Selinger: Minor edits and typos.

2022-05-06T11:41:20Z

Minor edits and typos.

Selinger: New article on bolstered templates.

2022-05-05T14:38:36Z

New article on bolstered templates.

New page

Many [[template]]s have one or more [[intrusion]] points of this shape:
<hexboard size="3x3"
coords="none"
edges="none"
visible="area(a2,a3,b3,c2,c1,b1)"
contents="R b1 a3 E *:b2 E x:a2 A:c1 B:c2 C:b3 S c1 c2 b3"
/>
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:
    <hexboard size="3x3"
float="inline"
coords="none"
edges="none"
visible="a2 b1 b2 a3 c1"
contents="R b1 a3 E x:a2 *:b2 R A:c1"
/>     <hexboard size="3x3"
float="inline"
coords="none"
edges="none"
visible="a2 b1 b2 a3 c2"
contents="R b1 a3 E x:a2 *:b2 B B:c2"
/>     <hexboard size="3x3"
float="inline"
coords="none"
edges="none"
visible="a2 b1 b2 a3 b3"
contents="R b1 a3 E x:a2 *:b2 R C:b3"
/>
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, [[dead cell|killing]] Blue's stone. This never improves Blue's position, and often makes it worse.
    <hexboard size="3x3"
float="inline"
coords="none"
edges="none"
visible="a2 b1 b2 a3 c1"
contents="R b1 a3 R 2:a2 B 1:b2 R A:c1"
/>     <hexboard size="3x3"
float="inline"
coords="none"
edges="none"
visible="a2 b1 b2 a3 c2"
contents="R b1 a3 R 2:a2 B 1:b2 B B:c2"
/>     <hexboard size="3x3"
float="inline"
coords="none"
edges="none"
visible="a2 b1 b2 a3 b3"
contents="R b1 a3 R 2:a2 B 1:b2 R C:b3"
/>

== Examples ==

=== Bolstered bridge ===

A [[bridge]] has two exposed intrusion points, here labelled x and y:
<hexboard size="3x2"
coords="none"
edges="none"
visible="area(a2,a3,b2,b1)"
contents="R b1 a3 E y:b2 E x:a2"
/>
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:
    <hexboard size="3x3"
float="inline"
coords="none"
edges="none"
visible="a2 b1 b2 a3 c1"
contents="R b1 a3 E x:a2 y:b2 R c1"
/>     <hexboard size="3x3"
float="inline"
coords="none"
edges="none"
visible="a2 b1 b2 a3 c2"
contents="R b1 a3 E x:a2 y:b2 B c2"
/>     <hexboard size="3x3"
float="inline"
coords="none"
edges="none"
visible="a2 b1 b2 a3 b3"
contents="R b1 a3 E x:a2 y:b2 R b3"
/>
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 of course reversed. Finally, if a bridge is bolstered on both sides, for example like this
<hexboard size="3x4"
coords="none"
edges="none"
visible="a2 b2 c1 c2 b3 d2"
contents="R c1 b3 E x:b2 y:c2 B d2 a2"
/>
or like this:
<hexboard size="3x3"
coords="none"
edges="none"
visible="a1 a2 b1 b2 a3 c2"
contents="R b1 a3 E x:a2 y:b2 B c2 R a1"
/>
then Blue cannot gain anything by intruding at x nor at y; in this case, x and y are already [[captured cell|captured]] by Red.

=== Bolstered trapezoid ===

The [[trapezoid]] has one exposed intrusion point:
<hexboard size="3x3"
coords="none"
edges="none"
visible="-c3"
contents="R a1 a3 b3 c1 E *:c2"
/>
However, if the trapezoid is bolstered, for example like this
<hexboard size="3x3"
coords="none"
edges="none"
visible="all"
contents="R a1 a3 b3 c1 E *:c2 R c3"
/>
or like this:
<hexboard size="3x4"
coords="none"
edges="none"
visible="-c3 d1 d3"
contents="R a1 a3 b3 c1 E *:c2 B d2"
/>
then Blue cannot gain anything by intruding at "*". In face, in this case, the entire carrier of the trapezoid is [[captured cell|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:
<hexboard size="11x11"
contents="R b5 c4 c8 d3 d4 d6 d7 e2 e4 e7 f2 f7 g4 g5 g6 g8 g9 h2 h6 h7 i9 j5 j6 j7
B b4 b6 c3 c9 d5 d8 e1 e3 e5 e6 e8 f1 f3 f6 f8 f10 g1 g7 g10 h4 h8 h9 i6 i7
E x:g3 y:h3 S h2 h3 g3 g4"
/>
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.
<hexboard size="11x11"
contents="R b5 c4 c8 d3 d4 d6 d7 e2 e4 e7 f2 f7 g4 g5 g6 g8 g9 h2 h6 h7 i9 j5 j6 j7
B b4 b6 c3 c9 d5 d8 e1 e3 e5 e6 e8 f1 f3 f6 f8 f10 g1 g7 g10 h4 h8 h9 i6 i7
B 1:h3 R 2:g3 B 3:i5 R 4:j4 B 5:j2"
/>

[[category: Templates]]
[[category: Definition]]
[[category: Theory]]

@@ Line 80: / Line 80: @@
    contents="R b1 a3 E x:a2 y:b2 R b3"
    />
-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 of course reversed. Finally, if a bridge is bolstered on both sides, for example like this
+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
 <hexboard size="3x4"
    coords="none"
@@ Line 119: / Line 119: @@
    contents="R a1 a3 b3 c1 E *:c2 B d2"
    />
-then Blue cannot gain anything by intruding at "*". In face, in this case, the entire carrier of the trapezoid is [[captured cell|captured]]. Of course, since the trapezoid contains a bridge, this is actually a special case of a bridge bolstered on both sides.
+then Blue cannot gain anything by intruding at "*". In fact, in this case, the entire carrier of the trapezoid is [[captured cell|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 ===

Bolstered template - Revision history

Selinger: Minor edits and typos.

Selinger: New article on bolstered templates.