal checkmate positions involving King and Guard against a lone King.
Space Shatranj 6x6x6
I have edited my [2007-06-12] comment here to include a Grande Acedrex 2007 preset, a game with complicated promotion rules. Space Shatranj 6x6x6 is a new chess variant based on the same initial setup - given in my [2007-06-9] comment. After I finalise the rules, I plan to copy this preset and rename it. Checkmate and stalemate both count as a full victory. A Bare King Ending is counted here as a partial victory (0.75 point) and a partial loss (0.25 point), see Rule 5 for more details. The 'Fifty Moves Rule' is extended to 60 moves in this variant, with a very restrictive clause added: after you have been reduced to a bare King, your opponent has at most 60 moves to either checkmate or stalemate you - failure to do so means a partial (0.75/0.25) victory. White Pawns move up one level at a time and promote to Queen, Unicorn, Bishop, Knight or Rook (of the same color) on level 6.
I use the names 'Alicorn' for the original triagonal mover in Raumschach and 'Unicorn' for the (Alicorn + Ferz) compound in this variant. Designing a game with these pawn walls (16 white on level 2 and 16 black on level 5), lead me to a 6x6x6 board: which is large, but perhaps not one of the Very Large CVs. Space Shatranj 6x6x6 can be played with two identical chess sets, provided you turn one King and one Queen on each side into Unicorns - by placing small bags on top of them, or something.
level 4 - level 5 - level 6 * * * | * * * q | * * * 6 * * * | * * * | * * * 5 * * * | * * * | * * * 4 * * * | * * * | * * * 3 P * * | * * * | * * * 2 k * * | t * * * | K * * 1 a b c d e f - a b c d e f - a b c d e f NOTE: T=Unicorn, G=Bishop, N=Knight in the preset above. White has one legal move here: 4b2-5b2, allowing the Black Queen to capture the Pawn: 5f6-5b2 stalemate, as both Queen and Unicorn control all three escape squares on level 6. __ All original content __ / o\-- --/o \ \ \/ copyright (c) 2008 \/ / / \ / \ [====] by David Paulowich [====]
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