3 Dimensional Cubic Chess 8x8x8 Board

Nah I used all the same standard chess pieces, just more of them and both 2d and 3d moves combines for each.

Your telling me that bishop should be able to change color is ridiculous. It's completely unnecessary, and I imagine you aren't actually visualizing what you are talking about, or you aren't stacking boards correctly. The example of putting a 2d classic chess board on it's side should show you that the pattern of colors on the board are a checkered pattern no matter what side you look at it from. Once you have that correct, you can see from simply looking at the 12 edges of the room you are in that the diagonal moves of the bishop follow the checkered pattern in all directions, all twelve directions. The bishop doesn't need to change color if the board is using the correct checker pattern across all three dimensions, as it should be for the board and the bishop. I'll say it again, you don't have a "real" 3D cube chess if you can't play it, you have a fantasy.

I literally just specified that a 2d bishop would never change color no matter what direction it moves. A 3d Cubic board the colors alternate in the 3d dimension too, each next layer is a mirror image of the one below it, simply placed on top of it. Of course no such board exists because how would one move the pieces in it? It would be solid. LOL

I actually dreamt about 3d chess last night and it inspired me to modify one of the rules. Casting in 3d chess could occur with 4 rooks since those rooks and the king would be set up like this:

White can castle toward any of the 4, but my modification is going to be that castling becomes a 2 step process. First, the king replaces whichever rook it castles with and the rook ends up next to the king, for example:

White castled "kingside" here. Next, provided the king and rook don't move again afterwards, they could castle a 2nd time with the rooks in the corners on whatever rank or file it ends up on:

Because remember, this is the initial set up in 3d chess:

So the king first castles with any of the 4 rooks directly in line with it, and then it can castle a 2nd time toward one of the corners with 1 of those 2 rooks. This would complete castling on a cubic chess board, fascinating stuff!

Games like this tend to be very drawish, as you need an unrealistically large advantage to force checkmate on a bare King. The problem is that pieces that move along lines just cover too small a fraction of space; it is very easy for a King to just step around those. What you need for an interesting 3d variant is pieces that are able to cover entire planes.

The so-called 'planar move' comes to mind; the Rook-like version of this can move to any square in a coordinate plane, as long as the rectangle of which the origin and destination squares are the opposit corners does not contain any pieces. This is a sort of restricted 'hook mover'; the latter could do two perpendicular Rook moves as well as just a single one. But it can use that to navigate around obstacles, which the Planar move cannot.

For other types of moves the plane of the move would also be defined by a pair of linear moves in different direction, which then define two sides of the 'rectangle' (which actually doesn't have to have 90-degree corners), while the same moves in the other order define the other two sides, and all cells within these boundaries should be empty for the move to be allowed.

It is true that the king could easily step out of the lines and has 26 possible moves from the center, but that's why this game would have 128 pieces on each side! Also, some of the pieces have access to 3d diagonal moves. While the king can move to 26 cubes the queen could move to 86 from the same position. Standard support mate of king and queen vs king still work on any edge, corner, or edge-plane. It is interesting to try and figure out the minimum material for forced checkmate though. 1 queen isn't enough. Is 2 Queens even enough?

The number of attacked squares doesn't necessarily tell you how useful the piece is for checkmating. For the latter you need a good concentration of the move targets, so you can close off all escape routes for the King. Moves that are widely dispersed are not helpful at all in this respect.

Your design is a bit strange in making the Bishop a compound piece by assigning it two non-equivalent move (the usual 3-d Bishop move, and the one along the body diagonal that is usually associated with the 3d Unicorn). I think it would be much more interesting to keep Bishop and Unicorn as separate elementary pieces, and then include all double compounds and the single triple compount of those. Since you already have so many pieces in the start position for geometric reasons, you might as well profit from it by offering some more diversity.

