Theory of ladder escapes - Revision history

Selinger: /* Sixth row ladders and up */ Updated the section in light of the existence of template IV1b.

2025-11-27T04:01:13Z

‎Sixth row ladders and up: Updated the section in light of the existence of template IV1b.

Bobson8: Fix a ladder escape

2024-10-19T18:14:15Z

Fix a ladder escape

Selinger: /* Examples */ Removed the "strange" example, which wasn't minimal and illustrated no point.

2024-10-19T16:00:51Z

‎Examples: Removed the "strange" example, which wasn't minimal and illustrated no point.

Bobson8: Fix the property of a ladder escape

2024-10-18T05:21:41Z

Fix the property of a ladder escape

Mason: Add 3rd row escape

2024-04-02T19:37:28Z

Add 3rd row escape

Mason: Add escape corresponding to the obtuse joseki that has popped up in recent times

2024-04-02T19:21:17Z

Add escape corresponding to the obtuse joseki that has popped up in recent times

Mason: Add 5th row ladder escape

2024-03-14T23:31:58Z

Add 5th row ladder escape

Selinger: /* Open patterns */ fixed a typo

2023-08-29T23:56:53Z

‎Open patterns: fixed a typo

Selinger: /* Examples */ Added a 4th row escape.

2023-06-03T21:25:46Z

‎Examples: Added a 4th row escape.

Mason: Add another non-2nd/4th row ladder escape, non 2-4 switchback, 2-4 parallel ladder template

2023-03-06T22:38:45Z

Add another non-2nd/4th row ladder escape, non 2-4 switchback, 2-4 parallel ladder template

@@ Line 1,448: / Line 1,448: @@
 Note that this argument does not show that 6th row ladders are categorically impossible. It only shows that the "usual" notion of ladder does not work. It is conceivable that 6th row ladders are possible under additional assumptions. For example, there might be a notion of 6th row ladder that requires additional space on the 7th row to its right, or on the 5th row to its left. It is currently unknown whether any viable notion of 6th row ladder exists.
-For 7th row ladders the situation is even worse. As explained in [[open problems about edge templates]], no amount of space under the ladder (even if we demand that the entire 5th row is clear) is known to guarantee a red connection if Blue just ignores the ladder and plays elsewhere. Thus, it is possible that 7th row ladders do not even exist in theory. Of course they do not occur in practice either.
+The situation for 7th row ladders is similar. The existence of [[edge template VI1b]] guarantees a red connection if Blue just ignores the ladder and plays elsewhere. But this requires a large amount of space. Just like for 6th row ladders, Blue has many options besides pushing the ladder, and it is not known whether a viable notion of 7th row ladder exists.
 == Second-to-fourth row switchbacks ==

@@ Line 720: / Line 720: @@
     coords="hide"
     edges="bottom"
-    visible="-a1 area(b3,c2,d2,d4,b4)"
+    visible="-area(b3,c2,d2,d4,b4)"
     contents="R ↓:d1 E +:a2 +:a3 +:a4"
     />

@@ Line 658: / Line 658: @@
     contents="E *:a1 E *:b1 R ↓:d1 E +:a2 E *:d2 E +:a3 E *:b3 E *:c3 E *:d3 E +:a4 E *:b4 E *:c4 E *:d4"
     />
 <hexboard size="5x4"
     coords="hide"
@@ Line 722: / Line 723: @@
     contents="R ↓:d1 E +:a2 +:a3 +:a4"
     />
 <hexboard size="5x5"
     coords="hide"
@@ Line 758: / Line 765: @@
     />
 The version of this last pattern on David King's website has the cells marked "+" (he uses arrows) sloping in the other direction; the location that is shown here makes the template minimal.
 == Fourth row ladders ==

@@ Line 669: / Line 669: @@
     visible="-a1 b1 c1 g1 g2"
     contents="E *:a1 E +:a3 E +:a4 E +:a5 E *:b1 E *:c1 R e1 R f3 E *:g1 E *:g2 S e3"
     />
 <hexboard size="5x6"
@@ Line 689: / Line 683: @@
     />
-The following third row ladder escape also escapes 2nd row ladders at distance 1 or greater (but not at distance 0):
+The following third row ladder escapes also escape 2nd row ladders at distance 1 or greater (but not at distance 0):
 <hexboard size="4x3"
     coords="hide"
@@ Line 696: / Line 690: @@
     contents="E *:a1 R b1 R c1 E +:a2 E +:a3 E +:a4"
     />
 The following third row ladder escapes also escape 2nd row ladders at distance 2 or greater (but not at distance 0 or 1):
 <hexboard size="4x4"

@@ Line 669: / Line 669: @@
     visible="-a1 b1 c1 g1 g2"
     contents="E *:a1 E +:a3 E +:a4 E +:a5 E *:b1 E *:c1 R e1 R f3 E *:g1 E *:g2 S e3"
     />
 <hexboard size="5x6"

@@ Line 708: / Line 708: @@
     visible="-d1"
     contents="E +:a2 E +:a3 E +:a4 R b1 R c1 E *:d1 S b2"
     />
 <hexboard size="5x5"

@@ Line 1,385: / Line 1,385: @@
     edges="bottom"
     contents="E +:a1 E +:a2 E +:a3 E +:a4 E +:a5 R c1 R b4"
     />

@@ Line 17: / Line 17: @@
 === Open patterns ===
-A ''pattern'' is a set of cells, each which may be empty or occupied by a stone of either color. In this article, we will only be concerned with patterns that include a red board edge. A pattern is ''open on the left'' if it comes with some cells marked "+" on its left side. No cells to the left of those "+"s may be part of the pattern. A pattern is ''open on the right'' if it comes with some cells marked "−" on its right side. No cells to the right of those "−"s may be part of the pattern. A pattern is ''open on both sides'' if it is open on the left and on the right. A pattern is ''closed'' if it is not open on either side. For example, the following four patterns are open on the right, open on both sides, open on the left, and closed, respectively:
+A ''pattern'' is a set of cells, each of which may be empty or occupied by a stone of either color. In this article, we will only be concerned with patterns that include a red board edge. A pattern is ''open on the left'' if it comes with some cells marked "+" on its left side. No cells to the left of those "+"s may be part of the pattern. A pattern is ''open on the right'' if it comes with some cells marked "−" on its right side. No cells to the right of those "−"s may be part of the pattern. A pattern is ''open on both sides'' if it is open on the left and on the right. A pattern is ''closed'' if it is not open on either side. For example, the following four patterns are open on the right, open on both sides, open on the left, and closed, respectively:
 <hexboard size="3x3"
    float="inline"

@@ Line 989: / Line 989: @@
     visible="-a1"
     contents="E *:a1 E +:a2 E +:a3 E +:a4 E +:a5 R b1 R c2"
     />
 <hexboard size="5x1"

@@ Line 1,980: / Line 1,980: @@
    contents="E +:a2 +:a3 +:a4 +:a5"
    />
+Other examples:
 Here are some other examples of 2-4 parallel ladder escapes that are neither 2nd nor 4th row ladder escapes nor 2nd-to-4th row switchbacks. They can be shown to be valid by Theorem 17, and are minimal. Unlike Tom's move, these ladder escapes don't require space on the 5th row.