Bottleneck - Revision history

Selinger: Added politigaarden

2025-11-30T16:26:00Z

Added politigaarden

2024-05-10T02:30:58Z

Added some info on how blocking and bridge ladders can lead to bottlenecks

2023-01-23T02:10:46Z

Copy-editing

2023-01-12T21:54:16Z

Removed non-existent link.

2021-09-11T14:25:00Z

Removed "bottleneck with bridges" section, since there is no explanation and it makes no sense (Blue would never play like this).

2020-12-28T18:43:33Z

Added category

2020-12-09T14:07:13Z

Converted to new hexboard diagrams

2008-01-30T00:07:50Z

added two more bottlenecks

2007-12-17T01:05:18Z

cat. strategy

2006-02-16T15:53:18Z

← Older revision		Revision as of 16:26, 30 November 2025
Line 17:		Line 17:

	It's important to note that, although the bottleneck can be an effective defense strategy, it also has its own weaknesses and can be exploited by a skilled opponent. Knowing how to both create and counter bottleneck formations is an important aspect of mastering the game of Hex.		It's important to note that, although the bottleneck can be an effective defense strategy, it also has its own weaknesses and can be exploited by a skilled opponent. Knowing how to both create and counter bottleneck formations is an important aspect of mastering the game of Hex.
		+
		+	== History ==
		+
		+	According to Hayward and Toft, the bottleneck was known to [[Piet Hein]] and Jens Lindhard in 1943, and they called it the <i>Politigården</i>, after the police headquarters in Copenhagen. The building of the police headquarters is such that upon entering it, one has to choose to go left or right.
		+
		+	[[File:Politigaarden.png\|center\|alt=xyz\|350px\|The police headquarters in Copenhagen]]
		+
		+	== References ==
		+
		+	* [[Ryan Hayward]] and [[Bjarne Toft]]. [[Hex: The Full Story]]. CRC Press, 2019. ISBN 978-0367144227.

	== See also ==		== See also ==

@@ Line 13: / Line 13: @@
    contents="R e1 e2 B d2 f2 d4 R 1:d3 B 2:c4 R 3:c3 B 4:b4 R 5:e3 B 6:e4 R 7:f3 B 8:f4"
    />
 It's important to note that, although the bottleneck can be an effective defense strategy, it also has its own weaknesses and can be exploited by a skilled opponent. Knowing how to both create and counter bottleneck formations is an important aspect of mastering the game of Hex.
 [[category:strategy]]
 [[category:definition]]

@@ Line 1: / Line 1: @@
-The '''bottleneck''' is a common defense pattern. The board fragment below shows a position where the vertical player (red) wants to connect to the bottom, but is being hindered by blue in a bottleneck formation.
+The '''bottleneck''' is a strategic formation in the game of Hex where one player blocks the opponent's progress by occupying key positions on the board, creating a narrow passage that is difficult for the opponent to break through. The board fragment shown below illustrates this concept, with Blue occupying the key positions in a bottleneck formation, hindering Red's ability to connect to the bottom of the board.
 <hexboard size="4x7"
    coords="none"
@@ Line 6: / Line 6: @@
    contents="R e1 e2 B d2 f2 d4"
    />
-The bottleneck formation invariably leads to a [[Ladder|ladder]] situation. Red gets ladders in both directions.
+This formation often leads to a [[ladder]], with Red getting ladders in both directions, as shown in the second board fragment.
 <hexboard size="4x7"
    coords="none"
@@ Line 13: / Line 13: @@
    contents="R e1 e2 B d2 f2 d4 R 1:d3 B 2:c4 R 3:c3 B 4:b4 R 5:e3 B 6:e4 R 7:f3 B 8:f4"
    />
 [[category:strategy]]
 [[category:definition]]

@@ Line 1: / Line 1: @@
-The '''bottleneck''' is a common [[Defense pattern|defense pattern]]. The board fragment below shows a position where the vertical player (red) wants to connect to the bottom, but is being hindered by blue in a bottleneck formation.
+The '''bottleneck''' is a common defense pattern. The board fragment below shows a position where the vertical player (red) wants to connect to the bottom, but is being hindered by blue in a bottleneck formation.
 <hexboard size="4x7"
    coords="none"

@@ Line 12: / Line 12: @@
    visible="area(d1,a4,g4,g1)"
    contents="R e1 e2 B d2 f2 d4 R 1:d3 B 2:c4 R 3:c3 B 4:b4 R 5:e3 B 6:e4 R 7:f3 B 8:f4"
    />
 [[category:strategy]]
 [[category:definition]]

@@ Line 1: / Line 1: @@
 The '''bottleneck''' is a common [[Defense pattern|defense pattern]]. The board fragment below shows a position where the vertical player (red) wants to connect to the bottom, but is being hindered by blue in a bottleneck formation.
+<hexboard size="4x7"
-[[Image:bottleneck.png]]
+  coords="none"
+  edges="bottom"
-<!-- <hex>R5, C5, Vd1, Hb2, Vc2, Hd2, Hb4</hex>-->
+  visible="area(d1,a4,g4,g1)"
+  contents="R e1 e2 B d2 f2 d4"
-The bottleneck formation invariably leads to a [[Ladder|ladder]] situation.
+  />
 == Bottlenecks with bridges ==
-<hex>R4, C4,
+<hexboard size="4x8"
- Hb1 Vc1 Hd1
+  coords="none"
+  edges="bottom"
+  visible="area(d1,a4,h4,h1)"
-     Hb4</hex>
+  contents="R f1 B e1 g1 e4"
+  />
-<hex>R4, C6,
+<hexboard size="4x8"
-     Vd1
+  coords="none"
-Hb2      He2
+  edges="bottom"
+  visible="area(d1,a4,h4,h1)"
-   Hb4</hex>
+  contents="R f1 B d2 g2 d4"
 [[category:strategy]]

← Older revision		Revision as of 00:07, 30 January 2008
Line 6:		Line 6:

	The bottleneck formation invariably leads to a [[Ladder\|ladder]] situation.		The bottleneck formation invariably leads to a [[Ladder\|ladder]] situation.
		+
		+	== Bottlenecks with bridges ==
		+
		+	<hex>R4, C4,
		+	Hb1 Vc1 Hd1
		+
		+
		+	Hb4</hex>
		+
		+	<hex>R4, C6,
		+	Vd1
		+	Hb2 He2
		+
		+	Hb4</hex>

	[[category:strategy]]		[[category:strategy]]

← Older revision		Revision as of 01:05, 17 December 2007
Line 6:		Line 6:

	The bottleneck formation invariably leads to a [[Ladder\|ladder]] situation.		The bottleneck formation invariably leads to a [[Ladder\|ladder]] situation.
		+
		+	[[category:strategy]]

← Older revision	Revision as of 15:53, 16 February 2006
(No difference)