What I meant is that the same way that the king has alot of options for directions to move, each piece has more of a scope as well. That's why I included 3d diagonal moves for all the pieces. So while a king could move to 26 cubes, the queen could also cut off alot of those cubes. While the king still has more escape options than the equivalent in normal chess, the pieces do have more attack options as well. I included both 2d moves and triagonal moves in the same pieces so that the pieces would be consistent with each other. Otherwise a king could attack a bishop diagonally and the bishop wouldn't be attacking back. A queen could move in every diagonal while a bishop could only move in some. It also keeps similar piece power ratios to the normal 2d chessboard. The same way a pawn is like an upshifted king move on a standard board, being able to move or capture to 3 of the 8 squares a king could go to from that same square, by including 3d diagonal moves in the 3d board, the pawn could potentially go to 9 cubes out of 26 in a similar "upshifted king move". The available move cubes for the pieces if either only 2d or only 3d moves were allowed would look very bizarre. We think of the king for example as being able to move to "any square surrounding it", so to keep it consistent I'm making the 3d king have the same ability, any cube "surrounding it one cube away" which included 3d diagonals. And then I'm giving the other pieces the same power for consistency. The knight is the only piece I debated for a while, on whether to restrict it to 2-1 or 2-1-1 or both. I decided on both because if I thought if it were restricted to 2-1 only, it would then be the only piece not accessible to integrated 3d moves, and if it were restricted to only 3d moves, then it couldn't access all of the board! So both made sense because it meet the definition of a knight move better "closest squares/cubes not on the same rank, file, diagonal, or "3d triagonal", and that included "slanted L-shape moves". I'm not trying to claim my version would make the most playable best game, just explaining my reasoning as best I can without visual aids. So while the knight ends up being able to move to more than twice the number of cubes a rook could, it still isn't as powerful because the rook is still an unlimited range piece while the knight is only moving "radical 5" length jumps. As you said, the pieces have a higher than normal "escape scope" so that cancels out some of the "piece power" inconsistencies. So I feel all pieces should have both 2d and 3d movements instead of some pieces having some movements in different combinations.

A few of the "mating material" questions I have figured out. A king and only 2 rooks can mate the king on a sharp edge of the board. For example a white king on 8c6, white rooks on 8f8 and 7f8, checkmates a black king on 8c8. The white king guards any of the black kings "frontward moves", and the king can't step down to the 7th plane due to the rook there. A back rank mate becomes a "back plane mate" but doesn't work the same way. A king on the 1st plane with pawns on top of it on all 9 possible upward moves, would need 3 rooks to cover all 9 possible horizontal moves on the same plane. "Smothered" mate would still be simple, a knight checking the corner, with all other cubes occupied, but it doesn't work exactly the same way. Because I am giving the knight both 2d and 3d L-moves, not every cube next to the king would have to be occupied. A knight on 7c8 attacks a king on 8a8, but it also attacks 8a7. By the same token a knight on 7c7 attacks both 8a8 and 8a7 as well. Certain well known chess patterns are also preserved by keeping all 2d and 3d movement abilities consistent. We know that a king cannot move in this type of position:

By allowing a knight to have access to 3d L-moves, a king also will not be able to move in the 3d extension of that same pattern. Imagine a king on 1e4, with pawns of its own color directly above on all the 9 cubes it could move to on plane 2. Now imagine a knight on 3e4. That king also cannot move at all. If we were to give a knight only 2d L moves or only 3d L moves, this pattern wouldn't hold, as the king would have 4 escape cubes.

Another basic pattern, when we stack a king and bishop directly on top of a king, like this:

The king cannot move anywhere on the same rank, it has to step down a rank. In 3d chess, by giving a bishop access to both 2d and 3d diagonals, this same stacking configuration forces the king to step down one plane.

Now one seemingly major issue is my version of 3d chess, that I realized myself almost immediately, is that "a bishop is nearly 3x more mobile than a rook, how is that consistent with normal chess!!". That's simply because when you add a 3rd dimension, there are more diagonal moves than linear ones. This is the problem with basing piece power on mobility and then comparing them to other pieces. Just because a bishop has more total cubes to move to than a rook, does not mean the bishop can dominate the rook anymore than it could in 2d chess. In fact, this well know bishop + pawn trapping a rook position in 2d chess...

Doesn't work at all in 3d chess.

Let's even look at how a bishop limits a rooks normal movement in standard chess vs 3d chess:

Assuming the bishop is defended, the rook has 2 squares it can't move to, g2 and g8. Now imagine this exact same positioning in 3d chess, a bishop on 5d5 and a rook on 5g5, the 3d rook can't move to 4 cubes, but can still move to 17 unattacked cubes (21-4). The fact that the bishop also controls 8g8 (along the line 5d5-6e6-7f7-8g8) is meaningless as the rook couldn't move there from 5g5 anyway. The rook still has more freedom to escape a 3d bishop that's 3x as "mobile", than a 2d rook has to escape a 2d bishop that's less than 1x as mobile (13 vs 14 squares).

