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Hex:
A Strategy Guide

Matthew Seymour


Chapter 7

Advanced strategy

7.1 Corners

The corners are some of the most valuable territory available on the board. Corners are the only area of the board where you can simultaneously strengthen your own edge while blocking your opponent’s edge. Since most ladders form in the obtuse corner and head towards the acute corner, it’s valuable to have ladder escapes prepared there for this possibility. The acute corner is also far from the center (and the far edge), so having stones there can help to bridge that gap. On the other hand, stones in the obtuse corner lie close to the center and often serve as the start of ladders.

There are two acute and two obtuse corners. In discussing the corners we will, for simplicity’s sake, look at the two corners from Black’s perspective. Naturally, everything we discuss can be applied for either player. The most common acute corner moves for Black in the east are j9 and k10, while the most common obtuse corner moves for Black in the south are e9 and d10.

Due to the value of the corners, they are usually occupied in the first moves of the game. It is a solid principle to play in at least one corner on each of your edges during the opening phase of the game.

Diagram 243 shows a typical opening. Black has occupied both acute corners, while White has occupied both obtuse corners. Each player has occupied a corner along each of their edges. is at j9, the most common acute corner opening, and is a j9-equivalent move. White’s and are e9-equivalent moves, the most popular obtuse corner opening.

1 5 4 6 3 S a b c d e f g h i j k l m 1 2 3 4 5 6 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 243

In Diagram 244 the situation is reversed, with Black in the obtuse corners and White in the acute corners. Again, each player has occupied a corner along each of their edges. is an e9-equivalent move. is at d10, another common obtuse corner opening, Black having played closer here due to the presence of S requiring a tighter play along the southeast edge. White’s and are both j9-equivalent moves.

4 5 1 3 6 S a b c d e f g h i j k l m 1 2 3 4 5 6 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 244

In Diagram 245 we have a more complex example. With i5, Black takes a corner along his northwest edge to go with along his southeast edge. Rather than play in the east acute corner to go with her stone in the west acute corner, White plays the d10-equivalent j4 under Black’s , simultaneously invading his corner while obtaining an obtuse corner stone along the northeast edge. Black himself makes an invading play with d5, blocking off White’s . White responds in the southern obtuse corner with e9.

2 4 5 3 6 1 a b c d e f g h i j k l m 1 2 3 4 5 6 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 245

As this last example shows, once corners are occupied players may start to invade them. While the first player to the corner will generally retain the advantage there, the invader seeks to reduce that advantage while securing some gain for themselves. Invasions often kick off a local corner fight as each player jockeys for advantage. The most common move sequences are called corner patterns, and these are the topic of the next section.

7.2 Acute corner patterns

A good opponent won’t let you take the corner unchallenged. After an invasion into a corner a corner fight typically ensues, where players strive to resolve the situation to their advantage. Players must weigh the advantage they can get from continuing to challenge in this fight with the initiative to be gained by being the first to play elsewhere on the board. If a player feels that continuing to fight over the corner is less valuable than having the first move in a new area, then they should move on. With this in mind it’s important to recognize what each player has gained at each stage of the common corner sequences and how it can affect the rest of the game. There are certain stages during the pattern at which it would be foolish to move on—doing so would leave your opponent with too much and yourself with too little. Eventually a point is reach at which the corner is effectively settled and there is so little to be gained from continuing that you are better off moving elsewhere.

Usually in corner fights, the player to invade is the one who keeps the initiative. This is similar to using weak blocks, where the player intruding typically retains the initiative after the response. Occasionally, though, the player who’s been invaded moves elsewhere, opening up play in another area of the board, possibly to return to the area later.

I will be discussing the most common variations seen in corner fights. This is not an exhaustive list of every variation possible. It’s important that you understand the reasoning behind the choices the players make in the variations I will show; do not simply copy these moves verbatim. Understanding the reasoning behind these choices will help you when your opponent does something unexpected.

Note: as I mentioned above, we will be discussing these patterns with Black playing first in the east corner. Naturally, however, either player could be the one to initiate the pattern and it could be played in either corner. It shouldn’t be much trouble to apply what follows to these situations.

7.2.1 J9 acute corner opening

Perhaps the most common acute corner opening is j9 (Diagram 246). As discussed in 5.5 J9 ladder escape, this stone serves as both a second- and third-row ladder escape, while still invading far into White’s edge. It can also be thought of as squeezing Template A-5 into the corner as far as possible. d5 plays the same role for Black in the west corner. i10 and e4 are White’s equivalent moves.

