3 Dimensional Cubic Chess 8x8x8 Board

Another reason why 2-1-0 is best.

The answer to your question is that it's half. To see this note that (2,1,1) + (-1,-1, -2) = (1, 0, -1). So you get all the 1-1-0 moves, which covers half the cubes. Parity (evenness of sum of moves in each of three directions) means you can't get more than half.

3d bishops are restricted quarterly though I think. (1,1,1 or 5,5,5..etc triagonal moves)

So your 3d bishop only moves N-N-N?

That gives you 2-0-0 which gives you 1/4 of cubes, but that is all.

To prove that informally, the parity (even/odd) of each dimension of a reachable location always has to be the same as the other two dimensions (because it is for each basic move). That means that you can't get to 1-0-0 or 1-1-0 or 2-1-0 (and same with signs) which leaves you with exactly 1/4 of the locations on the x-x-0 plane, and the same for any other plane, since you can get to at least one location in each.

No, that's why I don't prefer only 3d diagonal moves for the bishop, and my 3d bishop moves both like a 2d bishop and a 3d bishop, just like the knight. It basically can move to any cube a kings move away except the rook-like moves away. 60 cubes total I calculated. A bishop on "5d5" for example:

5th level:

Could move to these cubes:

Level 5:

Level 4:

Level 6:

Level 2:

Level 8:

Get the idea?

It's also interesting to note that bishops that move only triagonally is restricted quarterly, can only access 1/4 of the cubes (think of the four triagonal moves possible within any 2x2x2 sub-section). An exclusively 3d bishop on any one of those lines could only move back and forth between the 2 cubes on that line. 2 cubes on different triagonal systems could never both be reached by a 3d bishop, which is why I included 2d moves.

There is so much interesting information here.

Not to brag but probably the only actually interesting chess "variant". Although it's a dimensional extension, not a variant. No changes are being made to the rules, board size, or piece types. Everything is bring scaled up 1 dimension.

You need 8 boards irl

Would have to be a digital interface really.

Movement is that it can turn upwards or downwards

You can play it with less 3d players, i ma do it irl

I did it and it was a lot of fun, the movements of pieces turning upwards

Knights are very powerfull

Queens are devastating

And a rook can go to any other layer in the game

Careful, the site sometimes warns people for 5+ consecutive posts lol

But yeah the Queen can move any number of cubes in all 26 directions, which ends up being 86 cubes in total (from a central position).

I wonder how many queens it would take to force checkmate (not just a checkmating position) but actually able to force the long king from the center to the face/edge/corner of the board.

In fact just looking at the kings and queens for now is the best way to start discussing 3d chess because there's no argument about how the piece movement should be scaled up to 3d. King, one cubes in any direction. Queen any number of cubes in any straight line direction, just like 2d chess, simple. 2 queens can checkmate a king in the center with this well known pattern:

How many queens would be needed for a similar pattern in 3d where the queens have to cover 26 different cubes this time!

2 probably

Bishops can do straight but into other boards and its pretty fun to use them