The Chess Variant Pages



Breaking a Promise

A few hours ago, I wrote to hansb and promised I was finished adding 3D files. Usually, I do better at keeping my promises. For example, I promise at least one more file after this, about 3D Great Chess.

Pawns

Pawns are easy? Yes and no. You can't just say "Rook move, Bishop capture", because then the Pawns have too much mobility and don't feel like Pawns.

A 3D Pawn must move straight forward staying on the same level, and to capture it has 8 different squares available.

Think of the Pawn at the center of a 3x3x3 cube; of course, its scope is the 3x3 forward face of the cube. The center square of that face is where it can move, the other 8 squares are where it can capture. Now it feels like a Pawn.

Of course, the double step and en passant rules are still good.

Castling

It's nice, in 2D Chess, when you have the choice of castling in either direction, so you wait; when you see how the game develops, you castle to the safer side. It's even nicer when your opponent tries to do this, you sacrifice a piece, give check, and win because his King never gets to safety.

In 3D chess, you should be able to Castle in 3 dimensions. I've decided to allow castling in 8 directions. You can Castle with the furthest-away piece in the initial setup, by moving the King two squares towards it and hopping the other piece past it; and of course the normal rules apply, the other piece may not have moved, you can't castle into, over, or out of Check.

In one case, you have to pretend that the Rook started on a square that's past the end of the board: If the King starts on e1 of level 4, which we're going to call 4e1 for typographical reasons even though we'd rather have the level come last, in order to castle with the Rook on 1a1, the King goes to 2c1 and the Rook goes to 3d1.

I don't want you castling with the N on 1b1, even though I do allow you to castle with the Commoner on 1e1 or 8e1.

Sample Game

I should have mentioned that one other way to play this game is blindfold. That's what I'm doing here, so forgive my bad moves.

(In order to play 3D blindfold, I look at a 2D slice of the board, looking at different slices as needed.)

1. 4e2-4e4

Moving the Pawn in front of the King fights for the center and opens the way for 3 different Queens and 3 Bishops and 2 Commoners.

1. 4e2-4e4 4e7-4e5 2. Q4d1-4h5?! 4g7-4g6!? 3. Q4h5:4e5+ C5e1-4e7

Guilty of two-dimensional thought? Of course, 2. Q3d1-7h5 is weaker because it does not attack 4e5; and even in 3D, there is no Knight move that attacks the Queen while defending the Pawn. Now, the R on 4h8 is defended by the other Rooks on h8, and Black stands to gain some development: sacrificing one Pawn out of 64 doesn't seem like much.

The next move is also on the same level, because 4f3 has already been traversed by a piece (so blocking it is no big deal).

4. N4g1-4f3 B4f8-4g7 5. Q4e5-4g3 N4g8-4f6 6. N4b1-4c3 K4e8-4g8 (O-O)

What notation for castling????

Yes, I'm just moving on one level, mostly to be perverse. Although N4g8-4f6 blocks the Bishop's diagonal, N4g8-5f6 blocks a different diagonal; and so, who can say which is better?

7. 4d2-4d4? N4f6-4h5!

White gets center control, both Pawns attack 5e5 and 5d5 and 3e5 and 3d5; but it's a blunder.

7. 5e2-5e4 3d7-3d5

This attacks 4e4. Striking at the 3D corner of the 3D phalanx.

8. 4e4-4e5 N4f6-3e4

If instead N4f6-4e4, the advanced Black Pawn might help shield White's King. 9. N4c3:3e4 3d5:3e4 10. N4f3-5d3

Attacking the Pawn at 3e4, and of course Black will not defend it.

6d7-6d5

Counterattack, undermining 4e5, clearing the way for more pieces.

That's enough of a sample. I'd rather have Black in this position.

Other Opening Ideas

Starting with an e-Pawn is good, because it frees the way for some diagonal pieces that can check the enemy King, and starting with an e-Pawn near the King is good because it clears the way for pieces that must move so you can castle.