A B C 1 d e f g h i j k l m 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 246

j9 is the most common acute corner opening.

This move is quite strong, so it’s usual for White to challenge. She has two goals with her response: first, White would like to invade the attacking zone of j9. This puts moves along the k-, l- and m-files out of consideration. We will consider how Black responds to such moves in a later section. Second, White would like to strengthen her own edge by providing ladder escapes—this puts the files left of the j-file out of consideration. Of the remaining options, two are generally considered the strongest: the low intrusion A and the high intrusion B (Diagram 246). We will consider these in turn, starting with with the low intrusion.

The outside intrusion C doesn’t provide any ladder escapes for White, but it is sometimes played nonetheless.

7.2.2 Low intrusion to j9

The low intrusion response to j9, j11 (Diagram 247), serves as a second- and third-row ladder escape for White, while simultaneously blocking from serving the same functions. Black has a strong reply to this move at A , which we will look at next. We will also have a look at the “old” response B , which used to be popular but is now considered weaker.

A B 1 2 d e f g h i j k l m 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 247

The low intrusion.

7.2.3 Low intrusion to j9, standard response

We’ll start with the standard response to the low intrusion, k11 (Diagram 248). With this move, Black re-establishes second- and third-row ladder escapes, while blocking White’s escapes.

It should be clear how escapes a second-row ladder. For the third-row ladder, Black can jump to h10 (Diagram 249, below), threatening Template A-3 by playing either D or E . There is a single overlap to these threats, F , to which Black has the response indicated in Diagram 250 (using Template E-3).

White usually responds at either A or B (labeled back in Diagram 248), giving rise to the “closed” or “open” variations, respectively. We’ll consider these two responses in more detail.

A B 1 2 3 d e f g h i j k l m 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 248

Standard response.

D E F 4 d e f g h i j k l m 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 249

Black can escape the third-row ladder.

F 4 6 8 10 7 9 5 d e f g h i j k l m 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 250

Response to F .

7.2.4 Low intrusion to j9, standard response: closed variation

The closed variation is shown in Diagram 251. j12 re-establishes second- and third-row ladder escapes for White, while blocking the same for Black. It also gives White a two-stone group () connected to the northeast. Black responds with k12, reversing the situation once more (obtaining second- and third-row ladder escapes, and blocking White’s). k10 gives White a second-row escape, but not a third. After l8 White saves the edge connection of the group with l10.

From here, Black usually follows up by connecting this group with i11. White invades the Template A-3 to gain some more territory with g12 h13. Black now has a strong connection to the edge, while White has the territory on . Black also has two weak points at A and B . White can take advantage of these points, because a stone that invades them threatens to connect to the northeast edge, which can often require a response. Diagram 252 shows an example of White exploiting one of these weak points in order to force a connection. Try some alternatives to Black’s to see how White connects in response.

A B 7 1 6 8 9 2 3 10 4 5 11 d e f g h i j k l m 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 251

Black is connected but has two weak points at A and B .

2 1 5 3 4 h i j k l m 2 3 4 5 6 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 252

White takes advantage of the weak point to connect to the edge.

7.2.5 Low intrusion to j9, standard response: open variation

k10 i11 (Diagram 253). Black has second through fifth-row ladder escapes. White has a second-row ladder escape. White typically moves on here. Although i12 looks tempting (giving White a third-row ladder escape), Black has strong responses, discussed below in 7.5 Edges.

1 4 5 2 3 d e f g h i j k l m 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 253

Low intrusion, open variation.

7.2.6 Low intrusion to j9, old response

The old response to the low intrusion, l11 (Diagram 254), is worth studying. This move was formerly the standard response but has fallen out of favour with the top players given the strength of k11. Nonetheless, it’s important to know how to play this move if you’re White and responding to it.

With this move, Black re-establishes his second- and third-row ladder escapes. The third-row ladder escape makes use of and , similar to Diagram 249. He also breaks up White’s use of as a second- and third-row ladder escape. White’s strongest responses are at A and B . C is sometimes played as well. We will look at the A and B responses in more detail.

A B C 1 2 3 d e f g h i j k l m 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 254

The “old” response.

7.2.7 Low intrusion to j9, old response: closed variation

Playing at j10 (Diagram 255), White gives herself a second-row ladder escape. She also has Template C-4 presenting a surface for connections passing under . And finally, she blocks Black’s use of as a third-row ladder escape. She does choose, however, to leave Black with his second-row ladder escape.

