Ladder - Revision history

Selinger: Minor copy-editing, with the help of ChatGPT

2023-01-20T14:12:28Z

Minor copy-editing, with the help of ChatGPT

Selinger: Copy-editing

2023-01-17T00:07:58Z

Copy-editing

Selinger: Converted to new hexboard diagrams

2020-12-09T15:06:14Z

Converted to new hexboard diagrams

Selinger: emphasize the defined terms "attacking" and "defending".

2020-10-16T22:30:38Z

emphasize the defined terms "attacking" and "defending".

Wccanard: Added some more details.

2016-05-20T19:34:52Z

Added some more details.

Tommah: took number off escape piece

2015-08-22T15:45:17Z

took number off escape piece

Halladba: cat. ladder

2007-12-17T01:37:16Z

cat. ladder

Roland Illig: move number

2007-09-30T10:30:07Z

move number

Reiner Martin: removed capitalisation for consistency

2005-02-16T10:01:00Z

removed capitalisation for consistency

Turing: Found a newer page, copying that instead

2005-02-06T07:32:23Z

Found a newer page, copying that instead

@@ Line 1: / Line 1: @@
-A '''ladder''' is a sequence of moves in which both players play stones in straight lines, usually parallel to a nearby [[edge]].  Here is an example of a ladder.
+A '''ladder''' is a sequence of moves in which both players play stones in straight lines, usually parallel to a nearby [[edge]]. Here is an example of a ladder:
 <hexboard size="4x10"
     coords="hide"
@@ Line 7: / Line 8: @@
     contents="R d1 B c2 R d2 B e2 R 2:d3 R 4:e3 R 6:f3 R 8:g3 R j3 B 1:c4 B 3:d4 B 5:e4 B 7:f4"
     />
-Here Red is '''attacking''', and trying to make a connection to the bottom edge, whereas Blue is '''defending''' and blocking the connection at each step. If Red keeps playing along the second row with a view to connecting to the bottom, then Blue is forced to continue playing along the first row if Blue wants to prevent the connection.
+In this example, Red is '''attacking''' and trying to make a connection to the bottom edge, whereas Blue is '''defending''' and blocking the connection at each step. If Red continues to play along the second row with the goal of connecting to the bottom, then Blue is forced to continue playing along the first row to prevent the connection.
-Ladders usually occur close to an edge of the board. The edge in question usually belongs to the attacking player, whose stones are further from the edge than the defender's stones.
+Ladders usually occur close to an edge of the board, typically the edge belonging to the attacking player, whose stones are further from the edge than the defender's stones.
-If the above ladder continues, Red will be able to force a connection to the bottom, because of her [[Ladder escape|ladder escape]] piece on the very right of the second row:
+In the above ladder example, Red will eventually be able to force a connection to the bottom edge due to her [[Ladder escape|ladder escape]] piece on the right of the second row:
 <hexboard size="4x10"
     coords="hide"
@@ Line 17: / Line 18: @@
     contents="R d1 B c2 R d2 B e2 R d3 R e3 R f3 R g3 R 10:h3 R 12:i3 R j3 B c4 B d4 B e4 B f4 B 9:g4 B 11:h4"
     />
-When the ladder reaches this ladder escape piece, Blue can no longer block the connection.
+Once the ladder reaches this ladder escape piece, Blue can no longer block the connection.
-The ladder is named after how far the attacking player is from the edge. For example, the above diagram shows a second row ladder, also called a height-2 ladder.
+The ladder is named after how far the attacking player is from the edge. For example, the above diagram shows a second row ladder, also known as a height-2 ladder.
-A second row ladder is the most aggressive kind of ladder to defend against. Ladders can form on other rows too. Here is an example of a third row ladder.
+A second row ladder is the most aggressive kind of ladder to defend against. Ladders can also form on other rows. Here is an example of a third row ladder:
 <hexboard size="5x10"
@@ Line 28: / Line 29: @@
     />
-Again Red wants to connect to the bottom, and Blue is defending against this connection. This time Red will not succeed in connecting to the bottom, because the red pieces on the right do not form a 3rd row ladder escape. If Red continues to push the ladder, Blue is able to successfully block. For example:
+In this case, Red will not succeed in connecting to the bottom because the red pieces on the right do not form a 3rd row ladder escape. If Red continues to push the ladder, Blue is able to successfully block it. For example:
 <hexboard size="5x10"
@@ Line 35: / Line 36: @@
     contents="R b1 B c1 B i1 R j1 R b2 B d2 R j2 R c3 R d3 R e3 R f3 B b4 B c4 B d4 B e4 B f4 R 8:g3 B 9:g4 R 10:i3 B 11:h3"
     />
 Blue has successfully stopped the ladder from connecting.
 == Pre-ladder formations ==
-It is useful to recognise some basic positions where a player can force a ladder to occur. These formations can appear at any distance from the edge. The examples below result in 3rd row ladders. If they are one hex closer to the edge, they give 2nd row ladders; if they are one hex further from the edge, they give 4th row ladders, etc. The first formation is called the [[bottleneck]]. In all cases, it is Red's turn.
+It is useful to recognize some basic positions where a player can force a ladder to occur. These formations can appear at any distance from the edge. The examples below result in 3rd row ladders. If they are one hex closer to the edge, they give 2nd row ladders; if they are one hex further from the edge, they give 4th row ladders, etc. The first formation is called the [[bottleneck]]. In all cases, it is Red's turn.
 <hexboard size="5x8"

