Difference between revisions of "Parallel ladder"
Hex player1 (Talk | contribs) m (+category) |
(Rewrote the first example to make more sense.) |
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Vd4 Ve4 Hf4 Hg4 | Vd4 Ve4 Hf4 Hg4 | ||
Ve5 | Ve5 | ||
| − | Vc6 Vd6 He6 | + | Vc6 Vd6 He6 Hh6 Hi6 |
Hc7 Vd7 | Hc7 Vd7 | ||
Ha8 Hb8 Vc8 Hd8 | Ha8 Hb8 Vc8 Hd8 | ||
| Line 19: | Line 19: | ||
Hb10</hex> | Hb10</hex> | ||
| − | All of Red's pieces form a connected [[group]]. This group is [[connection|connected]] to the | + | 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]]: |
| − | : | + | <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> |
| − | + | ||
| − | + | ||
| − | + | 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: | |
| − | + | <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> | |
| − | + | 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 "*". | |
| − | + | ||
| − | + | ||
| − | + | ||
| − | Now Red | + | |
| − | + | ||
| − | + | ||
=== Conceptualisation === | === Conceptualisation === | ||
Revision as of 19:12, 17 August 2020
A parallel ladder is a situation in which the attacker can make two ladders on top of each other.
Contents
2nd and 4th rows
In game
Consider the following position with Red to play.
All of Red's pieces form a connected group. This group is 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:
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:
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 "*".
Conceptualisation
Here are presented the essential features of the parallel lader trick on 2nd and 4th row.
The star marked fields must be connected to the top edge.
Note that every blue move is forced. In the following diagram, the threat is connecting to bottom edge with a ziggurat.
Finally Red is assured to connect to top edge.
3rd and 5th rows
It is possible to use this trick off from one row farther back; i.e. with ladders on the third and fifth row but this occurs far less frequently and one has to examine some additional defensive possibilities. Consider the following position.
Red has just played e6 trying the parallel ladder trick. With the closer ladder on the second row, we saw that Blue was forced to respond with the parallel ladder play e7. But here Blue has two additional possibilities e8 and c9 (the only other possibility where Red doesn't have a way to force his group to connect to the bottom is c10. But Red can respond with f8 and now Blue has nothing better than e7, g6).
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.
For whom who understand The parallel ladder trick !
This trick is useful only for ladder 2nd and 4th!
A parallel ladder trick puzzle
Consider the following position with Red to play.
The solution is 1.f8 (this is, essentially, Tom's move). Let's see what are Blue's options.
Blue plays 2.d9
2.d9 3.e7 makes easy connection with edge template IIIa
Blue plays 2.e8
2.e8 is not better : 3.c9 4.c10 5.d9 6.d10 7.e9 8.e10 9.g9 connects through edge template III2b linking to bottom.
Blue plays 2.e9
2.e9 is the best move in almost all situations like this, but it does not work here: 3.c9 4.c10 5.d9 6.d10 7.g7.
Group g7,f8 is connected to bottom thanks to edge template IV2b. And it is connected to the big group with either f6 or e8
Red 3.c9 could not be e7 nor d9 ... try to think why.
