Local Battles

In Crumble, a local battle is one that plays out in a relatively small area of the board, often involving only a few pieces.

A local battle may not play out all at once, and it may be influenced by events nearby. But for the purposes of assessing which player has the advantage in a given local battle, it's useful to consider what would happen if both players focused all their attention on winning just that particular battle, without regard for anything else going on.

The simplest type of local battle is the fight to occupy a target piece with your color. Both players want that piece, but only one will end up with it. Which one?

In the following examples, there are obviously more pieces on the board (in Crumble, the playing field is always completely full), but we can assume that all the other pieces are impervious with respect to the pieces in the diagram. So we don't need to worry about them.

The Basic Fight

This first example is about as simple as it gets. With Black to move, Black can occupy the target piece, but then White can reoccupy it on the next turn:

The local battle has ended, and White has come out on top.

Complicating The Fight

What happens if we start adding more pieces to the picture?

In the above case, the extra piece resulted in a different outcome. What if it had been a rectangle instead of a square?

In the above case, Black was betrayed by its own rectangle. It produced a white square that was then used to have the last word with the target piece. This happens regardless of the alignment of the rectangle:

These turnabouts can get tricky. It pays to have a thorough understanding of all the different local battles involving the fight to occupy a single piece. There's not a huge number of them, because in order to interact, pieces must be of similar size and have (or be able to produce) a swappable alignment.

If Black has two large squares in this type of formation, it's possible to blunder and lose the battle by making perfectly ordinary moves. In the following case, Black tries to iterate a strong renewable in order to make sure White can never reoccupy the target piece. Usually this would work, but in this case White can win by breaking the renewable as part of occupying the target piece:

The above turned out to be the exact same case as when Black had only an extra rectangle. But Black could have won the battle by giving White the bad rectangle instead:

Sometimes you can lose a battle you didn't even know you were fighting. The following position isn't as safe for Black as it might appear, even though there are no other White pieces on the board at the start:

In the above example, the target piece was always going to be vulnerable to an invasion by White, because Black had a swappable rectangle right next to it.

Local Joining Battles, and Why Imperviousness Works

One of the central ideas in Crumble is that a piece can become 'impervious', and thus form a chain that can achieve the winning condition without being broken by the opponent. But unless a piece is so big that any other piece large enough to swap into it wouldn't fit on the board, there's no such thing as true imperviousness. Given enough moves, you can always swap, split, and join your way to being able to finally occupy any target piece.

In all of the above examples, the target piece was finally considered to be impervious when there were no more pieces that could directly swap into it. But in most cases, the impervious target piece did have swappable rectangles next to it - just of the wrong color. What prevents the opponent from splitting one of those rectangles, in order to swap into the target piece on their next turn?

This turns out to be very difficult to pull off on its own. The threat is transparent, and the opponent is almost always able to swap into the joining pieces before they can join. And any battle to make those pieces joinable again almost always favors the defender (the player not trying to do the join).

It would take a lot of examples to illustrate why this is so. Essentially it boils down to this. There are multiple pieces wanting to join, and each of them is a target piece. Trying to make them all simultaneously impervious is the same sort of problem as trying to make a larger chain impervious in order to win the whole game. That particular battle is a microcosm of the full game of Crumble; and that particular battle can become as complex as the whole game itself. But instead of trying to forge a pathway, the player is trying to keep an entire region a single color. It's a much harder winning condition. And the more splits occur inside the joining zone, the harder it becomes.

But there are some circumstances where it can be done. If, in the above example, White could play a combination involving multiple attacks, then Black might not be able to defend both.

Multiple attacks are legion in Crumble, so the above is just a simple, obvious example. Whichever of the target pieces Black chooses to shore up, White will occupy the other one instead.

Combining two preparatory moves into one, or a preparatory move with some other aggressive action, is often the only way to nail down an advantage. It can also be a beautiful culminating move in a combination that astounds your opponent.

To some extent, any game of Crumble can be seen as the struggle to influence the outcome of all the local battles that would connect you to all four sides of the board. You don't necessarily need to fight each battle as soon as it appears, if you already know you'd win it. And if you have a set of local battles that add up to connecting all four sides of the game board, you can have a completely won position without any long connections at all. Once you've reached a position where all your local battles would be won, you can then play them out one by one until you make the full connection. Though most likely a strong opponent would resign before making you prove it.