Ladder escape fork - Revision history

Selinger: Updated wording

2022-05-18T01:53:46Z

Updated wording

Selinger: /* See also */ Updated page name.

2020-11-30T02:18:29Z

‎See also: Updated page name.

Selinger: Removed section that does not belong here.

2020-11-30T02:16:49Z

Removed section that does not belong here.

Selinger: Moved material on "how high can the attacker climb" to "Climbing", and added this as a "see also".

2020-11-30T01:20:21Z

Moved material on "how high can the attacker climb" to "Climbing", and added this as a "see also".

Selinger: /* 3nd row ladder */ Finished "yielding" section.

2020-11-29T22:17:16Z

‎3nd row ladder: Finished "yielding" section.

Selinger: Added a 4th scenario for 2nd and 3rd row ladders; clarified yielding.

2020-11-29T22:04:02Z

Added a 4th scenario for 2nd and 3rd row ladders; clarified yielding.

Selinger: /* 3nd row ladder */ Added information on what happens when Blue yields.

2020-11-29T20:37:38Z

‎3nd row ladder: Added information on what happens when Blue yields.

Selinger: /* 3rd row ladder */ copy-edit

2020-11-29T19:44:38Z

‎3rd row ladder: copy-edit

Selinger: Added a section of "When to fork". Under construction.

2020-11-29T19:36:40Z

Added a section of "When to fork". Under construction.

Selinger: Added 4th row ladders.

2020-11-29T16:30:17Z

Added 4th row ladders.

← Older revision		Revision as of 01:53, 18 May 2022
Line 1:		Line 1:
−	A ~~[[Multiple threat\|forking~~ move~~]] which~~ creates a [[ladder escape]].	+	A ladder escape fork is a move that creates a [[ladder escape]] while also threatening another connection. It is a kind of [[double threat]].
		+
	== Example ==		== Example ==

@@ Line 50: / Line 50: @@
 == See also ==
-* [[Foiling ladder escapes]]
+* [[Foiling]]
 * [[Climbing#Climbing from a ladder|Climbing from a ladder]]
 [[category:ladder]]
 [[category:intermediate Strategy]]

@@ Line 47: / Line 47: @@
        Ha7 Hb7 H2c7
 </hex>
 == See also ==

@@ Line 47: / Line 47: @@
        Ha7 Hb7 H2c7
 </hex>
 == When to fork ==
@@ Line 175: / Line 81: @@
 == See also ==
-[[Foiling ladder escapes]]
+* [[Foiling ladder escapes]]
 [[category:ladder]]
 [[category:intermediate Strategy]]

@@ Line 102: / Line 102: @@
     />
-'''Scenario 4:''' If Red has a switchback threat and significantly more space on the right, Red can climb all the way to the 8th row, potentially bridging to a stone on the 10th row.
+'''Scenario 4:''' If Red has a switchback threat and significantly more space on the right, Red can climb all the way to the 8th row, potentially bridging to a stone on the 10th row. The cells marked "*" are not required to be empty.
 <hexboard size="8x9"
     coords="hide"
-    contents="R a5 a6 b6 c6 B a7 b7 c7 i5 R 1:e6 B 2:d6 R 3:e4 B 4:e5 R 5:g4 B 6:f4 R 7:g3 B 8:f3 R 9:h1"
+    contents="R a5 a6 b6 c6 B a7 b7 c7 i5 R 1:e6 B 2:d6 R 3:e4 B 4:e5 R 5:g4 B 6:f4 R 7:g3 B 8:f3 R 9:h1
     />
@@ Line 121: / Line 122: @@
 <hexboard size="8x9"
     coords="hide"
-    contents="R a5 a6 b6 B a7 b8 i5 R 1:b7 B 2:b8 R 3:f6"
+    contents="R a5 a6 b6 B a7 b8 i5 R 1:b7 B 2:a8 R 3:f6
-    oldcontents="R 1:e6 B 2:d6 R 3:e4 B 4:e5 R 5:g4 B 6:f4 R 7:g3 B 8:f3 R 9:h1"
+             E *:i1 *:i2 *:i3 *:i4 *:h3 *:g1 *:f2 *:e3 *:d3 *:a1 *:a2 *:a3 *:a4 *:b1 *:b2 *:b3 *:c1 *:c2 *:c3 *:d1 *:d2 *:e1 *:e2 *:f1"
     />
 === 4th row and higher ladders ===

