Tuesday, 15 May 2018

I read this: Chess Variants and Games for Intellectual Development and Amusement

Chess Variants and Games for Intellectual Development and Amusement by AV Murali is not a book about Chess. If it's about anything it's about geometry, puzzles, and education. It’s like Hoyle’s Book of Games but instead of well-established games, it has speculative and creative modifications to chess.

In this 350-odd-page book there are more than 100 suggested games. In many of them, especially in the first of three parts of the book, an alternative board geometry is suggested, such as a hexagon grid, a set of intersecting ellipsoids, or even a hyperbolic surfaces. The rules of the pieces are them made to work in that geometry as best they can.

Each game includes the following:

-         A king, whom makes one move in any direction and needs to be checkmated (or captured) for a player to be defeated.
-         Many pawns, whom are in the front to protect other pieces and which move slowly across the board.
-         A few bishops which move in one fashion.
-         A few rooks which move in a complementary fashion.
-         A few knights, which move in a way that is a combination of the bishop and rook moves.
-         A queen, which may move either as a bishop or a rook, but not both at once.

The information about each variant is bare. Only a diagram of the starting setup, a description of the moves, and key deviations from the Orthodox chess rule set are included.

Sometimes even some rules are left to the reader to interpret. One of the described variants restricts the kings to the middle 4x4 squares of an orthodox 8x8 square board, and restricts all other pieces to the remaining outer 48 squares. (As shown in Figure 1 here, or Figure 2.39 in the book) However, it's unclear if pieces can pass through the middle part without ending there or if they can only traverse along the outside squares. In the traverse-only interpretation, bishops are nearly useless, so the cannot-land interpretation is the reasonable assumption.

Figure 1

From an academic standpoint the lack of citations is frustrating. For example there is one variant that the author calls ‘long board chess’ which is played on a 4 by 16 board. In this variant, each player’s pieces fully occupy the four ranks at the ends of the board, with the pawns forming the front two rows. This is actually a variant of the ancient Indian version of chess, chaturanga. Both chaturanga and the long board variant are described in the 1960 book Chess Variations, Ancient, Regional, and Modern by John Gallon (reviewed in the blog post in this link). Murali's book does not mention chaturanga or Gollon’s book when talking about this variant. I suspect that Murali simply came up with the variant independently, but it would have been nice to have seen that the research was done on what already existed. Similarly, there is variant that Murali refers to as ‘infinite board chess’, which looks like an existing variant called infinite chess, described in this video that is part of PBS’s Infinite Series but with a few rules changed.

This is what I mean when I say this book is more about geometry than Chess. There is no in-depth analysis of strategies on these boards, it is more of a list of suggested mathematical exercises that involve chess. Amazon even lists the book under self-help, which is a better categorization than game analysis.

That being said, a major advantage to this approach is that many variants are showcased in relatively few words. A disadvantage is that without much analysis or discussion of each variant, it's hard to tell which ones are theoretically interesting without going through the work of trying a few of them yourself.

There are a few more notable ideas worth some play and analysis. In the diminishing board variant, after a certain number of moves, the board shrinks and any pieces that were on the board’s edge are considered captured. One such game could starts as a 10-by-10 board and after 20 moves it could diminish to an 8-by-8 board. After 40 moves, only a 6-by-6 board could remain. This leads to an alternate check and checkmate, because a king can be captured this way too (in reality the game would end in a checkmate the turn before the board diminishes, because that’s when capture would be unavoidable).  This variant feels like a chess version of a game like Ultra Hardcore Minecraft, Fortnite and Battle Royale, in which a large number of players fight to survive in an ever-diminishing landscape.

Another interesting variant was one where the board had one or two pinch points in the middle of the board (see Figure 2). When occupying such a point, a piece would effectively have an increased range of places it could move to. In this variant, in order to avoid a traffic jam, pawns are allowed to jump over the pinch points and continue in their respective files.

Figure 2

 One more idea from this book worth exploration is the idea of enhancer pieces. One such piece is the enabler, which can occupy the same space as another friendly piece. A peace that starts on an enabler may move twice that turn. Other such enhancer pieces are the angel and the devil. If the angel occupies the same space as a friendly piece, that piece cannot be captured. Likewise if the devil occupies the same space as an opposing piece, that piece may not capture. All of these enhancer pieces move as knights, cannot capture or be captured, and cost a turn to move. If a piece and an enhancer occupy the same space, that does not grant the ability to move both objects together in one turn.

(I'm skeptical about the angel because it makes the king invincible, and even immune to check, so perhaps with it there's a way to force a stalemate every game.)