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Positional Evaluation


This page gives some hints about how to assess a given position in Crumble, to clarify who is winning, without any specific regard to how the win would be carried out. In chess, positional assessment involves things like king safety and backward pawns. Chess software assigns a numeric value to a given position based on these qualities, and that number is intended to represent who is winning, and by how much. This page tries to identify the set of such qualities for Crumble.


Material Balance

All other things being equal, having your pieces cover more territory than the opponent's pieces is an advantage.

Edge Control

At the start of the game, both players have an equal grip on each edge. Without regard to the length of those connections, simply having a certain amount of territory on an edge is an advantage. Of course, only a single, thin, very solid connection is needed in order to win the game; but if that kind of connection isn't yet established, a general sizing up of territory can indicate the advantage along a given edge.

Size Balance

In general, it's better for a player's pieces to be one or two size-steps smaller than the opposing pieces that neighbor them, or that neighbor pieces swappable into them.

Individual Piece Assessment

Each piece can be assessed on these values:

  • level of imperviousness
  • level of redundancy
  • swappability with friendly neighbors
  • activity against opposing neighbors

Cluster Assessment

Each piece in a cluster can have its own positional value; and the cluster itself can be assessed in the following ways:

  • How many sides of the board does it touch?
  • What are its most assailable internal connections?
  • How swappable is it?
  • Are the pieces within it smaller than the opposing pieces that surround it?

Relationships Between Clusters

  • renewable resources (either a small piece nestled among its friendly neighbors, or several pieces that can keep splitting and swapping through the paths they expose
  • judicious splitting that allows many swaps through a single opening
  • smaller pieces that can swap into bigger ones