Root 2 Crumble

Imagine if you could take a set of chess pieces, stretch them a little, but not change the rules at all, and yet have a completely different game. Such magic is found in Root 2 Crumble.

Root 2 Crumble is a variant of regular Crumble that uses geometry to change the nature of piece splits, without altering the game rules in any way.

In regular Crumble, you split squares into half-squares, and split half-squares into squares. Thus, the act of splitting your game pieces results in this alternation between piece-types.

The significance of this, in terms of Crumble game play, is that a square piece has the option of splitting either vertically or horizontally, while a half-square may only be split across the narrow middle. This gives a greater set of options to square pieces, while making rectangular pieces more solid and stationary.

In Root 2 Crumble, the 'square' piece is slightly elongated into a 'root 2 rectangle’, a.k.a the same shape as A4 paper, whose sides have a ratio of 1x√2.

Because of this slight change, it’s possible to split the ‘square’ piece either into half-squares or into two additional 'squares'. This has the effect of making the tree of possible splits much more bushy:

If you consider this, it's a little bizarre. Without changing any of crumble’s rules of play, but just making a slight adjustment to one of the underlying laws of physics, the deep nature of the game tree has been completely transformed.

From a game playing point of view, this one change makes square pieces suddenly much more aggressive, because they can split not only into the more solid, stationary rectangular shape, but into the more dynamic square pieces. The game tree becomes bushier, and the availability of attacking moves increases. This affects all aspects of the game, including calculating piece destiny.

If you try to express this change in the realm of regular crumble — i.e. in terms of the rules governing real squares and half-squares, it’s a difficult and convoluted problem. Depending on how you split a square, the resulting rectangles would look the same but have different properties. Even if you could manage to describe the new rule set, it would be non-intuitive to try to play it with regular crumble pieces. But using the slightly modified shapes of Root 2 Crumble, the rules are so intuitive that they don’t even need to be stated.

So, which is better, regular crumble or Root 2 Crumble? I suspect they are both equally good. And over time, it will be very interesting to discover the strategic and tactical differences between the two.