It is very common at this point for Black to follow up with l8 l10. This blocks the second-row ladder escape. White keeps the group connected to the northeast with . Importantly, A is a strong intrusion point for White, connecting to the northeast edge through either B or C (similar to Diagram 252 above). It is for this reason that White doesn’t play l9 for her sixth move, for Black could follow up with k9 k10, removing the intrusion point.

Black’s final move in the sequence, i10, is connected to the bottom. If White attempts to block with h11, then Black can use to escape the second-row ladder. Continuations of this pattern along the edge are discussed below in 7.7 Undermining.

A B C 5 1 7 4 6 2 3 d e f g h i j k l m 6 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 255

Black has a weak point at A .

7.2.8 Low intrusion to j9, old response: open variation

In this variation, White plays l10 (Diagram 256) for her fourth move. This gives her second- and third-row ladder escapes. The main trade-off compared to j10 is that she gains the third-row ladder escape, but presents a smaller surface to connect under . It’s common for Black to take advantage of the empty A tile and respond with i11. This gives him ladder escapes all the way to the sixth row. However it leaves White with her ladder escapes.

A 1 4 5 2 3 d e f g h i j k l m 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 256

Open variation.

7.2.9 High intrusion to j9

Now for the second major response to the j9 opening, the high intrusion j10 (Diagram 257). Playing closer to , White gets a second-row ladder escape. Although this move doesn’t get her a third-row escape, the deflection k7 l7 k8 m8 l8 m7 l10 l9 i11 k9 h10 is still quite strong for her, with being connected to the northeast edge.

Black tends to respond at either A or B .

A B 1 2 d e f g h i j k l m 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 257

High intrusion to j9.

7.2.10 High intrusion to j9: first variation

The simplest variation is i10 (Diagram 258). is connected to the southeast by Template A-4. Black also has second- and third-row ladder escapes, as well as a fourth-to-sixth-row switchback. is a second-row ladder escape for White. It can also deflect third-row ladders as in Diagram 259.

1 3 2 d e f g h i j k l m 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 258

First variation.

1 2 6 3 5 4 10 8 7 11 9 d e f g h i j k l m 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 259

Deflecting a third-row ladder for White.

7.2.11 High intrusion to j9: second variation

The second and third variations both start with k9 (Diagram 260), with the difference being White’s response. In Diagram 260, is connected to the southeast by Template A-4. White has a second-row ladder escape, but third-row ladders are blocked entirely by .

1 3 5 2 4 d e f g h i j k l m 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 260

Second variation.

7.2.12 High intrusion to j9: third variation

Here is a more elaborate variation. As in the other variations, is connected to the southeast with Template A-4.

Some continuations of these variations along the edge will be discussed below in 7.7 Undermining.

1 3 7 2 5 4 6 d e f g h i j k l m 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 261

Third variation.

7.2.13 Outside intrusion to j9

The outside intrusion is interesting, since it leaves the corner in a symmetrical shape. Black is next to move, however, so he still has the advantage. Black usually responds at A , B , although C is also possible. We will look at the first two in more depth.

A C B 1 2 d e f g h i j k l m 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 262

Outside intrusion to j9.

7.2.14 Outside intrusion to j9: first variation

In this variation Black responds to the intrusion with i9, giving him second- and third-row ladder escapes. White typically responds at j11, blocking these and obtaining second- and third-row ladder escapes for herself. From this point there are numerous options. A typical example is shown in Diagram 264. Here Black finishes by connecting his group to the edge with Template A-4, although he is left with a weak point at A .

3 1 2 4 d e f g h i j k l m 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 263

First variation and typical response by White.

A 9 3 1 11 2 8 10 4 5 6 7 c d e f g h i j k l m 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 264

One possible continuation.

7.2.15 Outside intrusion to j9: second variation

In this variation Black responds to the intrusion with k10, connecting to the edge with Template A-4 and giving him second- and third-row ladder escapes. A few continuations are possible here. We’ll look at two.

1 2 3 d e f g h i j k l m 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 265

Start of the second variation.

In Diagram 266 Black is connected to the edge and has second- and third-row ladder escapes. White does not have any ladder escapes, although she can deflect a second-row ladder as shown in Diagram 267.

1 2 3 4 5 6 7 d e f g h i j k l m 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 266

Black can escape second- and third-row ladders. White could deflect a second-row ladder as seen in Diagram 267.

