The Rules


Introduction

Crumble is a two player game, where the first player controls the black pieces and the second player controls the white pieces. The game board is always entirely filled with pieces. The starting position looks like this:

Fig. 1

No, it's not an empty chess board. Each of those black and white squares is a distinct piece, independent of all the others. When you take your turn, you'll be taking one or more of those squares, and doing something to it that affects the layout of the position. Here's an example of what the board might look like after Black's first move:

Fig. 2

As you can see, the game doesn't look like a chess board for very long. After a few moves, the configuration of black and white pieces will have changed considerably.

In fact, it is just this configuration of color that determines the winner of the game. In fig 2 above, never mind for the moment how Black made that move; just notice that there are now two clusters of pieces that are different from the rest - Black has a cluster of four neighboring pieces, and White has a cluster of three:

Fig. 3

The four black pieces in that central cluster all have something in common - they don't just neighbor each other on the single point of a corner, the way all the other black pieces do; they touch each other along an edge. The three white pieces have their own central cluster that also touch along their edges, unlike the other white pieces on the board.

The way that any given piece borders another is very important in crumble; in fact those relationships determine all the strategic and tactical ideas that affect the game.

If Black could somehow extend that central cluster, for example, adding more pieces to it that neighbored each other along an edge instead of just a corner, then ultimately Black might end up with a cluster long enough to touch all four sides of the game board, like this:

Fig. 4

If that happens, Black wins the game. Likewise, from fig. 3, if White could extend it's own central cluster, adding more pieces that neighbored each other along an edge instead of just a corner, then White's cluster might end up touching all four sides of the board, and White would win the game:

Fig. 5

It should be clear that only White or Black can have a single cluster of pieces touching all four sides of the board like this. It's impossible to construct a position in which both players have clusters touching all four sides of the board. In that regard it's fitting that obtaining such a cluster would win the game for the player who achieved it. Regardless of any of the other rules of crumble, it's obvious that any progress by one player towards that goal, must include a corresponding setback for the other player in achieving the same goal. This is the fundamental battle that rages throughout the entire game.

Aside from being the instrument of winning the game, there's another way that clusters of pieces neighboring each other's edges can exert strength. They can surround opposing pieces in order to capture them.

Fig. 6

In fig. 6, Black has a cluster of pieces that border each other along an edge instead of just a corner. That cluster forms a ring around a white piece. Whenever that happens, the surrounded pieces become the color of the surrounding pieces.

Fig. 7

You can capture more than once piece at a time. In fact, the surrounding ring can be as big as you like, and it captures all the pieces within it:

Fig. 8

In fig. 8, the black ring captures 3 white pieces. There's no limit to how many pieces may be captured at once this way.

On the other hand, the ring of neighboring pieces has to be a real ring; it can't just come up against the side of the board and pretend to continue out beyond it.

Fig. 9

In fig. 9, the white pieces don't really surround that black piece, so the black piece isn't captured. What this amounts to strategically is that the sides of the game board offer a measure of protection against capture. That's a strategic strength that pieces along the sides have, that pieces in the middle don't. A piece on the edge can stand completely alone; pieces in the middle can't.

As you can see from the above examples, these clusters of pieces that neighbor each other along their edges can be very strong. When properly placed they can capture the opponent's pieces or even win the game.

What are the rules governing the way each player can affect the position on their turn? How are these clusters of pieces formed and controlled?

In the following pages, all the powers granted to you on your turn will be explained; and we begin by describing the simple form that every single turn of the game must take.

Taking A Turn

Black always plays first; and thereafter the players alternate until one player achieves the winning condition, or resigns, or forces a draw, or both players agree to a draw without it being forced. Drawn games in crumble are relatively rare because the game resists any sort of balance.

Every turn of the game takes the following form:

  1. You must start off with either a split or a join.
  2. After your split or join, you have the option to also do a swap.

And that's it. We'll explain what splits, joins, and swaps are in a moment, but the main thing to remember is that at the very start of each of your turns, you have to either split some pieces or join some pieces. It's not optional, no matter how much you wish it were. From a tactical standpoint, it would be very useful to be able to skip this first phase of the turn; and that's precisely why you're not allowed to. The obligation to play a split or a join at the start of each turn is what keeps the game sharp.

Then after that, if you choose, you can do a swap. Swapping, as we'll see shortly, is the only way to change the configuration of color on the board. So while you don't technically have to do a swap on your turn, you literally can't win without it. Also, swapping is the primary way to gain territory, so if you don't do it, you run the risk of giving your opponent too much control over the board.

All of this will make sense momentarily. The main thing to remember, however, is that you have no choice but to do either a split or a join as the first part of your turn; and then at your discretion you may also choose to do a swap. Every turn has that same rigid format, and it allows a tremendous diversity of change to take place on the game board.