@@ Line 54: / Line 54: @@
 === 2nd row ladder ===
-In the first example, Red's space is limited. Red can climb to the 4th row, potentially [[bridge|bridging]] to a stone on the 6th row.
+'''Scenario 1:''' In this scenario, Red's space is limited. Red can climb to the 4th row, potentially [[bridge|bridging]] to a stone on the 6th row.
-<hexboard size="6x7"
+<hexboard size="6x8"
     coords="hide"
     contents="R a5 b5 c5 B a6 b6 c6 d4 f5 R 1:e5 B 2:d5 R 3:f3"
     />
-If Red has slightly more space, Red can climb to the 5th row, potentially bridging to a stone on the 7th row.
+'''Scenario 2:''' If Red has slightly more space, Red can climb to the 5th row, potentially bridging to a stone on the 7th row.
-<hexboard size="6x7"
+<hexboard size="6x8"
     coords="hide"
     contents="R a5 b5 c5 B a6 b6 c6 f5 R 1:e5 B 2:d5 R 3:e4 B 4:d4 R 5:f2"
     />
-Finally, in a [[switchback]] situation, where a 2nd-to-4th row switchback would allow Red to connect, Red can climb to the 6th row, potentially bridging to a stone on the 8th row.  This kind of forking ladder escape is called a ''switchback fork''.
+'''Scenario 3:''' In this scenario, Red's 2nd row ladder comes with a ''switchback threat'', i.e., a 2nd-to-4th row switchback would allow Red to connect. In this case, Red can climb to the 6th row, potentially bridging to a stone on the 8th row. This kind of ladder escape fork is called a ''switchback fork''.
-<hexboard size="6x7"
+<hexboard size="6x8"
     coords="hide"
     contents="R a5 b5 c5 a4 B a6 b6 c6 f5 R 1:e5 B 2:d5 R 3:f3 B 4:e3 R 5:g1"
     />
-Of course, there are many variations of this, depending on what other pieces Red and Blue have on the board. But the three basic patterns shown above are the most common, and are good starting points for planning more complex ladder escape forks.
+'''Scenario 4:''' Finally, if Red has a switchback threat and slightly more space on the right, Red can climb all the way to the 7th row, potentially bridging to a stone on the 9th row. This is highly threatening; note that on an 11×11 board, the 9th row is almost on the opposite side of he board.
 === 3nd row ladder ===
-The situation for 3rd row ladders is largely similar to that of 2nd row ladders. In the most constrained case, Red can climb to the 5th row, potentially bridging to a stone on the 7th row.
+The situation for 3rd row ladders is largely similar to that of 2nd row ladders. Scenarios 1&mdash;3 work without much modification.
-<hexboard size="7x7"
     coords="hide"
     contents="R a5 b5 c5 B a6 b6 c6 d4 g5 R 1:e5 B 2:d5 R 3:f3"
     />
-If Red has slightly more space, Red can climb to the 6th row, potentially bridging to a stone on the 8th row.
+'''Scenario 2:''' If Red has slightly more space, Red can climb to the 6th row, potentially bridging to a stone on the 8th row.
-<hexboard size="7x7"
+<hexboard size="7x9"
     coords="hide"
     contents="R a5 b5 c5 B a6 b6 c6 g5 R 1:e5 B 2:d5 R 3:e4 B 4:d4 R 5:f2"
     />
-Finally, in a [[switchback]] situation, where a 3nd-to-5th row switchback would allow Red to connect, Red can play a switchback fork and climb to the 7th row, potentially bridging to a stone on the 9th row. This is extremely threatening; note that on an 11×11 board, the 9th row is almost on the opposite side of he board.