1 2 6 4 5 3 7 d e f g h i j k l m 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 267

How White can deflect a second-row ladder.

In Diagram 268 Black loses his ladder escapes. In compensation, his group is connected to the edge, with the hex A captured. As a result, and combine to present a large “surface” for attaching to.

A 1 7 2 3 5 4 6 d e f g h i j k l m 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 268

White blocks second- and third-row ladders.

7.2.16 K10 acute corner opening

Finally we consider the other major acute corner opening: k10 (Diagram 270). This opening is common when the edge in question is shortened due to the opening move, or when a player desires a fourth-row ladder escape. k10 fits Template A-4 into the corner, and can escape second-, third- and fourth-row ladders. White’s typical response, k12 is a second-row ladder escape and blocks Black’s ladder escapes. Black usually responds at either A (Diagram 270), or B (Diagram 271). In either variation, Black ends up with second through fifth-row ladder escapes, while White ends up with a second-row ladder escape.

A B 1 2 d e f g h i j k l m 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 269

More typical when the edge is shortened by the opening move.

1 3 2 d e f g h i j k l m 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 270

First variation

1 3 5 2 4 d e f g h i j k l m 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 271

Second variation

7.3 Obtuse corner openings

The obtuse corner is also a popular area for moves early in the game. In contrast to the acute corner, complex sequences occur less often here. Diagram 272 shows some of the more popular obtuse corner openings. The most common plays are on the short diagonal ( A D ). Moves equivalent to Black’s b10 ( E ) are also played frequently. As with the acute corner patterns, the equivalents of these moves can be applied to either corner by either player.

Let’s have a look at the short diagonal moves first. It’s common to open on the short diagonal from rows 3 to 6, with the fourth and especially fifth rows ( C and B , respectively) being the most popular. Moves along the short diagonal are attacking moves (see 4.12 Attacking stones), and since the short diagonal is “shared” by both players, playing here invades your opponent’s space as well.

A B C D E a b c d e f g 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 272

Obtuse corner openings.

Trying to block e9 from the edge generally allows the attacker to “loop around” the blocking stone (Diagram 273), rendering such blocks ineffective. The alternative line e10 d10 d11 c11 b13 c12 c13 d12 d13 f12 e12 f11 e11 g9 isn’t any better.

The presence of other stones on Black’s edge can make e9 even stronger. Second- and third-row ladder escapes are obviously helpful (since blocks of e9 result in such ladders). Also useful are stones that can switchback or deflect ladders. We will investigate this in more depth in 7.5 Edges.

While e9 can’t be effectively blocked outright, it can be threatened in order to gain territory and improve your position. We will consider such threats after we look at b10.

8 2 1 4 7 6 3 5 a b c d e f g h i 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 273

Looping around.

b10 (Diagram 274) is used as both as an opening and as a block to e9. This move accomplishes a few things.

a b c d e f g 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 274

b10 opening.

Now let’s look at some blocks to e9. b10, or it’s equivalent for White, d12, can be used as a block against e9, as in Diagram 275. Black would be held to a third-row ladder if he responds with d11. Therefore it’s probably best for White to play this response only if Black has no third-row ladder escape along the southeast edge. On the other hand, since is at best held to a fourth-row ladder along the southwest edge, naturally this move is stronger if White has a ladder escape there.

1 2 a b c d e f g 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 275

White could also block with d11 (Diagram 276). This isn’t a strong block: Black can follow up with f10 f11 e11 d13 b12, using a ladder-escape fork. Instead, White seeks to gain territory with something like f10 f9 e10 g11 e12, or perhaps f10 f9 e10 e12 g11 g10 f11 h12 f13. Note that can also switchback white second-row ladders along the southwest edge.

1 2 a b c d e f g h i 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 276

White can also respond to e9 with d10 (Diagram 277). Black can easily save the connection to the southeast with something like e10 or f10. White accepts this possibility in order to build some strength on her own southwest edge.

1 2 a b c d e f g 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 277

7.4 Corner patterns in the opening

As mentioned at the beginning of this chapter, it is a good strategy to play at least one corner on both of your edges during the opening of the game. Some players prefer wait until they’ve secured a corner on each edge before they begin invading occupied corners, while others prefer to attack as soon as a corner is occupied. Diagram 278 presents an example of the former. White doesn’t immediately invade the west corner with her fourth move, instead choosing to move into the southern obtuse corner. Black takes the east acute corner with j9. With all corners claimed White begins invading, first on the right with j10 i10 and then on the left with c2 d2.

