Difference between revisions of "Cornering"
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| − | In a [[ladder | + | In a [[ladder]] situation when no [[ladder escape]] exists, the [[ladder|attacking player]] can [[ladder]] into a corner and create a "quasi-escape piece" at the very last minute. This play is called '''cornering'''. |
| − | + | === Pivoting === | |
| − | + | The most common form of cornering is ''pivoting'': when the attacker [[ladder handling|breaks the ladder]] by playing one hex ahead. This usually results in a ladder for the opponent. Example: | |
| − | This results in a new [[ladder]], but now the attacking player is [[ | + | <hexboard size="5x10" |
| + | coords="hide" | ||
| + | edges="bottom right" | ||
| + | contents="R c1 R b3 B b4 R c3 B c4 R d3 B d4 R e3 B e4 R 1:f3 B 2:f4 R 3:g3 B 4:g4 R 5:i3" | ||
| + | /> | ||
| + | |||
| + | This results in a new [[ladder]], but now the attacking player is [[ladder|defending]] instead. | ||
| + | |||
| + | <hexboard size="5x10" | ||
| + | coords="hide" | ||
| + | edges="bottom right" | ||
| + | contents="R c1 R b3 B b4 R c3 B c4 R d3 B d4 R e3 B e4 R f3 B f4 R g3 B g4 R i3 | ||
| + | B 6:h3 R 7:i2 B 8:h2 R 9:i1" | ||
| + | /> | ||
| + | |||
| + | Red could have also cornered earlier, resulting, for example, in a 4th row ladder for Blue. | ||
| + | |||
| + | === C4 corner move === | ||
| + | |||
| + | Given enough space, the attacker can sometimes get an outcome that is better than merely turning the ladder, though not as good as a [[switchback]]. For example, starting from a 2nd row ladder, the following maneuver lets Red move towards the center, rather than parallel to Blue's edge: | ||
| + | |||
| + | <hexboard size="7x8" | ||
| + | coords="hide" | ||
| + | edges="bottom right" | ||
| + | contents="R a6 B a7 R 1:b6 B 2:b7 R 3:c6 B 4:c7 R 5:f4" | ||
| + | /> | ||
| + | |||
| + | Blue now has several options, but all of them allow Red to connect towards the center of the board: | ||
| + | |||
| + | <hexboard size="7x8" | ||
| + | coords="hide" | ||
| + | edges="bottom right" | ||
| + | contents="R a6 B a7 R b6 B b7 R c6 B c7 R f4 | ||
| + | B 6:e5 R 7:f6 B 8:e6 R 9:g3 E *:f5 *:h4 B 10:e4 R 11:f2" | ||
| + | /> | ||
| + | Note how Red's 9 is connected to the edge via a [[double threat]] at the cells marked "*". If Blue instead plays 6 on the second row, the position transposes to one commonly encountered with the D3 corner move (described below). | ||
| + | |||
| + | <hexboard size="7x8" | ||
| + | coords="hide" | ||
| + | edges="bottom right" | ||
| + | contents="R a6 B a7 R b6 B b7 R c6 B c7 R f4 | ||
| + | B 6:d6 R 7:e5 B 8:d5 R 9:e3" | ||
| + | /> | ||
| + | Note that Red's 7 is connected to the edge via [[edge template IV2b]]. | ||
| + | |||
| + | === D3 corner move === | ||
| + | |||
| + | Another useful corner move for second row ladders is this: | ||
| + | |||
| + | <hexboard size="7x10" | ||
| + | coords="hide" | ||
| + | edges="bottom right" | ||
| + | contents="R a6 b6 1:c6 3:d6 5:g5 B a7 b7 2:c7 4:d7" | ||
| + | /> | ||
| + | This allows the attacker to [[climbing|climb]], even without a [[Switchback#Switchback threat|switchback threat]], as follows: | ||
| + | <hexboard size="7x10" | ||
| + | coords="hide" | ||
| + | edges="bottom right" | ||
| + | contents="R a6 b6 c6 d6 g5 7:e6 9:h4 11:g3 13:f2 B a7 b7 c7 d7 6:f6 8:e7 10:f5 12:e4 S area(a1,a5,c5,e3,e1,a1) f1 g1 h1 h2 i1 i2 j1 j2 i3 j3 j4 E *:d3" | ||
| + | /> | ||
| + | This move has some similarities with [[Tom's move]], although it does not require a [[parallel ladder]]. Note that 5 and 9 are connected to the edge by [[edge template IV2b]]. The shaded area is not required for this - i.e., it can be occupied by Blue - although depending on what's to the left, 13 may again be threatening to connect back to the ladder (most likely by playing at "*"). | ||
| + | |||
| + | ===Strategic considerations=== | ||
| + | |||