However, many other moves are also good. 1. 5d2-5d4 is an obvious choice, but even 1. N2g1-3f3 is pretty reasonable. Bird's Opening, 1. 3f2-3f4, is not completely illogical, and even Grob's Angriff might possibly be playable.

The 3D version of the StoneWare opening, 1.1a1-1a4, must certainly be too decentralized, but it is interesting to notice that 1.2a1-2a4 allows the R at 1a1 to attack 7a7.

For serious openings, I'd suggest starting with any any d,e Pawn from the 3rd to 6th level, or a c Pawn from the 4th or 5th level. Beyond that range, it's probably too decentralized to be "perfect".

Clearly logical is 1. 4e2-4e4 4e7-4e5 2. N2g1-3f3, approaching the center in all senses, and preparing to castle "diagonally". I wonder, however, if White can then run into trouble by getting too many Knights crowding into one area.

Similarly, after 1. 4d2-4d4 4d7-4d5, the obvious Queens' Gambit move is 2. 3c2-3c4, approaching from far outside (can Black take and keep the gambit Pawn? Would it be wise to do so?); but on the other hand, 2. 3d2-3d4 is pretty tempting at first glance (but wouldn't you simply expose a Queen to loss of tempi?).

It is interesting that a Kings Gambit/Queens Gambit sort of position where Black tries to take and keep the gambit Pawn evidently must create an entire 3-dimensional area where both sides have weakened their formations; and so in the 3D game, the consequences are 3D but things are otherwise largely the same as in the 2D game.

1. 4d4 4d5 2. 3c4 4d5:3c4 4. 5e4 3b5 (better than 2b5, isn't it? After 2b5, in some lines the White B at 6f1 can capture 2b5 with check; likewise, after 4.3e4 2b5 is a better answer than 3b5.)

This looks like a tough position.....

Endgame Note

Imagine your King at c1, and the enemy Q at c2, defended. It's checkmate, 3D or not. With Queen plus King versus a bare King, it is possible to mate but not (I think) to force mate.

A 3D Problem

All pieces are on the 4th level:
White has King e1, Pawn g3 and h2, Rook h1, Knight d4, c4, b4,a4.
Black has King e4, Knight a1.
White to play and mate in two.

The solution is easy, and works in 2D as well as 3D (the moves are the same in 2D, but the position is strange because why would you have so many Knights?).


And how about this: White Kb3, Nc3, Be3, Black Kc1; this is mate either in 2D or 3D.

The interesting thing about this one is that it's pretty hard to mate in 3D with so few pieces.

Summary

Just by playing a few moves blindfold, I was able to determine that the game is easy to learn (though some of the 3D possibilities will take time to get used to), and that it is Chess, not a chess variant.

This really is a true translation of Chess into 3D, feels like Chess, what more could you want?

The problem, of course, is that the games are going to take a lot longer to play. Because there are 8 times as many squares and 8 times as many pieces, I think the game may take 8 times as many moves. If you play fast, something like a 5 minute game of 3D, the game will take 40 minutes or even an hour, just as long as if you were playing a fast game of Go. (Or maybe not; there are 8 times as many Rooks and Knights, but only one King! You might be able to mobilize some Really Big Mating Attacks.)

Oh, that's not so bad then. People do play Go. It is a pretty popular game, even though it takes a while.

In that case, the only problem with the game is that we don't know whether the King is too mobile. Is checkmate too difficult to achieve? I think it's okay, but I don't know it's okay. When I was thinking about this problem, I composed the problem you see above; perhaps this situation is exceptional, but mating the King in the middle of the board in this one case didn't require any more material in 3D than in 2D.

I also learned that any computer program that might be made for the sake of this game (whether the program is an opponent or merely a display that allows two people to play) should offer the player the option of seeing any of the 24 possible 8x8 slices of the board.


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