@@ Line 1: / Line 1: @@
-A '''ladder''' is a situation in which both players play a sequence of pieces in straight lines, often parallel to a nearby [[edge]], to make a straight unbroken [[chain]].  Here is an example of a ladder. The picture is of the bottom edge of the board, and red is trying to connect to this edge.
+A '''ladder''' is a sequence of moves in which both players play stones in straight lines, usually parallel to a nearby [[edge]].  Here is an example of a ladder.
-−
 <hexboard size="4x10"
     coords="hide"
@@ Line 8: / Line 7: @@
     contents="R d1 B c2 R d2 B e2 R 2:d3 R 4:e3 R 6:f3 R 8:g3 R j3 B 1:c4 B 3:d4 B 5:e4 B 7:f4"
     />
-Here red is '''attacking''', and trying to make a connection to the bottom edge, whereas blue is '''defending''' and blocking the connection at each stage. If red keeps playing along the second row with a view to connecting to the bottom, then blue is forced to continue playing along the first row if blue wants to prevent the connection.
+Ladders usually occur close to an edge of the board. The edge in question usually belongs to the attacking player, whose stones are further from the edge than the defender's stones.
-−
-Ladders often occur close to an edge of the board. The edge in question will usually belong to the [[attacking player]], and the attacking player's chain will almost always be parallel to the edge and further from the edge than the pieces of the defending player.
-−
-In the position above it is red (vertical) to move. For the last few moves red has been '''laddering''' along the second row, with blue playing underneath to stop red connecting. But red will be able to force a connection to the bottom anyway, because of their [[Ladder escape|ladder escape]] piece on the very right of the second row:
 <hexboard size="4x10"
     coords="hide"
     edges="bottom left right"
-    contents="R d1 B c2 R d2 B e2 R d3 R e3 R f3 R g3 R 2:h3 R 4:i3 R j3 B c4 B d4 B e4 B f4 B 1:g4 B 3:h4"
+    contents="R d1 B c2 R d2 B e2 R d3 R e3 R f3 R g3 R 10:h3 R 12:i3 R j3 B c4 B d4 B e4 B f4 B 9:g4 B 11:h4"
     />
-When the ladder reaches this ladder escape piece, blue can no longer block the connection.
+The ladder is named after how far the attacking player is from the edge. For example, the above diagram shows a second row ladder, also called a height-2 ladder.
 A second row ladder is the most aggressive kind of ladder to defend against. Ladders can form on other rows too. Here is an example of a third row ladder.
-Red could instead have stopped laddering to the right and laddered to the left instead:
-−
-<hexboard size="4x10"
-   coords="hide"
-   edges="bottom left right"
-   contents="R d1 B c2 R d2 B e2 R 4:b3 R 2:c3 R d3 R e3 R f3 R g3 R j3 B 5:a4 B 3:b4 B c4 B d4 B e4 B f4 B 1:g4"
-   />
-−
-but this does not help red to connect to the bottom edge, because on this side of the board red had no ladder escape and cannot break through.
-−
-The ladder above is called a '''second row ladder''' because the pieces of the attacker (in this case, red) are all on the second row of the board. A second row ladder is the most aggressive kind of ladder to defend against. Ladders can form on other rows too. Here is an example of a third row ladder forming.
 <hexboard size="5x10"
@@ Line 41: / Line 28: @@
     />
-Again red wants to connect to the bottom, and blue is defending against this connection. This time red will not succeed in connecting to the bottom, because the red pieces on the right do not form a 3rd row ladder escape, and if red continues to press then blue will be able to successfully block. For example:
+Again Red wants to connect to the bottom, and Blue is defending against this connection. This time Red will not succeed in connecting to the bottom, because the red pieces on the right do not form a 3rd row ladder escape. If Red continues to push the ladder, Blue is able to successfully block. For example:
 <hexboard size="5x10"
     coords="hide"
     edges="bottom left right"
-    contents="R b1 B c1 B i1 R j1 R b2 B d2 B 8:h2 R 3:i2 R j2 R c3 R d3 R e3 R f3 R 1:g3 B 6:h3 R 7:i3 B b4 B c4 B d4 B e4 B f4 B 2:g4 R 5:h4 B 4:i4"
+    contents="R b1 B c1 B i1 R j1 R b2 B d2 R j2 R c3 R d3 R e3 R f3 B b4 B c4 B d4 B e4 B f4 R 8:g3 B 9:g4 R 10:i3 B 11:h3"
     />
@@ Line 52: / Line 39: @@
 == Pre-ladder formations ==
-It is useful to recognise some basic positions where a player can force a ladder to occur. These formations can appear at any distance from the edge. The examples below result in 3rd row ladders. If they are one hex closer to the edge, they give 2nd row ladders; if they are one hex further from the edge, they give 4th row ladders, etc. The first formation is called the [[bottleneck]].
+It is useful to recognise some basic positions where a player can force a ladder to occur. These formations can appear at any distance from the edge. The examples below result in 3rd row ladders. If they are one hex closer to the edge, they give 2nd row ladders; if they are one hex further from the edge, they give 4th row ladders, etc. The first formation is called the [[bottleneck]]. In all cases, it is Red's turn.
 <hexboard size="5x8"
@@ Line 77: / Line 64: @@
 == Basic Terminology ==
-Sometimes it is important to say exactly how close to the edge a ladder is. A '''second row ladder''' is a ladder where the attacking pieces are on the second row -- just one row from the attacker's edge. A '''third row ladder''' is a ladder where the ladder's attacking pieces are on the third row. One could in theory continue this pattern forever but in practice one rarely talks about fifth or higher row ladders. This is because even though these ladders do sometimes form, the general intention by the attacker is typically not to connect to the edge: the attacker may instead want to try to connect to another group of their own pieces.
+Sometimes it is important to say exactly how close to the edge a ladder is. A '''second row ladder''' is a ladder where the attacking pieces are on the second row -- just one row from the attacker's edge. A '''third row ladder''' is a ladder where the ladder's attacking pieces are on the third row. One could in theory continue this pattern forever but in practice one rarely talks about sixth or higher row ladders. This is because even though these ladders do sometimes form, the general intention by the attacker is typically not to connect to the edge: the attacker may instead want to try to connect to another group of their own stones.
-Another reason why ladders much higher than the fourth row are not often considered is that if a ladder is sufficiently high, the defender can just ignore it and play elsewhere, and the attacker may not be able to instantly connect. This means that for a sufficiently high ladder it seems impossible to formulate a notion of a ladder escape as the defender can ignore the ladder and play in the escape area without losing immediately.
+Another reason why ladders much higher than the fifth row are not often considered is that if a ladder is sufficiently high, the defender can just ignore it and play elsewhere, and the attacker may not be able to instantly connect. This means that for a sufficiently high ladder it seems impossible to formulate a notion of a ladder escape as the defender can ignore the ladder and play in the escape area without losing immediately.
 == What every player should know ==
@@ Line 93: / Line 80: @@
 # [[Cornering]]
-== Specific ladder strategies ==
+== See also ==
-[[Parallel ladder|Parallel ladder trick]]
+* [[Parallel ladder]]
-[[Yielding]]
+* [[Theory of ladder escapes]]
 [[category:ladder]]

