The Chess Variant Pages

Check out Symmetric Chess, our featured variant for March, 2024.

This page is written by the game's inventor, Ralph Betza.

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.


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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