Parallel ladder - Revision history

Selinger: Reorganized and cleaned up the article.

2021-12-29T00:36:46Z

Reorganized and cleaned up the article.

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Demer: /* Another example */ removed bad example and renamed section

2021-09-12T22:38:48Z

‎Another example: removed bad example and renamed section

Demer: /* Conceptualisation */ fixed diagrams

2021-09-12T02:10:03Z

‎Conceptualisation: fixed diagrams

Selinger: Edited categories

2020-12-28T21:32:02Z

Edited categories

Selinger: Fixed diagram syntax.

2020-09-08T17:01:10Z

Fixed diagram syntax.

Selinger: Fixed link

2020-08-22T23:33:31Z

Fixed link

Selinger: Deleting the "puzzle", as it is the same as the example at the top of the page.

2020-08-17T20:02:16Z

Deleting the "puzzle", as it is the same as the example at the top of the page.

Selinger: /* Conceptualisation */ Rewrote conceptualization and cleaned up next example.

2020-08-17T19:58:30Z

‎Conceptualisation: Rewrote conceptualization and cleaned up next example.

Selinger: Rewrote the first example to make more sense.

2020-08-17T19:12:40Z

Rewrote the first example to make more sense.

Hex player1: +category

2012-11-09T15:27:20Z

+category

@@ Line 58: / Line 58: @@
 There also exist other example (besides Tom's move) of ladder escapes that work for parallel ladders, but not for individual ladders. This is discussed in more detail [[Theory of ladder escapes#Second_and_fourth_row_parallel_ladders|here]].
-=== Another example ===
+=== Other uses ===
-Here is an example of a parallel ladder that helps Red to connect, even though there is not enough space for Tom's move:
+Even when there is not enough room for [[Tom's move]], a parallel ladder is no worse
-<hex>R7 C6
+<hexboard size="4x6"
-Ha1 Hb1 Vc1 Hd1 He1
+  visible="-(a1 a2 b1 b2)"
- Ha2 Hb2 Vc2
+  edges="bottom"
-   Ha3 Vb3 Hc3
+   coords="none"
-   Ha4 Vb4
+  contents="R c1 a3 1:b3 3:c3 B c2 a4 2:b4"
-    Va5 Hb5
+  />
-     </hex>
-Red starts by pushing both ladders, then breaks the 2nd row ladder at 13. Note that every blue move is [[forcing move|forced]].
+than the lower ladder plus a [[Switchback#Switchback_threat|switchback threat]], and Red can [[Climbing#Climbing_from_a_ladder|climb]] from it.
-<hex>R7 C6
-Ha1 Hb1 Vc1 Hd1 He1
- Ha2 Hb2 Vc2
-  Ha3 Vb3 Hc3
-   Ha4 Vb4
-    Va5 Hb5
- N:on Vc4 Hc5 Vd4 Hd5
- Va6 Ha7 Vb6 Hb7 Vc6 Hc7 Vd6 Hd7 Vf6
-</hex>
-−
-Red then moves upwards and eventually connects to the top edge by a [[double threat]].
-<hex>R7 C6
-Ha1 Hb1 Vc1 Hd1 He1
- Ha2 Hb2 Vc2
-  Ha3 Vb3 Hc3
-   Ha4 Vb4
-    Va5 Hb5
- Vc4 Hc5 Vd4 Hd5
- Va6 Ha7 Vb6 Hb7 Vc6 Hc7 Vd6 Hd7 Vf6
- H14e6 V15f5 H16e5 V17f4 H18e4 V19f3 H20e3 V21f2 H22f1 V23e2 Sd2 Sd3
-</hex>
 == 3rd and 5th rows ==

@@ Line 32: / Line 32: @@
 A parallel ladder on the 2nd and 4th rows is a situation such as the following, with Red to move. The two red stones must be connected to the top edge (although the connection is not shown here). Red has the option of pushing the 2nd row ladder or the 4th row ladder:
-<hexboard size="4x5"
+<hexboard size="4x6"
-   contents="R c1 R a3 B a4 B c2 E *:a1 *:a2 *:b1 *:b2"
+  visible="-(a1 a2 b1 b2)"
    />
 The first essential point is that a parallel ladder can be pushed. If Red pushes on the 4th row, Blue does not have the option to yield, or else Blue will lose immediately.
-<hexboard size="4x5"
+<hexboard size="4x6"
-   contents="R c1 R a3 B a4 B c2 E *:a1 *:a2 *:b1 *:b2 R 1:d1 B 2:d3 R 3:c3"
+   visible="-(a1 a2 b1 b2)"
-   />
+  edges="bottom"
 Thus, Blue has no option but to push the ladder. Then Red can push the 2nd row ladder as well.
-<hexboard size="4x5"
+<hexboard size="4x6"
-   contents="R c1 R a3 B a4 B c2 E *:a1 *:a2 *:b1 *:b2 R 1:d1 B 2:d2 R 3:b3 B 4:b4"
+   visible="-(a1 a2 b1 b2)"
    />
 Note that pushing a parallel ladder only works if the 4th row ladder is "ahead" of the 2nd row ladder. Once the 2nd row ladder has caught up, it is too late to push on the 4th row, as Blue can then yield, resulting in an ordinary 3rd row ladder.

