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3D Chess, a Different Way of Looking at It. A scheme for a geometric translation of 2d piece moves into 3d.[All Comments] [Add Comment or Rating]
ChrisWitham wrote on Wed, May 1, 2002 07:12 PM UTC:
David Howe wrote on Wed, May 1, 2002 09:02 PM UTC:Good ★★★★This is an interesting idea. Here's a logical extension of it:
<p>In 2d chess (thinking in the abstract), pieces are 0 dimensional (ie. points) that move in a line (1 dimensional movement).
<p>Perhaps in 3d chess, pieces could be 1 dimensional (ie. line segments) that move (as suggested) in a 2 dimensional plane. Their direction of movement would be constant, it would simply be their area of movement that would cover a two dimensions.
<p>In the diagram below, the 3d Rook piece at [a1,d1] could move to [a2,d2] or [a3,d3]. It would be blocked by the 3d Bishop piece at [c4,d4]. It could, however move to [a1,d1] on the next level up, assuming no friendly pieces are blocking it. However for the 3d Rook to move to the other half of the board (ie. files e-h) it might have to rotate. Or then again, perhaps in that direction it only covers a single rank instead of a plane.
<pre>
+---+---+---+---+
| | | | | 6
+---+---+---+---+
| | | | | 5
+---+---+---+---+
| | |---B---| 4
+---+---+---+---+
| | | | | 3
+---+---+---+---+
| | | | | 2
+---+---+---+---+
|-------R-------| 1
+---+---+---+---+
a b c d
</pre>
Anonymous wrote on Thu, May 2, 2002 12:17 AM UTC:I hadn't even thought of that. The next step is to find out how to implement it. On an 8x8x8 board it would make sense to have each large piece to take one column. But then you would have a normal chess game, as near as I can see, for this reason they would need to be less than 8, which has been the standard size of everything so far, long. I would welcome your imput on how long they should be, and how to implement a 1 dimentional bishop, I don't think that it should be the same as a rook. If I can think of a way to do it i might try to make a second 3d chess variant that utalizes this idea, if you can think of a good way to implement it please tell me. All of this so far assumes not rotation, if rotation can happen then the best set up I can think of would be each piece in its normal place, taking up the entire column, if no one rotates any pieces it is a very odd looking game of normal chess, but when rotation does occur things get more complex elemets appear. If anyone knows of a good rule for rotation, or has any ideas on how to implement smaller than 8 sizes of 1d piece please say so here. On two final notes, I'm trying to find a system to extend chess into nth dimetions, useing point based pieces. This would be too big to have in reality, unless your nuts like me. Second I'm sorry about my gramma, spelling, and general writing style; I write how I think which is sometimes confuseing even to me.
A couple of off-the-cuff ideas: Rotation: A rotation of a piece would count as a move (a la 3M's Ploy), but perhaps should be limited in such a way as rooks remain rooks and bishops remain bishops, etc. Size: Pieces could start at eight squares, and change size as a move. That might be interesting, because a shorter piece would have less influence but might be able to slip through places otherwise blocked.
ChrisWitham wrote on Thu, May 2, 2002 01:05 AM UTC:This is how i see rotation as playing out, each piece is 8x1x1 and acts like a normal 2d piece because it can only move in two dimentions, but by rotateing it (in multiples of 90º) you can change which 2 dimentions it can move in. What I'm not sure about is what it would rotate around, if the piece is to rotate around it's middle it could only rotate when in one of the center squares. In this idea 3d moves don't really matter. But if the piece size is changeable then 3d moves could happen, then the question is what type of 3d should it be? I'm not sure how this (the 3d moves presented here) would translate with a piece that takes up more then one square, I'll look into it when I have the time.
David Howe wrote on Thu, May 2, 2002 06:25 PM UTC:I was thinking of a setup such as:
<p>Each piece is a vertical line of length 4. The leftmost white Rook (for example) would initially occupy a1 on levels 3 though 6. The leftmost white Knight would occupy b1 on levels 3 through 6. Etc. Black pieces would occupy similar positions on levels 3 through 6.
<p>Rotation would be allowed, but only allowing pivot points on the ends of the lines. Rotation would require an entire move and capture by rotation would not be allowed. For white pawns that have been rotated to be horizontal, forward is up. For black pawns, forward would be down. Pawn promotion would still only occur on the last rank (and not the last level).
ChrisWitham wrote on Thu, May 2, 2002 07:16 PM UTC:That sounds like a good set up, do you see moves occuring in the same patterns as I presented above, just wider in one dimention, or do you think that a more tradional, or even entirely new move system should be used? I'll draw up move diagrams with 4x1x1 pieces, do some calculations and see how it comes out, but I'm almost entirely sure that the pieces will come out stronger than they should be. It shouldn't be hard at all to do the same for tradtional 3d moves so I'll do the same for them.
