Difference between revisions of "Parallel ladder"
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== 2nd and 4th rows == | == 2nd and 4th rows == | ||
| + | |||
| + | === In game === | ||
Consider the following position with [[Red]] to play. | Consider the following position with [[Red]] to play. | ||
| − | <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</hex> | + | <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</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 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 | ||
| Line 25: | Line 37: | ||
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]]. | 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 === | ||
| + | |||
| + | 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. | ||
| + | |||
| + | <hex>R7 C6 | ||
| + | Ha1 Hb1 Vc1 Hd1 He1 Sf1 | ||
| + | Ha2 Hb2 Vc2 Sd2 | ||
| + | Ha3 Vb3 Hc3 | ||
| + | Ha4 Vb4 Sc4 | ||
| + | Va5 Hb5 | ||
| + | Sa6 </hex> | ||
| + | |||
| + | Note that every blue move is [[forcing move|forced]]. In the following diagram, the threat is connecting to bottom edge with a [[ziggurat]]. | ||
| + | <hex>R7 C6 | ||
| + | Ha1 Hb1 Vc1 Hd1 He1 | ||
| + | Ha2 Hb2 Vc2 | ||
| + | Ha3 Vb3 Hc3 | ||
| + | Ha4 Vb4 V1c4 V3d4 | ||
| + | Va5 Hb5 H2c5 H4d5 | ||
| + | </hex> | ||
| + | |||
| + | <hex>R7 C6 | ||
| + | Ha1 Hb1 Vc1 Hd1 He1 | ||
| + | Ha2 Hb2 Vc2 | ||
| + | Ha3 Vb3 Hc3 | ||
| + | Ha4 Vb4 Vc4 Vd4 | ||
| + | Va5 Hb5 Hc5 Hd5 | ||
| + | V1a6 V3b6 V5c6 V7d6 V9f6 | ||
| + | H2a7 H4b7 H6c7 H8d7 | ||
| + | </hex> | ||
| + | |||
| + | <hex>R7 C6 | ||
| + | Ha1 Hb1 Vc1 Hd1 He1 | ||
| + | Ha2 Hb2 Vc2 | ||
| + | Ha3 Vb3 Hc3 | ||
| + | Ha4 Vb4 Vc4 Vd4 H6e4 V5f4 | ||
| + | Va5 Hb5 Hc5 Hd5 H4e5 V3f5 | ||
| + | Va6 Vb6 Vc6 Vd6 H2e6 Vf6 | ||
| + | Ha7 Hb7 Hc7 Hd7 | ||
| + | </hex> | ||
| + | |||
| + | Finally Red is assured to connect to top edge. | ||
| + | |||
| + | <hex>R7 C6 | ||
| + | Ha1 Hb1 Vc1 Hd1 He1 | ||
| + | Ha2 Hb2 Vc2 Se2 V3f2 | ||
| + | Ha3 Vb3 Hc3 H2e3 V1f3 | ||
| + | Ha4 Vb4 Vc4 Vd4 He4 Vf4 | ||
| + | Va5 Hb5 Hc5 Hd5 He5 Vf5 | ||
| + | Va6 Vb6 Vc6 Vd6 He6 Vf6 | ||
| + | Ha7 Hb7 Hc7 Hd7 | ||
| + | </hex> | ||
== 3rd and 5th rows == | == 3rd and 5th rows == | ||
| Line 57: | Line 123: | ||
=== Blue plays 2.d9=== | === Blue plays 2.d9=== | ||
| − | 2.d9 3.e7 makes easy connection with [[edge template | + | 2.d9 3.e7 makes easy connection with [[edge template IIIa]] |
<hex>R10 C10 Q1 | <hex>R10 C10 Q1 | ||
Revision as of 21:05, 19 October 2008
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 ladders to f9. Then tries to escape with
- 5. h9 g9
- 6. h8 g8
- 7. h7 f7.
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?
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 stop Red from connecting to the bottom? d9 lets Red 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), 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.
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 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 blocks this, say with 11...g5, then Red continues 12.i3 i2 13.h3 h2 and 14.g3 completes the win.
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. 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.