Splitting

The vast majority of turns in crumble start with a split, so that's what we cover first.

You can only split your own pieces. If you're playing Black, that means you can only ever split the black pieces. If you're playing White, you can only split the white pieces.

A single piece may be split by replacing it with two equal halves. A square can be split by replacing it with two equal rectangles, and a rectangle can be split by replacing it with two squares. The replacement pieces have to fit exactly in the space occupied by the piece they're replacing. So from the starting position, we can examine the first phase of Black's first move, as shown in fig. 2 above.

Fig. 10

But the ability to split pieces would be too pedestrian if it were limited to just that. Depending on your own careful planning, and on the opportunities given to you by your opponent, the ability to split can become a much more powerful and aggressive weapon.

The official rule for splitting is this:

On the first phase of your turn, you may split as many of your own pieces at once as you like, so long as you meet the following conditions:

  • Each square is replaced with two equal rectangles, and each rectangle is replaced with two equal squares
  • The dividing line used to split any one of your pieces must be collinear with the dividing line used to split all the rest
  • The dividing line must not pass through any of your opponent's pieces, but it may run along the existing edges between any two pieces

How does this play out in a real position? In the following position, White might make a split this way:

Fig. 11

In fig. 11, White is able to split three pieces at once, because the dividing line is straight, it only passes through White's own pieces, and each split piece goes from either a square to two equal rectangles, or a rectangle to two squares.

Or from the same position, White could do this instead:

Fig. 12

In fig. 12, White is able to split two pieces because the dividing line is straight, it only passes through White's own pieces or along the existing edges of other pieces, and each split piece goes from either a square to two equal rectangles, or a rectangle to two equal squares.

Now, just because you can split lots of pieces up on the same turn, doesn't make it a good idea in all cases. Each split piece will have a new relationship with its surrounding neighbors; and that new relationship will have to be assessed on a case-by-case basis. In some cases the split pieces will be more aggressive; in some cases more defensive; and in other cases, more vulnerable to your opponent's own attack.

We've already examined some of the ways in which pieces can work together to be strong; to understand how they can also be weak you have to consider swapping. But before we come to that, we have to consider the join, which is the other option available at the start of your turn.

Joining

Joining is much less common than splitting; in fact in the starting position there are no joins available at all. You could play many games of crumble and never see a join. Likewise, you could play many games of chess and never promote a pawn. Still, the idea of pawn promotion is a very powerful strategic idea in chess, and joining is the same in crumble. You might not see it very often, but when you do, watch out!

Joining is not quite the opposite of splitting, but it's close. In splitting, one piece becomes two, or many pieces each become two. In joining, two pieces become one, or many pieces all become one. Unlike splitting, which can start with many pieces and end with many pieces, joining can start with many pieces but always ends with just one single piece. The official rule for joining is this

On your turn, you may join any number of your own pieces together to form one single piece, so long as the following conditions are met:

  • Taken as a group, the pieces you intend to join must have an outline that is either a square, or a rectangle that is exactly twice as long as it is wide
  • You may never replace one group of pieces with anything more than a single piece
  • You may only select a single group of pieces to join on your turn



Terse Rules

  • Crumble is a two-player game.
  • Each piece is either black or white
  • One person plays the black pieces, the other plays the white pieces
  • Each piece is either a perfect square, or a rectangle with a 1:2 ratio of length to width
  • There are no restrictions on piece sizes; but the dynamics of play prevent certain sizes from being created
  • The starting position is a 6x6 checkerboard pattern, oriented with black pieces at the upper left and lower right
  • The person playing the black pieces makes the first move
  • Players alternate turns
  • Types of neighbors
    • Two pieces are 'weak neighbors' if:
      • They are the same color as each other
      • The point of a single corner of one piece touches the point of a single corner of the other
      • There is no length of any side of one of the pieces that touches a length of any side of the other
    • Two pieces are 'strong neighbors' if:
      • They are the same color as each other
      • There is a length of a side of one of the pieces, more than the single point of a corner, that touches a length of a side of the other, more than the single point of a corner
      • If the point of one single corner of one piece touches the point of a single corner of the other piece, there is not another single point of a corner of either piece that touches the single point of another corner on the other
    • Two pieces are 'pathway neighbors' if:
      • They are the same color as each other
      • The points of two corners of one piece touch the points of two corners of the other piece
    • Two pieces are 'symmetric neighbors' if:
      • There is a length of a side of one of the pieces, more than the single point of a corner, that touches a length of a side of the other piece, more than the single point of a corner
      • The midpoint of that touching length of side, is also the midpoint of the full side of each piece

Verbose Rules







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