ChrisWitham wrote on Thu, May 2, 2002 08:11 PM UTC:Well I'm not going to figure out how my moves would work with larger pieces because I thought to begain with the biger pieces would be too strong, and I guess I was being optimistic, because the the pieces would probably be able to get to almost every square in one move. On the other hand I found the tradtional 3d moves gave intresting results: the bishop was far stronger than the rook. I think that an entirely new system of 3d moveing would have to be created for 1d pieces to maintain normal values. I don't think that I could make a new one that fits well with the 1d piece, on the other hand you guys seem pretty smart so maybe one of you can.
gnohmon wrote on Sun, May 12, 2002 05:32 AM UTC:Good ★★★★Although I haven't playtested your idea, it does seem to me that perhaps it makes the pieces more powerful; and this could be a good thing because the 3D King (as I found in my own examinations of 3d chess) is difficult to checkmate.
benito wrote on Sat, Aug 3, 2002 01:52 AM UTC:Good ★★★★who is they?
Nicholas Kuschinski wrote on Thu, Mar 20, 2003 09:49 AM UTC:While a technically correct study of the geometrical tossing of chess moves onto a three dimensional plane, I think this should remain in the 'concept' stage, being more of a mathematical framework than an actual game. I mean . . . would you LOOK at your diagram for the queen? She can move to well over half of the places on the 512 square board! The knight, on the other hand, having a total of 40 moves, is actually an extremely weak, well nigh insignificant, piece. It MIGHT be possible to actually play the game, but it would have little relation, if any, to chess. If you wanted to go through with this, either make the nights more powerful, or get rid of them; and do something to the pawns because all they really are is obstacles and I see no reason to pretend that they aren't. Also, I'm pretty sure that no matter what the initial board arrangement you chose is, white has a one move advantage that will tip the scales dramatically in its favour. I suggest that you change the goal from checkmate into capturing all of the opponent's pieces, for fairness.
Chris Witham wrote on Thu, Mar 20, 2003 08:13 PM UTC:I agree it would be hard to play. In fact I think I might go nuts if I tried. But you comment on the moves available to the queen seems ill placed; the queen, when on a centersquare can move to 44% of the places on a normal board (four less than half). This queen moves to 53% of the places (15 more than half) when on a centersquare. There is a 19% difference (which any scientist would say makes the idea of them being the same absurd) but all things considered I don't think it's that bad. As for the knight it is quite different in power, it has changed from control of 12% of the board to 7% (percent difference equals 52%) and this is because I worked off of a basic concept of the knight which didn't give it much power. I agree it is a weakling. The one move advantage might be defeated by surrounding the pieces with pawns rather than using the traditional 8, or more likely could be solved by having a plane of pawns rather than a line. I think that the game should be quite playable, although I have not personally tortured anyone with it. All and all your points are good, and I tried to make the pieces be like chess not the game, so that is why it would not play like chess. It’s nice to know that people do read it. By the way, pawns are meant to be obstacles, as I understand it, so had I given them more movement options it would have changed everything.
gnohmon wrote on Fri, Mar 21, 2003 05:19 AM UTC:Excellent ★★★★★Having the second part of the move be 'up to' the same number of squares (rather than exactly the same, as has been done in some two dimensional games) is correct, it's a very good idea. I have raised my rating from good to excellent.
Charles Gilman wrote on Fri, Apr 18, 2003 08:41 AM UTC:All this effort to make checkmate easier seems a lot more complicated than simply reverting to counting bare King as a win, as was the case in 2d before the Queen and Bishop were introduced.
Chris Witham wrote on Fri, Apr 18, 2003 11:01 PM UTC:I've been thinking about this and the bishop move seems far to complex. Also I think that there is a simpler way to give the rook it's move, If the rook moves as a bishop, or as a rook followed by an optional bishop move outward it will cover the same squares. However it will not cover any twice, and it will follow a path that at least somewhat resembles a straight line. For the bishop I think that a 3-d move followed by an optional bishop move outward. And of course the option to move as a bishop. The possible moves make the outline of a cube at any given distance from the piece, this is good because the rook move makes the outline of an octahedron (a cube's dual.) This has a few advantages over the old one, first off it separates the playing field into 6 equal parts (assuming it were in the center of an odd-ordered board) as opposed to the old one which separated it into 14 unequal parts. Second it is far more elegant and easy to understand than the older version. There were others but I’ve forgotten. The biggest problem I see is that the new piece isn't colorbound. Finally the Knight is missing part of it's move, it should move as shown as well as jumping diagonally one space followed by a obligatory three spaces in a non coplanar three squares rook like. In three-dimensional notation that is (1,1,3). The extra moves return the knight to the exact percent coverage it should have, but other pieces have more than they used to so it is still weaker. This changes every piece, because the queen's move is changed, and the king's is also because now 3d moves are diagonal, so it can now move to every space in a 3x3x3 cube around it. The pawn can now move one space forwards, or capture in a donut around the space it can move to. As I said before, I think that an entire plane of pawns occupying the second and seventh rows of each level might be a good idea. I guess that’s it, maybe I'll send in an update. P.S. Thanks gnohmon I appreciate the changing to excellent.
