< Hexagain

Edge Templates

Take a look at this board. It’s white’s turn to play. Where is black weakest?

Edge templates are shortcuts that you can use when analyzing connectivity. Recognizing edge templates in play allows you to quickly short-circuit path analysis when identifying weak points.

Templates are shortcuts for recognizing when pieces are connected, and for quickly responding when a strongly connected piece is threatened.

Third row templates

The Trapezoid

The most useful template to recognize is the following one:

We’ll call this template the trapezoid. You might see it referred to as “the ziggurat” elsewhere.

This template comes up so frequently when analyzing connectivity that we’ll use a separate notation for it:

The Snub Trapezoid

A trapezoid with a corner taken out is not connected – unless both the top pieces are occupied.

The Small Suspension Bridge

The small suspension bridge consists of two bridges that “span” over a white piece, supported by two triangular pylons. It doesn’t come up as frequently as an edge template as the trapezoid, but it can be useful to recognize as an an interior template. More on that later.

Fourth row templates

The Large Suspension Bridge

This symmetric template consists of two bridges spanning a white piece, supported by larger trapezoidal pylons. It requires eight empty points along the edge, though, so it doesn’t occur as frequently as the other single-stone fourth-row edge template.

The Triple

The triple only requires seven edge pieces, so it shows up more frequently.

This template consists of three separate paths to the edge, and there is no one point where all three paths overlap. Any stone that breaks two of the paths always leaves a third option: the single point at which the first two paths overlap happens to be exactly the point that is spanned by a small suspension bridge.

There is another response to this intrusion, though, that does not make use of another edge template.

Why does that work?

This move serves two purposes: it strengthens the left-hand path, forcing white to block it. But it also sets up a ladder-escape that makes the right-hand path viable again.

White must block in response, which cuts off the left-hand path, leaving the board in this state:

Now what? It’s not obvious that the right-hand path is viable: after all, there’s a white piece inside that trapezoid. Doesn’t that mean that piece isn’t connected?

No! It just means that it can’t be connected within that trapezoid. But it can be connected if we leave the trapezoid borders – which we will do.

Black bridges into the trapezoid, and play continues.

White is forced to play in the intersection of those two paths, which sets up a trivial ladder to the left.

And that’s it.

Why would you ever want to use this alternate intrusion response? I don’t know.

Fifth-row templates

There is one edge template for a single stone on the fifth row.

Because it requires ten empty edge points, it’s not very likely that this template will come up if you’re playing on an 11x11 board. Its area is so large that intruding on it is easy, and it doesn’t get a catchy name. The shape of the template is also very large and irregular, so it’s hard to visually recognize it in play.

Still, it’s very interesting to study, as it has many template intrusions that require nontrivial responses. But because it’s so involved, the proof for this template is on a separate page.