Bolstered template

Many templates have one or more intrusion points of this shape:

Here, the cells x and "*" are empty and are part of the template's carrier. The shaded cells A, B, and C are outside of the template's carrier and may or may not be empty. The cell "*" is the intrusion point in question; we call it an exposed intrusion point.

We say that the template (or more specifically, the intrusion point "*") is bolstered if A is occupied by Red, B is occupied by Blue, and/or C is occupied by Red. In other words, there are 3 ways to bolster it:

    

    

    

The point is that it is never a good idea for Blue to intrude at a bolstered intrusion point. Because if Blue attempts to do so, Red can simply choose to respond at x, killing Blue's stone. This never improves Blue's position, and often makes it worse.

    

    

    

Examples

Bolstered bridge

A bridge has two exposed intrusion points, here labelled x and y:

In general, Blue may intrude either at x or at y, hoping to gain some territory on the left or right side of the bridge, respectively. However, if the bridge is bolstered on the right:

    

    

    

then Blue should never try to intrude at y. Blue may still try to intrude at x. If the bridge is bolstered on the left, the situation is reversed. Finally, if a bridge is bolstered on both sides, for example like this

or like this:

then Blue cannot gain anything by intruding at x nor at y; in this case, x and y are already captured by Red.

Bolstered trapezoid

The trapezoid has one exposed intrusion point:

However, if the trapezoid is bolstered, for example like this

or like this:

then Blue cannot gain anything by intruding at "*". In fact, in this case, the entire carrier of the trapezoid is captured. Of course, since the trapezoid contains a bridge, this is actually a special case of a bridge bolstered on both sides.

In a game

Consider the following position, with Blue to move:

If Blue wants to intrude in the highlighted bridge, should Blue intrude at x or at y? The answer is: Blue should intrude at y (or not at all). This is because the bridge is bolstered on the left. As a matter of fact, in this position, y is winning for Blue, whereas x is losing.