| + | The above sequences are useful if one has the goal of climbing to a particular hex, or when space is limited. However, it's not uncommon to have an empty corner with lots of space available, especially on larger boards like 19×19. In these cases, the attacker generally shouldn't be fixated on climbing to a particular hex and should aim to "make the most" of her lack of a ladder escape. There are a few ways to do this. [[KataHex]] frequently prefers the following Red 7, followed by move 9 at one of (*): | ||
| + | <hexboard size="8x9" | ||
| + | coords="hide" | ||
| + | edges="bottom right" | ||
| + | contents="R a7 B a8 R 1:b7 B 2:b8 R 3:c7 B 4:c8 R 5:f6 B 6:e7 R 7:g4 B 8:e6 E *:(f5 h2)" | ||
| + | /> | ||
| + | |||
| + | If there are no nearby stones, both moves often result in Red climbing towards the center. For example: | ||
| + | |||
| + | <hexboard size="8x9" | ||
| + | coords="hide" | ||
| + | edges="bottom right" | ||
| + | contents="R a7 B a8 R b7 B b8 R c7 B c8 R f6 B e7 R g4 B e6 | ||
| + | R 9:h2 B 10:d5 R 11:e3 B 12:c4 R 13:c5 B 14:d4 R 15:d2" | ||
| + | /> | ||
| + | |||
| + | It's unknown whether these sequences represent "optimal" play in some theoretical sense. However, practically speaking, it's nearly impossible to work out the tactics by hand on large boards. These KataHex sequences are by no means the only ways to climb from an empty corner, but they seem pretty consistently solid choices. | ||
| + | |||
| + | |||
| + | [[category:ladder]] | ||
| + | [[category:definition]] | ||
Latest revision as of 14:57, 18 November 2023
In a ladder situation when no ladder escape exists, the attacking player can ladder into a corner and create a "quasi-escape piece" at the very last minute. This play is called cornering.
Pivoting
The most common form of cornering is pivoting: when the attacker breaks the ladder by playing one hex ahead. This usually results in a ladder for the opponent. Example:
This results in a new ladder, but now the attacking player is defending instead.
Red could have also cornered earlier, resulting, for example, in a 4th row ladder for Blue.
C4 corner move
Given enough space, the attacker can sometimes get an outcome that is better than merely turning the ladder, though not as good as a switchback. For example, starting from a 2nd row ladder, the following maneuver lets Red move towards the center, rather than parallel to Blue's edge:
Blue now has several options, but all of them allow Red to connect towards the center of the board:
Note how Red's 9 is connected to the edge via a double threat at the cells marked "*". If Blue instead plays 6 on the second row, the position transposes to one commonly encountered with the D3 corner move (described below).
Note that Red's 7 is connected to the edge via edge template IV2b.
D3 corner move
Another useful corner move for second row ladders is this:
This allows the attacker to climb, even without a switchback threat, as follows:
This move has some similarities with Tom's move, although it does not require a parallel ladder. Note that 5 and 9 are connected to the edge by edge template IV2b. The shaded area is not required for this - i.e., it can be occupied by Blue - although depending on what's to the left, 13 may again be threatening to connect back to the ladder (most likely by playing at "*").
Strategic considerations
The above sequences are useful if one has the goal of climbing to a particular hex, or when space is limited. However, it's not uncommon to have an empty corner with lots of space available, especially on larger boards like 19×19. In these cases, the attacker generally shouldn't be fixated on climbing to a particular hex and should aim to "make the most" of her lack of a ladder escape. There are a few ways to do this. KataHex frequently prefers the following Red 7, followed by move 9 at one of (*):
If there are no nearby stones, both moves often result in Red climbing towards the center. For example:
It's unknown whether these sequences represent "optimal" play in some theoretical sense. However, practically speaking, it's nearly impossible to work out the tactics by hand on large boards. These KataHex sequences are by no means the only ways to climb from an empty corner, but they seem pretty consistently solid choices.