S 8 9 3 4 5 7 6 1 a b c d e f g h i j k l m 1 2 3 4 5 6 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 278

Diagram 279 shows a more elaborate example. The first corner pattern begins on move 6, evolving into a longer battle for territory along Black’s edge which ends when White relents the initiative with i8. Black then invades the southern obtuse corner with b10 b12 c10. The final corner pattern of this game occurs in the western acute corner with d4 e4.

S 24 25 3 20 4 5 7 21 23 18 13 6 11 9 15 19 12 8 10 1 22 16 14 17 a b c d e f g h i j k l m 1 2 3 4 5 6 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 279

7.5 Edges

Now that we’ve seen the common corners patterns in isolation, it’s time to look at the whole edge. Some common corner patterns have continuations that can move out along the edge (as we saw in Diagram 279), where it may interact with the far corner. Additionally, moves in one corner can be influenced by stones at the other corners, in particular the two corners with which it shares an edge.

7.6 Corner pairs

As we saw in 5.8 More complex switchbacks (particularly Diagram 213), having two stones on the fifth row can be very strong, even if they are far apart. Each stone can switchback second- or third-row ladders that might result from attempts to block the other from the bottom, mutually supporting each other. And being on the fifth row, the whole structure lies very close to the center of the board.

The fifth row in the obtuse corner makes a great response should a player respond to j9 on the k-file. In Diagram 280, Black responds to White’s k10 in the obtuse corner with e9, greatly expanding his territory to the other end of his edge, while maintaining the connection of 1 to the south edge.

The fourth row (d10) can work as well, should the circumstances warrant it, for the same reasons: it can switchback second- and third-row ladders.

3 1 2 a b c d e f g h i j k l m 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 280

Black responds in the obtuse corner.

Diagram 281 shows a continuation of the open j9 variation (Diagram 253) where White plays i12. This move has some merits on its face: it gives White a third-row ladder escape (since such a ladder would cascade to the second row through after which A can make a ladder-escape fork with ), and it breaks the connection of the group to the bottom. However, the connection is not totally broken: White would need to play h12 or g13 to keep this group away, leading to a second- or third-row ladder.

A 1 4 5 2 3 6 a b c d e f g h i j k l m 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 281

Black to move.

One strong response to this move is d10 (Diagram 282), playing the fourth row in the obtuse corner along the same edge. This is similar to the situation above with Diagram 280. can help turn the aforementioned second- or third-row ladder into a switchback, which could then connect back to . Hence, it keeps the group connected to the bottom, all while occupying a new corner of the board.

1 7 4 5 2 3 6 a b c d e f g h i j k l m 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 282

What’s more, is itself connected to the bottom. White’s only nontrivial block is d11 (Diagram 283) after which Black can use B to get a switchback and reconnect to (Diagram 283), or alternatively use A to deflect the ladder.

A 7 21 9 8 B 11 13 15 17 20 19 10 12 14 16 18 a b c d e f g h i j k l m 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 283

e9 (Diagram 284) is another strong response for Black. It can switchback the potential second- or third-row ladders coming from the acute corner, and is closer to the center of the board. While it can’t be guaranteed to be connected to the bottom as in Diagram 282 was above, the threat of e10 d10 c12 d11 d12 f11 e11 g9 is very strong, as is the deflection through A after e10 d10 c12 d11 d12 e11 e12 f11 f12 g12 g11.

c11 and b12 are other variations that can work for largely the same purposes.

7 A a b c d e f g h i j k l m 7 8 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

Diagram 284

Given these responses available to Black, i12 is is usually not a good continuation of the open variation corner pattern depicted in Diagram 253. This is not a hard rule however, sometimes the third-row ladder escape is worth it for White despite the strong responses Black has available.

Continuing on this theme, in Diagram 285, Black makes a somewhat unorthodox play in the corner pattern with e3. White could respond in the same corner, but perhaps she could do better. Note that from this position, an attempt by Black to block from the southwest edge will at best hold White to a second-row ladder: c5 d6 c7 c6 a7 and so on. Other blocks allow connection, for example d5 d4 d3 c5; b6 d4 d3 c5 b5 c7; or b7 d4 d3 b6 c5 d6 c6 c8. Rather than respond in the acute corner, White instead plays d11. This could be used to switchback or deflect any second-row ladders, while simultaneously blocking off A from the southeast edge.

As a rule of thumb, if your opponent’s block in a corner can at best hold you to a ladder, consider looking for responses in the far corner.