Beginner Levels

In regular crumble, it’s legal to split pieces down to arbitrarily small sizes. But when teaching the game to beginners, you can use crumble levels to limit the number of splits to half-sized or quarter-sized or eighth-sized and so on.

The level refers to the number of splits a single starting-sized piece can receive, before it’s illegal to split it again.

In level 1 crumble, the starting sized piece can split once, but the resulting rectangles may not be split.

In level 2 crumble, the starting piece may be split once, and the resulting rectangles may then be split a second time, but the resulting quarter-sized squares may not be split.

Level 3, 4, 5, and so on follow the same idea.


What about big joins?

In regular crumble, there no limits on the sizes of joined pieces. So long as they are squares and half-squares, any big join is acceptable.

When playing any ‘level’ crumble, big joins are still legal, but only if they produce canonical-sized pieces, i.e. pieces that could be split back down to the smallest-sized pieces legal at that crumble level.


Why?

It can be hard to wrap one’s head around the infinite. When teaching crumble to beginners, it can be easier to start them off at level 3 or level 4 crumble, so the game won’t get away from them before they’re ready. As their level of understanding improves, you can increase the level until finally switching to regular crumble.

Why Not?

Any level crumble is a lesser game than regular crumble, because of the interactions of the pieces at the split-limit. Once you hit that limit, there’s a tendency for the position to harden in a way that neither player wants. to see this in effect, play a game of level 1 crumble. As you’ll see, the likelihood of either side winning is very small, and it’s more likely that both players simply run out of moves.

Higher level crumble reduces this risk to some extent, but it is always possible for one player to use the split-limit to intentionally try to ossify a position where the pieces have been split down near that limit.

Some might call that a legitimate tactic to produce a draw, and it’s certainly a question for debate. As crumble’s inventor, I felt that such tactics were not beautiful. Ultimately, crumble levels are an attempt to compromise with my desire to help beginners learn the game.

When I make my own sets, I generally choose a starting piece size that could reasonably be splittable to level 8 crumble. At that level I don’t tend to hit the split limit, so the tactical drawback of level crumble doesn’t generally come into play. In my personal games I also don’t play with level limits on big joins. So my over-the-board games are as close to regular crumble as I can manage in the physical world. When I use the open source java implementation, of course, I only play regular crumble.

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