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| Line 47: |
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| | Ha7 Hb7 H2c7 | | Ha7 Hb7 H2c7 |
| | </hex> | | </hex> |
| − |
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| − | == How far can the attacker climb? ==
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| − |
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| − | The effectiveness of a potential fork can be measured by how far the attacker can potentially [[climbing|climb]]. Let us consider some typical ladders and potential forks:
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| − | === 2nd row ladder ===
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| − |
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| − | '''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.
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| − | <hexboard size="6x8"
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| − | coords="hide"
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| − | contents="R a5 b5 c5 B a6 b6 c6 d4 f5 R 1:e5 B 2:d5 R 3:f3"
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| − | />
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| − |
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| − | '''Scenario 2:''' If Red has slightly more space, Red can climb to the 5th row, potentially bridging to a stone on the 7th row.
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| − | <hexboard size="6x8"
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| − | coords="hide"
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| − | 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"
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| − | />
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| − |
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| − | '''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''.
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| − | <hexboard size="6x8"
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| − | coords="hide"
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| − | 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"
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| − | />
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| − |
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| − | '''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.
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| − | <hexboard size="7x8"
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| − | coords="hide"
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| − | contents="R a5 a6 b6 c6 B a7 b7 c7 h5 h6 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"
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| − | />
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| − | Of course, there are many variations of these basic scenarios, depending on what other pieces Red and Blue have on the board. But the four scenarios shown above are common, and are good starting points for planning more complex ladder escape forks.
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| − |
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| − | === 3nd row ladder ===
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| − | The situation for 3rd row ladders is largely similar to that of 2nd row ladders. Scenarios 1—3 work without much modification.
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| − |
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| − | '''Scenario 1:''' In the most constrained scenario, Red can climb to the 5th row, potentially bridging to a stone on the 7th row.
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| − | <hexboard size="7x9"
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| − | coords="hide"
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| − | contents="R a5 b5 c5 B a6 b6 c6 d4 g5 R 1:e5 B 2:d5 R 3:f3"
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| − | />
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| − |
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| − | '''Scenario 2:''' If Red has slightly more space, Red can climb to the 6th row, potentially bridging to a stone on the 8th row.
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| − | <hexboard size="7x9"
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| − | coords="hide"
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| − | 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"
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| − | />
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| − |
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| − | '''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.
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| − | <hexboard size="7x9"
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| − | coords="hide"
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| − | 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"
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| − | />
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| − |
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| − | '''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.
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| − | <hexboard size="8x9"
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| − | coords="hide"
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| − | 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
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| − | 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"
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| − | />
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| − |
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| − | '''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:
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| − | <hexboard size="7x9"
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| − | coords="hide"
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| − | 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"
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| − | />
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| − | 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:
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| − | <hexboard size="7x9"
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| − | coords="hide"
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| − | 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"
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| − | />
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| − | 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:
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| − | <hexboard size="8x9"
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| − | coords="hide"
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| − | contents="R a5 a6 b6 B a7 b8 i5 R 1:b7 B 2:a8 R 3:f6
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| − | 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"
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| − | />
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| − | After this, there are several possibilities, depending on how Blue responds. The main line is as follows:
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| − | <hexboard size="8x9"
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| − | coords="hide"
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| − | contents="R a5 a6 b6 B a7 b8 i5 R 1:b7 B 2:a8 R 3:f6
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| − | B 4:c7 R 5:d6 B 6:c6 R 7:d4 B 8:d5 R 9:e4 B 10:e5 R 11:g4 B 12:f4 R 13:g3 B 14:f3 R 15:h1
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| − | 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"
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| − | />
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| − |
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| − | === 4th row and higher ladders ===
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| − | The situation for 4th row and higher ladders is essentially similar, provided that the attacker can guarantee that the pivot piece connects to the edge. For example, in the following situation, the pivot piece "1" is not connected to the edge, and Blue could [[foiling|foil]] by playing at "a":
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| − | <hexboard size="6x9"
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| − | coords="hide"
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| − | contents="R d3 e3 B c4 d4 e4 b2 i2 R 1:g3 E a:g4 E *:c3 *:i5"
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| − | />
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| − | 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.
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| | | | |
| | == When to fork == | | == When to fork == |
| Line 175: |
Line 81: |
| | == See also == | | == See also == |
| | | | |
| − | [[Foiling ladder escapes]] | + | * [[Foiling ladder escapes]] |
| | + | * [[Climbing#Climbing from a ladder|Climbing from a ladder]] |
| | | | |
| | [[category:ladder]] | | [[category:ladder]] |
| | [[category:intermediate Strategy]] | | [[category:intermediate Strategy]] |
Revision as of 01:20, 30 November 2020
A forking move which creates a ladder escape.
Example
In the following position, Red has no edge template.
The only option seems to be a ladder.
However, pushing the ladder too much is useless, and it actually enables Blue to win.
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.
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:
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:
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":
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.
See also