← Older revision		Revision as of 21:32, 28 December 2020
Line 94:		Line 94:


−	[[category:~~ladder~~]]	+	[[category: Ladder]]
−	[[category:Advanced Strategy]]	+	[[category: Advanced Strategy]]
		+	[[category: Definition]]

@@ Line 33: / Line 33: @@
 A parallel ladder on the 2nd and 4th rows is a situation such as the following, with Red to move. The two red stones must be connected to the top edge (although the connection is not shown here). Red has the option of pushing the 2nd row ladder or the 4th row ladder:
 <hexboard size="4x5"
-   contents="R c1 R a3 B a4 B c2 E *:a1 a2 b1 b2"
+   contents="R c1 R a3 B a4 B c2 E *:a1 *:a2 *:b1 *:b2"
    />
 The first essential point is that a parallel ladder can be pushed. If Red pushes on the 4th row, Blue does not have the option to yield, or else Blue will lose immediately.
 <hexboard size="4x5"
-   contents="R c1 R a3 B a4 B c2 E *:a1 a2 b1 b2 R 1:d1 B 2:d3 R 3:c3"
+   contents="R c1 R a3 B a4 B c2 E *:a1 *:a2 *:b1 *:b2 R 1:d1 B 2:d3 R 3:c3"
    />
 Thus, Blue has no option but to push the ladder. Then Red can push the 2nd row ladder as well.
 <hexboard size="4x5"
-   contents="R c1 R a3 B a4 B c2 E *:a1 a2 b1 b2 R 1:d1 B 2:d2 R 3:b3 B 4:b4"
+   contents="R c1 R a3 B a4 B c2 E *:a1 *:a2 *:b1 *:b2 R 1:d1 B 2:d2 R 3:b3 B 4:b4"
    />
 Note that pushing a parallel ladder only works if the 4th row ladder is "ahead" of the 2nd row ladder. Once the 2nd row ladder has caught up, it is too late to push on the 4th row, as Blue can then yield, resulting in an ordinary 3rd row ladder.

@@ Line 47: / Line 47: @@
 The second essential point is that a parallel ladder is stronger than either a 2nd row ladder or a 4th row ladder individually. The best-known way of escaping a parallel ladder is by using [[Tom's move]], or a variation thereof, as shown in the example above. Tom's move only requires a certain amount of empty space, and does not require any pre-existing Red pieces. Even if there is not enough space before the ladder to perform Tom's move, a parallel ladder is awkward to defend against and will often give an advantage to Red.
-There also exist other example (besides Tom's move) of ladder escapes that work for parallel ladders, but not for individual ladders. This is discussed in more detail [[Proving_that_a_pattern_is_a_ladder_escape#Second_and_fourth_row_parallel_ladders|here]].
+There also exist other example (besides Tom's move) of ladder escapes that work for parallel ladders, but not for individual ladders. This is discussed in more detail [[Theory of ladder escapes#Second_and_fourth_row_parallel_ladders|here]].
 === Another example ===

@@ Line 93: / Line 93: @@
 e8 yields a second row ladder after d8, e7, c8, c10, d9. The play c9 also leads to a second row ladder after the likely f7, f8, e8 (d9 is met by e7) d10. In the latter case, Red could again try the parallel ladder trick by playing g7. Of course, the presence of other pieces in the area can change the possibilities.
 [[category:ladder]]
 [[category:Advanced Strategy]]