+'''Scenario 3:''' If Red's 3rd row ladder comes with a switchback threat, Red can play a switchback fork and climb to the 7th row, potentially bridging to a stone on the 9th row.
-<hexboard size="7x7"
+<hexboard size="7x9"
     coords="hide"
     contents="R a5 b5 c5 a4 B a6 b6 c6 g5 R 1:e5 B 2:d5 R 3:f3 B 4:e3 R 5:g1"
     />
-We also note that [[yielding]] to the 2nd row does not help Blue in any of these scenarios: if Blue yields, Red can still climb exactly the same amount as if Blue does not yield. In the first scenario, Red still climbs to the 5th row, and actually requires less space to do so. It does not matter when Blue yields.
+'''Scenario 4:''' If Red has a switchback threat and significantly more space on the right, Red can climb all the way to the 8th row, potentially bridging to a stone on the 10th row.
-<hexboard size="7x7"
+<hexboard size="8x9"
     coords="hide"
-    contents="R a5 b5 c5 B a6 b6 c7 d4 g5 R 1:c6 B 2:b7 R 3:e6 B 4:d6 R 5:e5 B 6:d5 R 7:f3"
+    contents="R a5 a6 b6 c6 B a7 b7 c7 i5 R 1:e6 B 2:d6 R 3:e4 B 4:e5 R 5:g4 B 6:f4 R 7:g3 B 8:f3 R 9:h1"
     />
-In the second scenario, Red still climbs to the 6th row:
-<hexboard size="7x7"
+'''Yielding:''' [[Yielding]] to the 2nd row does not help Blue in any of these scenarios. If Blue yields at the last possible moment in scenarios 1–4, Red can use a few extra moves to achieve the same outcome as without yielding, and actually require slightly less space. For example, this is how scenario 1 plays out if Blue yields:
     coords="hide"
-    contents="R a5 b5 c5 B a6 b6 c7 g5 R 1:c6 B 2:b7 R 3:e6 B 4:d6 R 5:e5 B 6:d5 R 7:e4 B 8:d4 R 9:f2"
+    contents="R a5 b5 c5 B a6 b6 c7 d4 g5 R 1:c6 B 2:b7 R 3:e6 B 4:d6 R 5:e5 B 6:d5 R 7:f3"
     />
-The third scenario, with 3rd-to-5th row switchback threat, works similarly:
+If Blue tries to yield earlier in scenarios 1–3, Red can play, respectively, scenarios 2–4 for 2nd row ladders to achieve the same outcome, and does not even require the 3rd-to-5th row switchback threat. For example, this is how scenario 3 plays out if Blue yields early:
-<hexboard size="7x7"
+<hexboard size="7x9"
     coords="hide"
-    contents="R a4 a5 b5 c5 B a6 b6 c7 g5 R 1:c6 B 2:b7 R 3:e6 B 4:d6 R 5:e5 B 6:d5 R 7:f3 B 8:e3 R 9:g1"
+    contents="R a5 b5 B a6 b7 g5 R 1:b6 B 2:a7 R 3:d6 B 4:c6 R 5:d4 B 6:d5 R 7:f4 B 8:e4 R 9:f3 B 10:e3 R 11:g1"
     />
-Finally, if Blue tries to yield earlier in the 2nd or 3rd scenarios, Red can always climb to the 7th row and does not even require the threat of a 3rd-to-5th row switchback. Red can play as follows:
+In scenario 4, if Blue yields any earlier than the second-to-last opportunity, Red can simply yield back to the 3rd row. The final and most interesting case is when Blue yields exactly at the second-to-last opportunity. In that case, after optionally invading Blue's bridge, the unique winning move is 3:
-<hexboard size="7x7"
+<hexboard size="8x9"
     coords="hide"
-    contents="R a5 b5 B a6 b7 g5 R 1:b6 B 2:a7 R 3:d6 B 4:c6 R 5:d4 B 6:d5 R 7:f4 B 8:e4 R 9:f3 B 10:e3 R 11:g1"
+    contents="R a5 a6 b6 B a7 b8 i5 R 1:b7 B 2:b8 R 3:f6"
     />
 === 4th row and higher ladders ===

