Difference between revisions of "Ladder escape fork"

Revision as of 19:44, 29 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.

How far can the attacker climb?

The effectiveness of a potential fork can be measured by how far the attacker can potentially climb. Let us consider some typical ladders and potential forks:

2nd row ladder

In the first example, Red's space is limited. Red can climb to the 4th row, potentially bridging to a stone on the 6th row.

If Red has slightly more space, Red can climb to the 5th row, potentially bridging to a stone on the 7th row.

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.

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.

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.

If Red has slightly more space, Red can climb to the 6th row, potentially bridging to a stone on the 8th row.

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.

4th row and higher ladders

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 foil by playing at "a":

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:

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

Foiling ladder escapes