@@ Line 5: / Line 5: @@
 <hexboard size="4x10"
     coords="hide"
     contents="R d1 B c2 R d2 B e2 R 2:d3 R 4:e3 R 6:f3 R 8:g3 R j3 B 1:c4 B 3:d4 B 5:e4 B 7:f4"
     />
@@ Line 16: / Line 17: @@
 <hexboard size="4x10"
     coords="hide"
     contents="R d1 B c2 R d2 B e2 R d3 R e3 R f3 R g3 R 2:h3 R 4:i3 R j3 B c4 B d4 B e4 B f4 B 1:g4 B 3:h4"
     />
@@ Line 25: / Line 27: @@
 <hexboard size="4x10"
     coords="hide"
     contents="R d1 B c2 R d2 B e2 R 4:b3 R 2:c3 R d3 R e3 R f3 R g3 R j3 B 5:a4 B 3:b4 B c4 B d4 B e4 B f4 B 1:g4"
     />
@@ Line 34: / Line 37: @@
 <hexboard size="5x10"
     coords="hide"
     contents="R b1 B c1 B i1 R j1 R b2 B d2 R j2 R c3 R 2:d3 R 4:e3 R 6:f3 B b4 B 1:c4 B 3:d4 B 5:e4 B 7:f4"
     />
@@ Line 41: / Line 45: @@
 <hexboard size="5x10"
     coords="hide"
     contents="R b1 B c1 B i1 R j1 R b2 B d2 B 8:h2 R 3:i2 R j2 R c3 R d3 R e3 R f3 R 1:g3 B 6:h3 R 7:i3 B b4 B c4 B d4 B e4 B f4 B 2:g4 R 5:h4 B 4:i4"
     />
@@ Line 47: / Line 52: @@
 == Pre-ladder formations ==
-It is important to recognise some basic positions where a player can force a ladder to occur:
+It is useful to recognise some basic positions where a player can force a ladder to occur. These formations can appear at any distance from the edge. The examples below result in 3rd row ladders. If they are one hex closer to the edge, they give 2nd row ladders; if they are one hex further from the edge, they give 4th row ladders, etc. The first formation is called the [[bottleneck]].
-<hex>R5 C5 Hb2 Vc2 Hd2 Hb4</hex>
+<hexboard size="5x8"
-<hex>R5 C5 Vb2 Va4 Ha5</hex>
+<hexboard size="5x7"
 == Basic Terminology ==