In fact, this kind of thing is why I absolutely cannot stand the way they teach beginners the "values" of the pieces. Even just in terms of 2d chess, the reasoning is inconsistent and sometimes just flat out wrong.

They say a bishop is worth about 3 and a rook about 5, but this only applies when both pieces are existing on a board with other pieces. A king and rook vs a king and bishop endgame is usually a draw. A king and rook vs king and knight endgame is usually a draw as long as the pieces stay close together. A rook vs pawn is a draw if the pawn and king are advanced enough. In fact the number of squares a bishop and rook can move to differ by 1. Only when the bishop is in the corner or the edge is it half the strength of a rook, (7 squares vs 14) but that's only because a rook can move to 14 other squares from any square, while the bishop has to be in the center to have its full 13 square options. A king and knight can move to the same number of squares from the center (8), but a knight can still easily outrun a king on an empty board. The problem is they assign piece values as if they exist in a void, which they don't. We say things like "a knight is roughly 3 pawns", yet find yourself in an endgame trying to defend against 3 pawns with a king and knight and you'll likely have trouble. The queen being 9 is the one that really gets me lol, first of all, no clue how they get that number, but 2nd, that's only 1 point more than a rook + bishop. I'd argue a queen = a rook + two bishops since it has access to both colors. A queen can move like a bishop while attacking like a rook, but you can't move your rook and bishop at the same time. The queen can fly like a rook and then suddenly attack on an opposite color diagonal, which even 9 same colored bishops couldn't do. You also can't move both your bishops at once. A king and 2 knights can control as many as 24 squares on a chess board, yet they cannot force mate against a king on the edge that can only move to 5. My point in bringing this up is that if the piece values aren't even accurate in 2d chess, they certainly can't be generalized to 3d chess in any meaningful way.

"Otherwise a king could attack a bishop diagonally and the bishop wouldn't be attacking back."

So what? That is normal, right? Under FIDE rules a King should be able to attack a Bishop without being attacked back.

I think the problem is that you think there should be only 6 piece types. While 3 dimensions leave room for many more. There are not 2 types of neighbor cells, but 3 types. By squeezing that into just 6 pieces you are forced to make unusual compounds. And then you can argue that this was the best way to do such squeezing, but the point of course is that there was no necessity to do any squeezing at all.

In 3d there are three different elementary sliders, moving in 6, 12 or 8 directions (together filling the adjacent 'layer' of 26 cells). In the next layer there are 5x5x5-3x3x3 = 125 -27 = 98 cells. Take out the 26 that could be reached by the sliders in two steps, and you are left with 72 'oblique' destinations. These are (0,1,2) moves, (1,1,2) moves and (2,2,1) moves, 24 of each. So there are three different types of elementary oblique leapers with range two, where in 2d there is only one. So why include only one of those, or combine several of the moves in one? You could include all, and/or three compounds of two of thoose moves.

That's a good point, but I think you might be misunderstanding what I'm trying to get at somewhat. I'm not saying a king shouldn't be able to attack a bishop. I'm saying a diagonal should be considered a valid diagonal regardless of what piece is using it. In 2d chess, if a queen is seeing a bishop along a diagonal, we automatically know that the bishop is also seeing the queen. If this isn't the case in 3d chess, it would essentially imply one-way diagonals. It would mean a queen exceeds the power of that of a rook and bishop simulatenously on the same cube. I did seriously consider at one point having separate pieces for "triagonal moves only" or what you said about the 2-2-1 knights which would be called "leapers". One thing I read online even suggested 3-2-1 pattern. But the problem there is that the moves get too random. It becomes less like chess and more like some weird 2d chess variant. One would need as many as 6 extra pieces to account for every unique pattern of moving, and would be too chaotic. Note a bishop only capable of moving on 3d diagonals but not 2d ones, would only have access to 1/4, (not 1/2), but 1/4 of the board. As it can only move to 2 cells in any 2x2x2 8-cube volume. It would also alter the definition of some of the already standard chess pieces. We know a king can move 1 square in any direction, and a queen is the same movement but can move any number of squares. A 3d rook and a 3d bishop as I described them here, would be equivalent to a queen mobility just like normal chess.