@@ Line 13: / Line 13: @@
         Vd4 Ve4 Hf4 Hg4
              Ve5
-      Vc6 Vd6 He6          Hi6
+      Vc6 Vd6 He6         Hh6 Hi6
         Hc7 Vd7
 Ha8 Hb8 Vc8 Hd8
@@ Line 19: / Line 19: @@
        Hb10</hex>
-All of Red's pieces form a connected [[group]]. This group is [[connection|connected]] to the [[Top edge|top]]. At the bottom, Red has a [[second row]] ladder with no possible [[ladder escape]] on the left. The potential escapes on the right are inadequate. For example, suppose Red ladders to f9. Then tries to escape with
+All of Red's pieces form a connected [[group]]. This group is [[connection|connected]] to the top. At the bottom, Red has a second row [[ladder]] with no possible [[ladder escape]] on the left. The potential escapes on the right are inadequate. For example, suppose Red breaks the ladder at e9 and then tries to [[zipper]]:
-:5. h9 g9
+<hex>R10 C10 Q1 Hc1 Vd2 Vd3 He3 Vf3 Vd4 Ve4 Hf4 Hg4 Ve5 Vc6 Vd6 He6 Hh6 Hi6 Hc7 Vd7 Ha8 Hb8 Vc8 Hd8 Hb10 N:on Vc9 Hc10 Ve9 Hd9 Vf7 He7 Vg5 Hf5 Vh4 Hh3</hex>
-:6. h8 g8
-:7. h7 f7.
-<hex>R10 C10 Q1 Hc1 Vd2 Vd3 He3 Vf3 Vd4 Ve4 Hf4 Hg4 Ve5 Vc6 Vd6 He6 Hi6 Hc7 Vd7 Ha8 Hb8 Vc8 Hd8 Hb10   Vc9 Hc10 Vd9 Hd10 Ve9 He10 N:on Vf9 Hf10 Vh9 Hg9 Vh8 Hg8 Vh7</hex>
+At this point Red fails to connect. Is Red done for? No! Red can create a sufficient escape by making use of a '''parallel ladder''', and essentially using [[Tom's move]]. Red plays like this:
-Now Red's only reasonable try is 8.g7 f8. Now 9.g6 loses to 9...f5 and 9.h5 loses to the forcing sequence 9...g6 10.h6 h4 11.g5 f5. All the other escape attempts likewise fail. Is Red done for?
+<hex>R10 C10 Q1 Hc1 Vd2 Vd3 He3 Vf3 Vd4 Ve4 Hf4 Hg4 Ve5 Vc6 Vd6 He6 Hh6 Hi6 Hc7 Vd7 Ha8 Hb8 Vc8 Hd8 Hb10 N:on Vc9 Hc10 Vf8 He9 Vd9 Hd10 Vg7 He8 Vf6 Sf5 Se7</hex>
-No! Red can create a sufficient escape by making use of a '''parallel ladder'''. In the original position Red plays 1.e7. How can [[Blue (player)|Blue]] stop Red from connecting to the bottom? d9 lets Red [[bridge|two-chain]] from e7 to f8 connecting to the bottom;  e9 and e10 allow d9 which is connected to the bottom and threatens to connect to Red's big group through c9 and e8; d10 loses to e8, f9 ([[Forced move|forced]]), c10; hence, Blue is forced to play the parallel ladder move 1...e8.  It is simplest for Red to repeat this and ladder to f7 forcing the 2...f8 response.
+Note that all of Blue's moves are forced. If Blue moves anywhere but 4, Red will easily connect to the edge. 3 and 7 are connected to the bottom edge by [[Edge template IV2b]], so that 8 is also forced. Now Red is connected by [[double threat]] at the two cells marked "*".
-−
-<hex>R10 C10 Q1 Hc1 Vd2 Vd3 He3 Vf3 Vd4 Ve4 Hf4 Hg4 Ve5 Vc6 Vd6 He6 Hi6 Hc7 Vd7 Ha8 Hb8 Vc8 Hd8 Hb10   Ve7 He8 Vf7 Hf8</hex>
-−
-Now Red now goes back to the [[second row]] [[ladder]] and tries to escape. What have we gained by preceding this with the parallel ladder moves? When trying to escape, the [[threat]] to connect to d7-e7-f7 is stronger than the previous weak threat to connect to d7. This [[Multiple threats|extra threat]] will let us push our escape chain farther up the board and in this case, just far enough to win the game.
-−
-Red's winning sequence is long but rather simple because every one of Blue's replies is forced. As before, Red ladders to f9 and escapes with 7. h9. Play continues 7...g9 8.h8 g8 9.h7 g7 10.h6 g6 11.h5. Red is threatening to play g5 with the double winning threats f5 and f6. But if Blue [[blocking|blocks]] this, say with 11...g5, then Red continues 12.i3 i2 13.h3 h2 and 14.g3 completes the [[win]].
 === Conceptualisation ===

← Older revision		Revision as of 15:27, 9 November 2012
Line 178:		Line 178:

	[[category:ladder]]		[[category:ladder]]
		+	[[category:Advanced Strategy]]