Notation

Game Notation

Crumble has an efficient notation system that successfully works around the fact that, unlike chess and go, there is no natural grid that can be used to refer to pieces. In Crumble, the position itself defines the landmarks used to notate each move.

When notating a game, each player should just use their own sense of forward, backward, left, and right. Don't try to transpose to your opponent's sense of direction, you'll only increase the likelihood of making a mistake.

While you're learning the notation system, I recommend taking a photo of the game position after each move, so that if you make a mistake notating the game, you'll be able to correct it later.

Identify a Piece with Fraction Notation

There are actually two methods of identifying a piece: Fraction Notation, and Staircase Notation. Both are acceptable, and either may be easier or clearer in a given situation. See below for a description of Staircase Notation.

In Fraction Notation, each player’s lower left corner of the board is the origin point, from which locations are calculated.

The origin is position 0. The piece associated with a given position is the one that has its lower left corner on that position.

To identify any piece, simply identify the lower left corner of the target piece as the fraction of the board from the left, and the fraction of the board from the bottom.

In the above diagram, the outlined piece is at position 1/2.

In the above diagram, the outlined piece is at position 1/2, 2/3.

If the piece is up against the left edge of the board, the first number of its position is 0. For example:

In the above diagram, the outlined piece is at position 0, 1/2.

The same principles work with pieces anywhere on the board, at any stage of gameplay.

In the above diagram, the outlined piece is at position 3/4,1/2.

In the above diagram, the outlined piece is at position 2/3, 1/12.

During a game of crumble, players might start off with Fraction Notation at first, and then switch to Staircase Notation as described below, when the pieces get small enough that Fraction Notation becomes difficult.

Identify a Piece with Staircase Notation

As with Fraction Notation, each player's lower left corner of the board is the origin point, from which locations are calculated.

The origin is position 0. The piece associated with a given position is the one that has its lower left corner on that position.

To identify any piece on the bottom row, simply count the number of intersections, starting from the origin, and moving right.

In the above diagram, the black piece outlined in red is at position 3.

To get off the first row, just add a comma to the number you've got so far, consider your current position the new origin point, and then count intersections upwards.

In the above diagram, the black piece outlined in red is at position 3,4.

To identify a piece on the left edge of the board, just include the 0 as the horizontal position, and continue as before.

In the above diagram, the black piece outlined in red is at position 0,3.

What about more complex positions? Sometimes counting to the right and then upwards isn't enough.

How can we notate the position of the black rectangle outlined in red? The solution is to use a staircase pattern, separating each new count with a comma.

The above black rectangle is at position 4,3,1.

The general rule goes like this: alternate between going to the right, and going up. There will always be a path to the piece you want.

But what about the fact that there are innumerable ways to notate the position of each piece? Which is correct?

The same black rectangle can be notated as having position 1,1,1,1,2,1,1.

The main requirement is to start off moving to the right (even if it's only by 0), and thereafter only move either to the right or upward, you've identified a legal position. After that, the goal is primarily to minimize the quantity of numbers, and secondarily to minimize the magnitude of each number.

In the above position, the most natural path to identify the black rectangle is more complicated because of a lot of smaller pieces, with many intersections to count. In this kind of situation, it's better to avoid the complicated region if possible. So the better way to notate the black rectangle is 3,3,2 instead of 4,7,1.

The most important thing to remember about identifying piece position is the direction of each number in the sequence. The first number counts intersections to the right. The second number counts intersections upwards. The third counts to the right again. The fourth upwards. And so on, like a staircase.


Now you know how to identify pieces, either with staircase notation or fraction notation. Once you’ve identified a piece, you still need to express your move as either a split or a join, followed by an optional swap.

Split

To notate a split, we use the letter H for a horizontal split-line, and V for a vertical split-line.

The notation for the above split is 2,2H.

To do a long split, just append the number of pieces to split. Horizontal splits always happen rightward, and vertical splits always happen upward.

The notation for the above split is 2,2H2.

When a split-line passes along the edges of opposing pieces, it makes no difference - we only notate the number of pieces actually split.

The notation for the above split is 2,2H3. Even though the split-line passed through a wider region of the board, we say H3 because three white pieces were split with a horizontal split-line.

For vertical splits it's exactly the same, but using a V instead of an H.

The notation for the above split is 2,2V2.

Join

To notate a join, we use J. The piece position identifies the lower left corner of the joined piece. To specify the upper right corner, we count intersections to the right and upwards.

The notation for the above join is 3,1J1,3.

Note that regardless of whether the initial piece position ends with a rightward or upward movement, the joined piece is always defined by first a rightward and then an upward movement.

The notation for the above join is 2,3,1J3,1. Notice that even though the notation for the initial piece position ended on a rightward movement, the join was still defined by first a rightward, then an upward movement.

Swap

The final - and optional - part of any move is the swap. The notation for the direction of swapping uses NSE, and W, for the North, South, East, and West directions on the board.

The above join and swap is notated 2,3,1J3,1WSEES. Which is a mouthful, but gets the job done. Obviously, the longer the swap, the longer the notation for that move. You can't leave out any step along the swap path, in order to make sure that all captures are made.

To notate a swap that follows a split, it's necessary to identify the specific piece being swapped. If there's only one piece that could legally perform the swap, then we can assume that's the piece being swapped.

The above split and swap is notated 2,2HS.

Even when splitting only a single piece, it's sometimes necessary to identify which piece is swapping.

The above split and swap is notated 3,2HS-E. The S indicates the southernmost split piece, and the hyphen separates the piece identification from the actual moves of the swap. It was necessary to identify which split piece we intended to swap, because the northernmost piece could also have swapped to the East.

The above split and swap is identical to the one before, except that now the northmost piece swaps instead of the southmost. The move is notated 3,2HN-E.

To swap after doing a long split, you have to which piece you split, and which of the two split halves you want to swap.

The above long split and swap is notated 3,2H2-1N-N. The 3,2 identifies the starting piece position. The H2 says to make a horizontal split through two pieces. Then there's a hyphen to separate the split from the identification of the swapping piece. The 1N indicates the northernmost portion of the first split piece. Then there's another hyphen to separate the piece identification from the swap path. And finally the last N indicates that the piece swaps northwards. It's another mouthful, but it's clear.

The above long split and swap is notated 3,2H2-2S-WNN.

Check and Crumblemate

To express 'check', put a '+' at the end of the notated move, as in 3,2H2-2S-WNN+. To express 'crumblemate', put '++' at the end of the move, as in 3,2H2-2S-WNN++.

Now you should be able to notate any move in Crumble.

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