But to go back to your suggestion for a second, I would only add 2 "new pieces" in total. Break the bishops up into 2d and 3d diagonal moves, and break the knights up in 2-1 and 2-1-1 (its deceptive to say 2-1-1 because even that technically is a 2-1 move, just the "1" aspect is diagonal - it is still perpendicular to the initial "2" move), but I would start adding weird L moves like 3-2-1 or 2-2-1 or 3-2-2, because those no longer meet the definition of a knight anymore according to FIDE: "The knight may move to the closest squares not on the same file rank or diagonal".

"In 2d chess, if a queen is seeing a bishop along a diagonal, we automatically know that the bishop is also seeing the queen. If this isn't the case in 3d chess, it would essentially imply one-way diagonals."

But that is because orthogonal vs diagonal is a distinction that is only meaningful in 2d. In 3d there is not such a thing as THE diagonal. There are two different kinds of non-orthogonal directions, so calling both by the same name is bound to lead to confusion. By reserving the term 'diagonal' for the (1,1,0) directions, and calling the (1,1,1) directions 'unicornal', a Bishop that moves only diagonally would attack a Queen back that attacks it diagonally. It would just not attack a Queen back that attacks it unicornally. But so what? It would also not attack a Queen back that attacks it orthogonally. That is quite normal, for a piece that attacks you from a direction you cannot move in yourself.

"The knight may move to the closest squares not on the same file rank or diagonal"

You definitely should not consider steps that involve a coordinate change of 3; these would be generalized Camels/Zebras, not Knights. But the FIDE definition is ambiguous, because 'closest' can be interpreted in terms of geometric distance or in terms of King steps. In the latter case (2,1,0), (2,1,1) and (2,2,1) are all equally distant. But in the former case only (2,1,0) qualifies. (And this is indeed how the Knight in Raumschach moves.)

I didn't realize this at first but this statement is actually something I fundamentally disagree with. The thing with chess is that the rules aren't really arbitrary. They are based on pure geometry. The current 6 pieces account for every type of unique geometric movement in any dimensions. There are 3 ways to separate out different types of piece movements:

1. Limited vs unlimited range: The king vs Queen covers this distinction.

2. Different types of linear movements: The Queen, Rook, and Bishop take into account all those possibilities.

3. Non-linear movements: The knights

And technically a 4th one: Direction-limited: Pawns.

These cover all of the possible unique geometric movements. Linear vs non-linear, linear sub-types, and range. That is why chess is such a beautiful game, because every simple unique type of piece movements is covered once and exactly once by a piece. If you start adding other modifications to already-covered piece movements, like altering the shape of the L the knight takes or splitting hairs between different types of diagonals, it becomes random and arbitrary. A knight that follows some kind of prime number L, like a 5-3-2 pattern or something, or a 7-5-3-2 pattern in 4 dimensions..etc, isn't a new piece, it's just an arbitrarily altered knight. What I am doing is simply extending the existing piece movements into 3 dimensions, not adding new types altogether. There aren't any new types possible. Linear, diagonal, one-cell movements, non-linear, and Checker-pieces (pawns that can only move up) are the only 5 types possible.

Finally, there is also the issue of where new pieces would go in the starting position. If we follow standard chess rules, the rooks going on the outer most perimeter, followed by the knights, bishops, and queen, we get this set-up:

Plane 1:

And Plane 8:

Where would the hypothetical new pieces go anyway? I mean I guess you could alternate 2d bishops with 3d ones or something, and do the same with the knights, but I feel like that would be even more confusing.

Now the kings in my set-up are on different vertical files (1e4 vs 8e5), but from a 3d perspective I don't think this really matters at all.

Very true, but just 3 things I would like to expand on:

1. The types of knight moves aren't actually equally distant. 2 dimensional 2-1 knight moves are of distance [radical 3], 3 dimensional knight moves are of distance [radical 5]. It's interesting how even when you extend to 3 dimensions, the exponents do not change in measuring "distance". The 3 dimensional "hypotenuse" of a right triangle or "right pyramid", you add the 3 squares and take the square root, you don't take the cube root! Same for the formula for a sphere. A circle is X^2 + Y^2 = R ^ 2, and for a sphere it's X^2 + Y ^ 2 + Z^2 = R ^ 2, not X cubed + Y cubed + Z cubed = R cubed. It's stays squared!

