Bubbles

The white group on the right is just alive despite the internal cutting points. Given a board without sides or corners, it is the most efficient boundary shape for connecting the four marked white stones (5-skip as are the handicap stones on a standard go board). Such idealised bubbles demonstrate a number of features which have relevance to the topographically more complicated go board.

·

The ideal boundary shapes are predominantly based on straight lines.

·

The larger the bubble the more territorially efficient the boundary.

·

At more than 4-skip sizes, more stones are required to contain the bubble than to define it. Therefore containment of such bubbles by the opponent is only efficient if additionally fencing off even more opposing territory.

·

Due to the need for the marked black stones to protect against double atari, there is an optimal efficiency step at the 5-skip size.

·

The size of a standard go board limits the size of an optimal bubble, not only because there are a finite number of intersections but also because those intersections must be shared between the opposing sides. By considering aspects of the topography of the standard board together with principles of symmetry, it can be argued that the 5-skip framework connections provide the ideal size and positions for bubble formation.

Blisters

The diagram to the right shows the smallest possible central live group. It is normally territorially inefficient because it is likely that the surrounding stones can form much more territory on the outside. However if the opponent's territory is already fully formed, then such an invasion is very efficient. Note that the shape is constrained by the need to make eyes rather than connect framework stones.

Pins

When trying to destroy territory formed by large bubbles the most efficient method is often the pin. Where destruction of territory is a priority no attempt should be made to expand a small bubble. Instead, an extension of a single  line of connected stones (not necessarily straight), thrust into the opponent's potential territory forces the opponent to expend double the number of stones to envelop it, and so in the long-term is the more efficient option. Note that framework connections, if not forming bubbles, automatically form pins.