Rules of game:
There is a rectangular array of dots.
Players take turns connecting a pair of horizontally or vertically adjacent dots with a line.
When a player completes a square, that square is theirs.
After completing a square they get to (must) move again.
When the grid is complete, the player with the most squares wins.

It seems simple but some deep strategy can arise. I've spent hours analyzing a single position attempting to discover a forced win or draw and still ended up making imperfect moves.

Obviously the larger the grid, the more complex the resulting game.
Has there been any work done in solving or analyzing this game?

If not, what do you think would be the best approach for writing an analysis tool or engine to attempt to solve or predictively score certain positions.

I was thinking minimax would be reasonable for a small grid. And perhaps for larger grids, like Go, there would be a need for more specific regional methods.

Note: It's been difficult for me to look up information about this game since it doesn't really have a name. Connect the dots could refer to draw-by-numbers or puzzles in which you must draw minimum numbers of lines to cover arrays of dots. And "Connect the dots and make squares" isn't really a name, it's a description, and a vague one at that.

It's called "the dots and boxes game". You are going to love this.

That's a very good question. Would be cool to see progress being made in answering the question that such a problem proposes. I think that it is, in its own way, more complex than chess.

That's a very good question. Would be cool to see progress being made in answering the question that such a problem proposes. I think that it is, in its own way, more complex than chess.

Tough to say. But you could definitely make the argument that on a reasonably sized grid, its brute force solution would require more computation than chess'. (Both probably being intractable given the limit of energy in our universe)