EVER WONDERED WHAT WOULD CHESS BE LIKE IF PIECES CAN MOVE TO THE INTERSECTION POINTS? WANTED TO SEE THE GOOD-OLD FAIRY CHESS IN A COMPLETELY NEW PERSPECTIVE?
There is a whole new group of variants that can be made out of this idea, so I believe it deserves a separate topic from the workshop thread.
Microgrid Chess gets you covered!
Microgrid Chess Concepts: The Board
Here's how to construct a Microgrid Chess board.
1. Start with a 8x7 board.
2. Then, we take all intersection points except those on the two 7-long edges (left and right), then making them a new grid. By this way we get a set of a 8x7 grid and an 7x8 grid.
3. Here are two choices: we can rather place normal chess pieces on the original 8x7 grids and allowing pawns to promote to "grid-set travelers", or we can place another set of chess on the intersections and play them both at a time. For simplicity's sake, here we use the first one.
4. Define a standard "grid-set traveler".
Let's call this piece "Viking" (Vk). It can either move to a nearby intersection or a nearby grid.
The moves for the Viking are (+1, 0), (0, +1), (-1, 0), (0, -1), (+0.5, +0.5), (+0.5, -0.5), (-0.5, +0.5), and (-0.5, -0.5).
A New Custom Chess Variant? How?
You may now wonder, why is this guy posting on the Custom Variants club? How could this ever be implemented in Chess.com?
Do we need to propose major changes for it to happen? NO!
The secret is coordinate transformation.
Coordinate transformation happens when you "see" the position from a different angle (in this case, literally).
By rotating the Microgrid Chess layout above by 45° and adding a good scaling factor (here it's √2), it aligns perfectly with a normal 14x14 grid that we can use on Chess.com right now!
(The image was recolored to show consistency with previous images)
Let's say the normal chess board was generated by two independent generators: (0, 1) and (1, 0). To generate the above Microgrid Chess board, we can use three generators: (0, 1), (1, 0), and a (0.5, 0.5) to indicate movements between grid-sets.
However, (1, 0) can be constructed using (0, 1) and (0.5, 0.5) (as 2 × (0.5, 0.5) - (0, 1) = (1, 0)), so we're left with (0, 1) and (0.5, 0.5) as two linearly independent generators.
To map into the 14x14 grid generated by (0, 1) and (1, 0), we need to make sure the independent generators keep linearly independent.
Here we propose the linear transform: f(x, y) = (x - y, x + y). It comes with the inverse transform f^{-1}(x, y) = (0.5y+0.5x , 0.5y-0.5x).
Therefore, (0, 1) after such a transform becomes (-1, 1), and (0.5, 0.5) becomes (0, 1). Since they are still linearly independent, and they give out integer results, we have proved that you can perfectly map the above "8x7 + 7x8" grid into whole grids in a 14x14 normal chess board without a problem.
Pieces In Chess.com Viewed as Microgrid Chess Pieces
We can't treat most normal pieces (like a knight) in Chess.com as normal pieces in Microgrid Chess (projected to a 14x14 normal chess board), as they may "cross the dimension" (grid-set traveler). We can prove this by putting their moves into the inverse transform.
For example, the King on Chess.com has moves (1, 0), (-1, 0), (0, 1), (0, -1), (1, 1), (-1, -1), (1, -1), (-1, 1) totally 8 moves.
Putting them into f^{-1} we get:
(1, 0) -> (0.5, -0.5)
(1, 1) -> (1, 0)
...
Are you spotting a pattern? The King in a 14x14 normal chess board acts the same as our Viking in a Microgrid Chess board!
In fact, we can apply the same idea to other pieces too! Try it out on your own for the horse, how does it move?
Microgrid Chess Pieces Implemented by Chess.com Pieces
We've applied the inverse transform to chess moves in the previous section, now it's time to apply them the other way.
Remember f(x, y) = (x - y, x + y).
The Rook
Take the rook as an example: It moves like (0, n), (n, 0), where n is an integer.
Applying f, we get f(0, n) = (-n, n), and f(n, 0) = (n, n), which is the moves of a bishop.
The bishop in Chess.com IS the rook in Microgrid Chess.
The Bishop
For the bishop, similarly we get (2n, 0) and (0, 2n), that is how dabbaba-riders moves.
The dabbaba-rider in Chess.com IS the bishop in Microgrid Chess.
The Knight
Here is the formula: f(2, 1) = (2 - 1, 2 + 1) = (1, 3). By symmetry we know that these are moves for a camel.
The camel in Chess.com IS the knight in Microgrid Chess.
Limitations of the Custom Variants System
To simulate "a full functional Chess + Microgrids", there are a few limitations yet to be solved. Right now, you may treat them as the features of this variant.
The Missing Pieces
Pieces like King, Queen are completely missing. I've even posted another post discussing the potential solutions to this. Unfortunately, it seems like unless a new piece would be added, we can't bypass this limitation and have a queen.
By far, I've been using the Ferz for King (so it moves like a Wazir in Microgrid Chess), and the Bishop for Queen (so it moves like a Rook in Microgrid Chess). This isn't perfect, and I'd like to see future variants under this group to solve it.
Pawn Movements and Promotion
In Chess.com, pawns can only move forward. This way, if we use the only usable pawn that stays in the same grid set (the stone general), it can only move (from Microgrid Chess perspective) to right or up one square at a time, and there's an "end square" for all pawns of one side. This asymmetry makes it somehow interesting.
In Chess.com, promotion is by reaching a promotion rank, which cannot be tweaked into a diagonal line. Right now, it's set to the last rank, which means there's only one square for pawns to promote. It's namely the "end square", so you could also argue this variant to be a bit of "racing pawns".
Since we don't have queens and the promotion condition is too hard, I added the King (Viking from the Microgrid Chess perspective) and the Knight ("Warping Knight"?) as promotion options. The Viking moves slowly, while it can never be trapped if the opponent hasn't promoted; The "Warping Knight" moves fast, but it must switch back and forth between grid-sets, making it possible to be trapped, although still immortal.
Current Layout
Taking all limitations into account, this is the current layout I'm using:
Example Games
I've played the game a few times with one of my friends. I'm sharing our games, so you can use the rules and don't have to reinvent the wheels.
Custom Variants Chess - PF_Official vs Mewnojs - Play Chess Variants Online - Chess.com
Custom Variants Chess - Mewnojs vs PF_Official - Play Chess Variants Online - Chess.com
Future Development / To Dos
- 4-Player Microgrid Chess.
It is technically possible, but the winning conditions for Teams mode are not satisfactory, as checkmates lead to early ending of the games.
We may have workarounds by making the royal King being able to escape from a grid-set to another.
- Improvement through testing. Since I've been working on multiple projects, I decided that letting the community to improve the idea would be a better choice. It's all about a new entertaining way of playing chess.
- Diagonal Chess: We could make the diagonal chess upright this way. Also, as in the Pawn Promotion section, since Chess.com only has horizontal promotion line options, which transforms into diagonal line in Microgrid Chess, we can use the diagonal chess layout and then the diagonal promotion line makes sense! (Notice: The original rules of Diagonal Chess do NOT have a diagonal promotion line. It's only intuitively making sense, not authentic)