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In the summer of 2010, while working on a chapter about grids in "The Evolution of Draughts Variants", Query happened. I was contemplating the relationship between the hexgrid and the square grid.

grid 1

grid 2

grid 3

grid 4

In (1) and (2) the diagonal grids are divided in a red and a blue half. Removing the blue half from each brings us to (3) and (4). In (3) we recognize the Alquerque board. Its twin (4) is the 'triangular' grid, albeit in a square jacket. But topologically (4) is equivalent to the hexgrid. That led to the question whether (3) would also fit a 'connection' theme. The most basic one in the hexgrid is Hex itself. Query is 'square Hex' with a twist.

The rules are so simple that I might as well include them here. Black and White take turns to put one stone on a vacant c8 intersection or two stones on two vacant c4 intersections. Black moves first, after which White is entiteld to a swap.

  • White tries to connect the upper and lower side of the board, Black the left and right side, following the lines of the board. The cornerpoints belong to both sides.

The twist is of course the choice between two c4 placements and one c8 placement.

Because there are bad opening moves as well as good ones, a swap balances the game implicitly. At the same time, comparing the value of a c8 move that of two c4 moves is not very fruitful because you will need both options at different times.