## 3D Chess On Smaller Boards

These are actually 3D chess variants, not Real Chess.

What they have in common is that they are played on boards smaller than 8x8x8.

## 2x4x8 3D Chess

Cut the board in half, put one half on top of the other, apply the normal rules, and just like that you've got a game.

Let's say e1 is on top of a1, so we know which way is up.

#### Why This Won't Work

It seems that there are quite a few problems, but the major one is that the board is too narrow and shallow. Knights can reach from side to side and the King is always next to the edge.

#### When I Tried This Game

This seems to be an good game despite the cramped board.

It uses the normal set and board, and although you have to remember the up-down mapping, one or two games should be enough practice for you to get used to it. Thinking in 3D will still be hard, of course.

The Bishops are too short.

The most common error is wanting to move across the invisible borderline, for example Qd1-h5.

### Kings with Abstract Translation

When I first thought of 2x4x8 Chess, I was still using the old translation.

When you use the old-fashioned "abstract" translation to derive your 3D rules of movement, there's a 3D "diagonal" that isn't part of the game: imagine a White K on a1, a Black King on f2 (that is, one square above b2). In this position, White is stalemated.

So the first new rule is that if you're stalemated you lose, and the second new rule is that Kings may not make up/down moves except to capture (and Black's King starts the game at d8).

This is marvelous because King versus King is usually *not* a drawn endgame! One side always loses if the Kings are on different levels, and you need to figure it out long before you trade that last piece!

### Improved Rules for 2x4x8 3D chess: Bishops

Bishops and Rooks are too short. I offer two alternate rules; you can use either or both, or neither.

#### Three-and-a-half dimensions

Since you want to play Qd1-h5, why not allow it? The game is now a form of chess in three-and-a-half dimensions!

Perhaps Kings can use this extra dimension as well; I think they should be forbidden to.

#### 3D Cylinders

Each 4x8 level can be a cylindrical board (or a billiards board, of course).

This allows the Bishops to make nice long moves, but makes it very hard to checkmate. (And so perhaps billiards is better than cylindrical, unless you forbid the King to use wraparound moves.)

#### Both Rules at Once

Bishops must be stronger than Rooks if you use both rules at once.

When a Bishop moves Northwest from e1, it gets to choose either d2 or h2 as its next square; from d2 it could continue to a5 and then d6 to b8; from h2 it could continue to e5 and then either b6 to d8 or h6 to f8!

## My Opinion of This Game

You won't find a better 3D chess that uses the normal board and pieces.

Of course, the "best" 3D chess would logically be 8x8x8, but that is difficult in many ways.

## The 3x3x8 Board

A 3x3x8 board would be about the right size.

In order to fix the short-length problem of the Bishops, make it a billiards board. Getting used to the 3D bounces might be tricky.

To bring it back to 64 squares, cut out the middle square of the 3x3. This looks a lot like the Cylindrical Chess board, but it's different because the Knight can jump over the hole.

Mapping this to the normal board, we get something like: a1 on the middle level, and under b1; b1, c1, d1, top level; e1 under d1; and so on. (I'm far from certain that this is the best mapping).

Using a physical board, I would prefer to stack 8 of the 3x3 doughnuts on top of each other and have the players move up and down. The reason is that it's hard to reach into the middle of a wide 3D board.

You could use a similar trick with a 4x4x8 board, of course; on each 4x4, 8 squares would be missing. Different squares might be missing on different levels! (This would create interesting terrain.)

## The 4x4x4 Board

I should mention that you can buy 4x4x4 boards with a commercial 3-dimensional tic-tac-toe game.

## 747 Chess

What if only the center were 3 dimensional? A small 3D area, 4 squares in total, placed above e4-d4-e5-d5, would be easy to use and would have interesting effects on the game. This reminds me of the famous first-class lounge on the Boeing 747.

Rooks, Bishops, and Queens in the lounge would be near the center but would have very limited mobility; Pawns would be unable to advance and promote; Kings might seek deceptive safety here, and Knights would be okay (although even their mobility would be limited).

It seems like the lounge is a place where pieces get some safety in the center, but at the cost of some mobility.

## Bomber Chess

Here is a 2x8x8 game of 3D chess with two normal sets and two normal boards: Pieces (including Pawns and Kings) can never move up or down, but any piece on the upper board could drop a bomb straight down to the lower board (this would take a turn, and capture a piece on the lower board). The Kings would be on the lower board, of course; the King on the upper board would be a non-royal King, and wouldn't have to worry about check. You could give check either by occupying the square above the enemy King or by normal play on the bottom board.