@@ Line 8: / Line 8: @@
     />
-Here red is attacking, and trying to make a connection to the bottom edge, whereas blue is defending and blocking the connection at each stage. If red keeps playing along the second row with a view to connecting to the bottom, then blue is forced to continue playing along the first row if blue wants to prevent the connection.
+Here red is '''attacking''', and trying to make a connection to the bottom edge, whereas blue is '''defending''' and blocking the connection at each stage. If red keeps playing along the second row with a view to connecting to the bottom, then blue is forced to continue playing along the first row if blue wants to prevent the connection.
 Ladders often occur close to an edge of the board. The edge in question will usually belong to the [[attacking player]], and the attacking player's chain will almost always be parallel to the edge and further from the edge than the pieces of the defending player.

@@ Line 1: / Line 1: @@
-Red (vertical) to move. In this situation red has a sure win due to his [[Ladder escape|ladder escape]] on j3. Of course he can start another ladder playing a4 but in that case, blue has a ladder escape on b2.
+A '''ladder''' is a situation in which both players play a sequence of pieces in straight lines, often parallel to a nearby [[edge]], to make a straight unbroken [[chain]].  Here is an example of a ladder. The picture is of the bottom edge of the board, and red is trying to connect to this edge.
 == Pre-ladder formations ==
 <hex>R5 C5 Hb2 Vc2 Hd2 Hb4</hex>
@@ Line 12: / Line 54: @@
 <hex>R5 C5 Ve1 Vd3 He3 Hc4 Hd4</hex>
 == Ladder handling ==

@@ Line 1: / Line 1: @@
 A '''ladder''' is a situation in which both players move perpendicularly to an [[edge]] making a straight unbroken [[chain]]. The [[attacking player]]'s chain is almost always further from the edge. Here is an example of the ladder starting from b4 and c3.
-<hex>R4 C10 Q1 Vc1, Vc2, Hb2, Hd2, N:on Hb4, Vc3, Hc4, Vd3, Hd4, Ve3, He4, Vf3, Hf4, Vj3</hex>
+<hex>R4 C10 Q1 Vc1, Vc2, Hb2, Hd2, N:on Hb4, Vc3, Hc4, Vd3, Hd4, Ve3, He4, Vf3, Hf4, N:off Vj3</hex>
 Red (vertical) to move. In this situation red has a sure win due to his [[Ladder escape|ladder escape]] on j3. Of course he can start another ladder playing a4 but in that case, blue has a ladder escape on b2.

← Older revision		Revision as of 01:37, 17 December 2007
Line 26:		Line 26:

	[[Yielding]]		[[Yielding]]
		+
		+	[[category:ladder]]

← Older revision		Revision as of 07:32, 6 February 2005
Line 3:		Line 3:
	<hex>R4, C10, Vc1, Vc2, Hb2, Hd2, Hb4, Vc3, Hc4, Vd3, Hd4, Ve3, He4, Vf3, Hf4, Vj3</hex>		<hex>R4, C10, Vc1, Vc2, Hb2, Hd2, Hb4, Vc3, Hc4, Vd3, Hd4, Ve3, He4, Vf3, Hf4, Vj3</hex>

−	Red (vertical) to move. In this situation red has a sure win due to his ladder escape on j3. Of course he can start another ladder playing a4 but in that case, blue has a ladder escape on b2.	+	Red (vertical) to move. In this situation red has a sure win due to his [[Ladder escape\|ladder escape]] on j3. Of course he can start another ladder playing a4 but in that case, blue has a ladder escape on b2.
		+
		+	== Pre-Ladder Formations ==
		+
		+	<hex>R5 C5 Hb2 Vc2 Hd2 Hb4</hex>
		+
		+	<hex>R5 C5 Vb2 Va4 Ha5</hex>
		+
		+	<hex>R5 C5 Ve1 Vd3 He3 Hc4 Hd4</hex>
		+
		+	== Ladder Handling ==
		+
		+	There are three ways for the attacking player to "win" in a ladder situation:
		+
		+	# Making use of an existing [[Ladder escape\|ladder escape]] piece
		+	# Creating a new ladder escape with a [[Ladder escape fork]]
		+	# [[Cornering]]
		+
		+	== Specific Ladder Strategies ==
		+
		+	[[Parallel ladder\|Parallel ladder trick]]
		+
		+	[[Yielding]]