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## Friday 20 July 2018

### Chess Variant - Laser Chess / Khet / Deflexion

Khet, Deflexion, and Laser Chess are different names for the same game.  The currently commercially available game is called Laser Chess, and it has a space theme. Deflexion, Khet, and Khet 2.0 have an ancient Egyptian theme. The themes and some of the suggested starting boards differ between versions, but the pieces and board are functionally identical. They have also introduced a couple of new starting positions and improved the accuracy of the laser, but otherwise kept the fundamentals the same.

The lasers are not strictly necessary for playing Khet, as the path of the beam can be abstractly traced along right angles. However, the lasers make this tracing more convenient and a lot more appealing on a viceral level. Pew pew!

Comparison to Chess

I would classify Khet as a chesslike, but not a chess variant. The primary method of capture is not to move into the space occupied by an opposing piece. Furthermore, the pieces are not differentiated by their movement, but by their effect on a beam of light. Ignoring rotation, all the pieces are immobile or move like a chess king.

In spirit, it is VERY much like chess. There are tactics to be discovered in much the same fashion. There is a level of depth in the same league of chess, although the exactly comparison is hard when considering orientation. There are easy to identify strong formations, and hanging pieces. There are equivalent states to checks and pins respectively.

 The recommended starting board for new players.

Pieces and Rules

There are four pieces which may move on the board: the Pharaoh, Anubis, scarab, and pyramid.
The Pharaoh plays the role of the king. The Pharaoh has no mirrors and absorbs the laser from any direction. If a player's Pharaoh absorbs a laser, that player immediately loses the game.

The Anubis is the closest analogue to the pawn. Like the Pharaoh, it has no mirrors and absorbs lasers from any direction. If it absorbs a laser from any direction except its front it is removed from the game. If it absorbs a laser from the front the Anubis remains, effectively blocking the laser beam. The Anubis replaces the Obelisk piece from Khet 1 and Deflexion, which was the same, except it was vulnerable from every direction.

The scarab has a diagonally placed mirror on both sides, such that if the laser strikes it, the Scarab will deflect the laser 90° clockwise or counterclockwise depending on the scarab's orientation and that laser's initial direct. Because of its two mirrors, the scarab does not absorb the laser beam from any direction, and therefore it cannot be removed.

 Red and Silver Pyramids

The pyramid is halfway between the Anubis and the scarab. It has only one diagonally placed mirror, which faces two cardinal directions. Like either mirror on the scarab, the mirror deflects beams either a quarter turn clockwise or counterclockwise.   The other two faces of the pyramid absorb the laser, and if this happens, the pyramid is removed from the game.

There is one more piece, which was sold as an expansion, called The Eye of Horus. The eye is a prism which splits the laser beam into two. With the Eye of Horus it's possible for more than one piece to be hit by the laser in the same turn.  In the case were both pharaohs are hit on the same turn, the game is a draw.

 The Sphinx Being Fired

The movement of the pieces is relatively simple. The Sphinx is the laser source; its only move is to toggle between one of two possible orientations. The Sphinx never changes the square upon which it occupies, and it can never be taken or removed from the game.

The pyramid, Anubis, and Sphinx all have the same moveset. They can move from their current Square to any of the up to eight adjacent squares, or they can rotate 90 degrees, but not both.

The Scarab can also move like the other pieces, but it may also switch places with an Anubis or pyramid instead. If it switches places neither of the pieces changes its orientation. A scarab can switch places with pieces from either side.

Strategy
Predicting the consequences of a move can be difficult, especially if a laser reflects off of many mirror pieces. Moving or rotating a piece on one corner of the board can radically change the outcome on the far corner. A related defensive challenge is accounting for two possible laser paths as the sphinx, the beam source, can be rotated.

The instructions that come with the game also suggest 3 starting board states, as opposed to one. The three setups that were provided were obviously well thought out, but it makes me wonder how many other comparably good ones are out there, in case anyone wanted to write support material.
Orientation matters, especially for pieces like the scarab, in which orientation determines deflection, and the pyramid, for which it determines both deflection and vulnerability.

 Recommended Starting Board

One neat twist that it is possible to capture one of your own pieces or even to lose the game on your own turn. I'm still trying to work out the heuristics in which removing one of your own pieces is an improvement in your board state, other than when your piece is diverting a laser to your phahroh.

Another clever property of this game is that there's no possibility of rendering your pharaoh untouchable from all angles. Even if both players only have their pharaohs and their two scarabs remaining, vulnerable from one side. Furthermore, regardless of the number of pieces remaining just one face will always be open to attack.

Potential for artificial intelligence
The online mobile version of the game, had an artificial intelligence to play against at multiple levels. Even though the game does not involve capturing in the classical sense, the alpha-beta agorithm should be able to produce some sort of intelligent play, assuming that orientation doesn't complicate things too much.

Although the mobile game is no longer available, there are closely related puzzles available in the game RayTrace.

Establishing the relative and positional value of pieces has an additional complication: the two-mirror scarab pieces are invincible. There's no point to estimating the value of such a piece relative to its removal because removal is impossible.

Final word

I would recommend this game as a gateway to other chesslike games. The laser has that immediate appeal that an abstract game often lacks.