This would work, of course; the only problem would be reaching into the center of the lower board when you needed to make moves there.

You could also extend this idea by adding a submarine board.

You could also cut it back a bit, and have only a few bomber pieces and just a partial board on the upper level. For example,

## Cloud-Hopper Chess

Above the normal board and pieces, there are 8 floating clouds and 4 Cloud-Hopper pieces (two of each color).

Each move, each player may either make a normal move on the normal board, move a CloudHopper from one cloud to another (possibly capturing an enemy CloudHopper), drop a bomb from a CloudHopper onto an enemy piece directly below (thereby removing that piece from the board), or move an empty cloud (but if you have no more CloudHoppers, you may not move clouds).

Clouds are grey, neither White nor Black, and can be moved by both sides now, except the one that was most recently moved, which is said to have a silver lining (and so it is marked by putting a silver coin on it). One exception: if you move a cloud, move a CloudHopper onto it, and then hey you get offa that cloud, it becomes the little white cloud that cried, and can move again.

Clouds move like Kings, but do not capture each other; and of course only one cloud may be above each square.

Cloudhoppers move like Knights, but only from one cloud to another. CloudHoppers may capture each other.

White's CloudHoppers start the game above b1 and g1; Black's Cloudhoppers start above b8 and g8.

Clouds start the game above b1, g1, b8, g8, e4, e5, d4, d5.

The built-in strategic tension is that in an open game, there may not be time to use the CloudHoppers, but in a closed game, they can be very important.

This game is only slightly 3-dimensional, is certain to be a good game and easy for chessplayers to play, and building the extra equipment wouldn't be very hard.

A silly variant: squares under clouds are wet and slippery.

## 3D or Not 3D?

Cloudhopper Chess is a clever new approach to 3D chess. Rather than having a stack of chessboards, it uses the normal board as a base, and allows only aerial units to employ the third dimension.

Unfortunately, the aerial part of Cloudhopper Chess isn't very 3-dimensional. Of course, this happened because I wanted a game for which it would be easy to make physical equipment, but wouldn't it be nice to have a game with more 3D?.

### Betza's Flying Circus

The ground forces are on the normal 8x8 chessboard, with the normal 16 pieces. Of course, I think you should use different armies, but that's another story.

Above the ground there are 3 levels of airspace, in which two kinds of unit may be found.

Each turn, you can make either a ground move or an air move.

#### The Bomber

The Bomber is a dive-bomber. It can move one square on the same level, like a King, or down one level in any direction (that is, it can move to any of the 9 air-squares below itself), or straight up one level (only straight up).

The Bomber cannot attack other aerial pieces.

In order to capture, the Bomber must start from the topmost aerial level; it descends in one fell stoop to the botommost aerial level, diving straight down, and kills the enemy piece on the square just below it.

Of course, before it can capture again, it must climb to the topmost level.

Each side starts with two Bombers, on the lowest aerial level, above the King and Queen.

#### The Interceptor

The Interceptor is a fighter-plane. It can move one square in any direction (it is at the center of a 3x3x3 cube that defines its moves), or two squares (non-jumping) in a straight line in any of the 9 downward directions.

The Interceptor cannot attack ground forces.

The Interceptor can destroy enemy aerial units by moving into the same square.

Each side starts with two Interceptors, on the lowest aerial level, above the Rooks.

#### How to Play

Although it is possible to imagine some physical apparatus that would let you play this game on a real board, I suspect that a computer display would be better.

#### Strategy in the Game Design

The air is relatively uncrowded. This seems more realistic.

The strength of the air units is limited so that they will not be overly important. In fact, an exciting gambit is to ignore the enemy air force; the tempi "lost" by aerial moves may allow a winning attack on the ground.

Oddly enough, bombers defend against bombers. A bomber directly below an enemy bomber prevents the fatal stoop. Of course, this is a defensive posture, and gives up the initiative.

I deliberately chose not to have helicopters, paratroopers, anti-aircraft fire, or reinforcements.

The basic principle of fighters and bombers in a game like this must be that fighters are faster; a basic principle of early aerial combat is that an advantage in altitude is precious.

#### Variants

The choice of having 3 levels, and the lengths of the moves of the aerial pieces are arbitrary. However, if you have more levels, the bomber should be able to dive all the way to the bottom in one turn; and perhaps both kinds of air unit should be able to climb a bit faster.

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