@@ Line 128: / Line 128: @@
    contents="R e3 B e4 R d4 B c6 R 1:d5 B 2:d6 R 3:f5 B 4:g6 R 5:e7 B 6:e5 R 7:g3 B 8:f3 R 9:h1"
    />
-On the other hand, if Red pivots without first pushing the ladder, Red can still climb to "c", but Blue does not get the forcing move. This confers a small but significant advantage on Red.
+On the other hand, if Red pivots without first pushing the ladder, Red can still climb to "c", but Blue does not get the forcing move. This confers a small but potentially significant advantage on Red.
 <hexboard size="7x8"
    coords="hide"
    contents="R e3 B e4 R d4 B c6 R 1:f5 B 2:d6 R 3:g3 B 4:f3 R 5:h1"
    />
 == See also ==

← Older revision		Revision as of 19:36, 29 November 2020
Line 103:		Line 103:
	However, if Red had, for example, one more piece at either of the locations marked "*" (or pretty much anywhere else near the bottom edge), then the pivot piece would be sufficiently connected for the fork to work in the same way as for 2nd or 3rd row ladders.		However, if Red had, for example, one more piece at either of the locations marked "*" (or pretty much anywhere else near the bottom edge), then the pivot piece would be sufficiently connected for the fork to work in the same way as for 2nd or 3rd row ladders.

		+	== When to fork ==
		+
		+	In all of the above examples, we have shown Red pushing the ladder until Red is two hexes away from the pivot location, and then pivoting. This serves well for illustration purposes, as it makes it more obvious why the pivot piece is forcing. However, in practice, it is often unnecessary, and sometimes detrimental, to start by pushing the ladder. Instead, Red can often (but not always) play the pivot piece right away.
		+
		+	=== 2nd row ladder ===
		+
		+	In the case of 2nd row ladders, pushing the ladder before pivoting usually does not hurt the attacker, and can sometimes be necessary. For example, consider this situation, with Red to move:
		+	<hexboard size="6x8"
		+	coords="hide"
		+	contents="R a1 a2 a3 a4 a5 f3 g2 B a6 c4 d4 e2 g1 h1 E a:e5 b:g5"
		+	/>
		+	In this situation, Red must push the ladder all the way to "a" before pivoting at "b", or else the pivot does not work.
		+
		+	=== 3rd row ladder ===
		+
		+	In the case of a 3rd row ladder, pushing the ladder before pivoting is sometimes necessary, for the same reason as for 2nd row ladders. However, in situations where pushing the ladder is not necessary, the attacker may gain a small advantage from not pushing the ladder. Consider the following situation, which frequently develops near an obtuse corner in actual games. With Red to move:
		+	<hexboard size="7x8"
		+	coords="hide"
		+	contents="R e3 B e4 R d4 B c6 E a:d5 b:f5 c:h1 x:g6"
		+	/>
		+	Red threatens a 3rd row ladder at "a", and would like to pivot at "b" to climb to "c". Red can indeed do this, but the problem is that if Red starts by pushing the ladder, Blue gets an additional forcing move at "x":
		+	<hexboard size="7x8"
		+	coords="hide"
		+	contents="R e3 B e4 R d4 B c6 R 1:d5 B 2:d6 R 3:f5 B 4:g6 R 5:e7 B 6:e5 R 7:g3 B 8:f3 R 9:h1"
		+	/>
		+	On the other hand, if Red pivots without first pushing the ladder, Red can still climb to "c", but Blue does not get the forcing move. This confers a small but significant advantage on Red.
		+	<hexboard size="7x8"
		+	coords="hide"
		+	contents="R e3 B e4 R d4 B c6 R 1:f5 B 2:d6 R 3:g3 B 4:f3 R 5:h1"
		+	/>
	== See also ==		== See also ==

@@ Line 36: / Line 36: @@
 </hex>
-Red needs the two pieces at the top right hand-corner of the board. Red pushes the ladder just enough to use a '''ladder escape fork'''. This pivot piece threatens to connect to the top group and acts as a [[ladder escape]] as well.
+Red needs the two pieces at the top right hand-corner of the board. Red pushes the ladder just enough to use a '''ladder escape fork'''. Piece number 3 is called the '''pivot piece'''. It threatens to connect to the top group and acts as a [[ladder escape]] as well.
 <hex>R7 C7 Q1
@@ Line 93: / Line 93: @@
     contents="R a5 b5 c5 a4 B a6 b6 c6 g5 R 1:e5 B 2:d5 R 3:f3 B 4:e3 R 5:g1"
     />
 == See also ==