2. I guess where we disagree is whether 2d and 3d diagonals are considered "different" or not. I view a diagonal as a move where the at least 2 of the 3 coordinates change. Emphasis on the words "at least", so the definition of a diagonal I'm using is "at least" 2 coordinates change. This includes diagonals where all 3 change (3rd dimension). Differentiating the two types out would imply diagonals where either "exactly 2 of the coordinates change" or "exactly 3 of the coordinates change". But to me, they are all just diagonals. In fact, 3d diagonal moves are weaker than 2d ones because there are 12 total directions a 2d bishop could move, but only 8 in 3 dimensions. In fact a "unicorn" would arguably be the weakest piece as it could only move to 1/4 of the board. Even a "zebra/camel" restricted to "only" 2-1-1 moves could access half.

3. I wasn't interpreting the knight move based on king steps or closeness. I was interpreting it based on the "closest non-linear moves it could make". Technically a 2-1-1 knight move is "further" from a 2-1 move strictly in terms of measuring the length of the straight line it forms connecting the cells, (radical 4 or radical 5 vs radical 3 - I didn't work out the math yet), but it is the same shape as a 2d knight move, it is only slanted. Think of a knight move as having to make the 1 sqaure move in a perpendicular direction to the 2 square part, when moving the knight 2 cells "up", any 1 square moves including diagonally, is perpendicular to the 2 cell part".

"Man, when computers solve chess, chess will become soooooo boring."

Meanwhile, 3D 8x8x8 chess being virtually unsolvable:

Think of a vertical L shape, being rotated 45 degrees clockwise. That turns it into a 3d knight move. But it can still be considered a 2-1 move, just a slanted one.

I doubt chess will ever be solved by computers. Even Quantum computers might not be able to, because the number of possible chess games is exponentially higher than numbers with the term googol in it. Maybe it could solve 10-12 piece tablebases or something, but 32 pieces is just too complex.

"Different types of linear movements: The Queen, Rook, and Bishop take into account all those possibilities."

They do in two dimensions, but not in three. 'Splitting hairs' over different kind of diagonal movement is not anything different from splitting hairs over the difference between othogonal and diagonal moves in 2d. The difference between a 3d Bishop and a 3d Unicorn is just as real as that between a 2d Bishop and Rook. They are not the same, so they are different. Mathematically that is all there is to say about it. That you appear to think (1,1,1) is somehow less different from (1,1,0) than (1,1) is from (1,0) is nothing but an unfounded personal prejudice, fueled by linguistic habits and limited vocabulary.

And your arithmetic leaves to be desired: in 2d the length of the Knight move is also sqrt(5), not sqrt(3), and the length of the (2,1,0) and (2,1,1) moves are sqrt(5) and sqrt(6), respectively.

Yes you are correct, as I said yet I didn't verify all the math, I was just using it to make the point that the distance being microscopically longer was irrelevant to the definition of a knight move. I forgot to squares the 2s.

Huge differences do exist in those comparisons between orthogonal and diagonal moves in 2d vs 3d. In 2d, orthogonal moves can access all of the board whereas diagonal moves can't. In 3d, the same holds true only if you restrict diagonal moves to 2d. Allowing a bishop to make unicorn movements as well, gives it access to the entire board, but it doesn't change the relative balance of power between the pieces. A 3d rook could escape a 3d-unicorn-bishop combo just as easily as a 2d rook can escape a 2d bishop. If what I was saying about the bishop vs unicorn movement was wrong, we would also have to argue for two types of kings, one that can make any 2d move and another that could also make 1 cell unicorn moves. But we don't. We just say the king could move 1 cube in any direction whatsoever and keep it as simple as that. Why does this change depending on how many moves you go along a diagonal. Why do we consider a king moving 1 cell over all the same, yet a bishop using a diagonal in one direction vs a diagonal in another direction, different? Should there be a 2nd type of queen that also can't move unicorn-like while the 1st type can? Should there be one type of pawn that captures within a plane and another type that only captures in a unicorn motion? If you are arguing that it makes no sense to only split hairs with the bishop.