Charles Gilman wrote on Mon, May 5, 2003 08:21 AM UTC:Good ★★★★Having looked at this again I have got to grips with your idea. What puit me off was the use of names. To me and, I suspect, to most people into 3d Chess, Rook means something confined to the 6 orthogonal directions, Bishop something confined to the 12 diagonal directions, and Knight a 2:1:0 leaper. Queen may be either Rook+Bishop or Rook+Bishop+Unicorn; I prefer the former, with Duchess for Rook+Unicorn, Governor for Bishop+Unicorn, and Empress for all three, along with Emperor for a King that also moves one square triagonally. For your pieces I would suggest names making a clear break with these linear ones, based on the theme of Plane as a reflection of the scope of the moves and a pun on a far greater flier than a Rook! Plane itself cannot be used as it shares the initial of Pawn, but you might reflect the relative powers of the pieces by calling your first piece a Jetplane and your second a Biplane, which has the advantage of starting with the first two letters as Bishop. The combined piece might be called a Hyperplane, and the ruling piece is the same as my Emperor above. This frees up the initial K to call your fifth piece a Kite, which rhymes with Knight.
I've been thinking on this a lot lately and I think I've made the game better. I still have yet to program it into a computer or find someone who is crazy enough to play, so it is all theoretical. First off the diagonal move has changed. That changes the bishop, king, queen, and pawn. Second I’ve redefined the knight. Also as suggested I have come up with new names for some of the pieces. The rook is now the octahedron, because it’s move makes the outline of an octahedron. The new bishop is a cube, because it’s move makes the outline of a cube. The old bishop, not used, would be a cubeoctahedron. (When I say 2d rook or bishop I mean the normal chess version as translated into three dimensions. So a 2d rook moves in a line forward, backward, sideways, straight up, and straight down.) The new bishop (cube) move is one moving as a 2d bishop, moving as a three dimensional mover (unicorn) or moving as a 2-d bishop then a three-dimensional mover outward. The new bishop is not colorbound. A picture of the spaces covered is here: http://members.lycos.co.uk/christhecynic/hpbimg/Chess/cube.bmp The pawn moves one step straight forward, or one step forward as a cube, which is one step as an ordinary bishop or one step as a unicorn. http://members.lycos.co.uk/christhecynic/hpbimg/Chess/pawn.bmp The king moves as a bishop or as a rook, thus covering the entire 3x3x3 cube around it. The queen moves as a bishop (cube) or a rook (octahedron) http://members.lycos.co.uk/christhecynic/hpbimg/Chess/king.bmp The knight moves one step as a bishop then one step straight (orthogonally) outward. This no longer follows the “squares a queen can’t go to” rule, but it is closer to the appropriate value, though still weak, and it does seem a bit more elegant than anything else. I wanted to show a picture of each of the pieces, especially the ones that were changed, but my computer goes to hell every time I try to upload a new image. The rook (octahedron) as I think I’ve already stated moves as a 2d rook, a 2d bishop, as a 2d rook then outward as a 2d bishop. http://members.lycos.co.uk/christhecynic/hpbimg/Chess/Rook.bmp The queen moves as a bishop (cube) or a rook (octahedron) I don’t know what you would call it as cubeoctahedron would be the name of the old bishop. http://members.lycos.co.uk/christhecynic/hpbimg/Chess/RookCube.bmp - There may be space for additional rules. For example a rook blocked on orthogonal adjacent squares could still move as a 2d bishop. So perhaps it would be better to say that it moves once as a rook, then again at a right angle and then continues out as a bishop. While this sounds a bit confusing it should be simple to remember and will prevent the rook from moving when blocked. The same can be said for the bishop, if all three diagonals surrounding a 3d move are blocked it shouldn’t be able to use that 3d move. This is not likely to happen often, but if it does these two rules would eliminate an annoyance. On the other hand the rule itself might prove more annoying to remember. One thing that annoys me to no end is the freedom of movement behind the pawns. I can’t just add additional pieces to block it up, but I don’t want the pieces there so free to move around. One possibility, not elegant at all but the best I can come up with, is to have the space behind an unmoved pawn impassable. The exception would be the starting spaces of the major pieces. This would definitely restrict movement, and it would be easy enough to tell what was impassable, but it’s a bit of an odd rule I think. - I’ve also been thinking about other pieces. I think it is best to consider the Wazir as it is now, that being a one-dimensional single step. That does something I consider odd though, it makes it so that a Wazir rider is different from a rook (octahedron) also the Wazir, Dabbabah and (0,3) leaper are all very, very weak compared to their bishop based counterparts, which are not even colorbound. The crooked bishop has two possible moves, one where it makes a line, and one where it mirrors the rook (octahedron) I chose the second for the reason I always thought of the crooked bishop as a bishop version or a rook. I wanted to show a picture of this, but as I said I can’t upload right now. It looks sort of like ripples on a pond, if that makes sense. - At some point I should probably ask them to updatye the page, but before then I need to get the picture of the knight and probably make all of the pictures smaller.
What a brilliant concept.
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