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Hex:
A Strategy Guide

Matthew Seymour


Chapter 5

Advanced tactics

5.1 Template A-5

Diagram 175 shows Template A-5. Despite being a template on the fifth row, this template is too large to be a significant threat. Nonetheless, it does appear occasionally. More significantly, some of the tactics involved are important to know, being applicable in various situations that occur outside this template.

Reset board to initial state Next move Previous move

Diagram 175

Template A-5

This one is rather complex to analyze. Diagram 176 shows six reductions to simpler templates. Note that the points A , B and C are included in all six reductions. Therefore, responses are required to White intrusions in these three hexes.

A B C Reset board to initial state Next move Previous move

Template A-4 reduction.

A B C Reset board to initial state Next move Previous move

Template A-4 reduction.

A B C Reset board to initial state Next move Previous move

Template B-4 reduction.

A B C Reset board to initial state Next move Previous move

Template B-4 reduction.

A B C Reset board to initial state Next move Previous move

Template A-3 reduction.

A B C Reset board to initial state Next move Previous move

Template B-3 reduction.

Diagram 176

Template A-5 reductions. These overlap at points A , B and C .

We begin with the intrusion at A (Diagram 177). Black’s response is simple: he bridges to the right with , threatening to connect after another bridge to the right with Template A-3. White blocks with , resulting in a ladder. Black then plays a ladder-escape fork with , connecting either via the ladder or a double bridge. Convince yourself that White has no alternatives to .

2 1 4 3 6 5 Reset board to initial state Next move Previous move

Diagram 177

Intrusion at A .

Next up, intrusions at B and C . The response here is compact enough that we can use it for both if we just mirror the moves, so we only need to discuss one of these intrusions. Diagram 178 shows Black’s response to an intrusion at C . After , Black threatens to either connect directly with a bridge at E , or to play at F and connect with Template D-4. White is forced to block at G , the point where these threats overlap. Diagram 179 shows how Black uses a series of forcing moves to connect after the block by White.

F G E 2 1 Reset board to initial state Next move Previous move

Diagram 178

Intrusion at C .

3 4 5 6 7 8 Reset board to initial state Next move Previous move

Diagram 179

Response to White’s block at G .

5.2 Template C-5

Diagram 180 shows the two-stone, fifth-row template, Template C-5:

Reset board to initial state Next move Previous move

Diagram 180

Template C-5

This template takes up significantly less room and can be very threatening. There are four basic reductions (Diagram 181), each of which uses a bridge plus either Template A-3 or Template B-3.

A B Reset board to initial state Next move Previous move
A B Reset board to initial state Next move Previous move

A B Reset board to initial state Next move Previous move
A B Reset board to initial state Next move Previous move

Diagram 181

Template C-5 reductions, using Template A-3 (left) and Template B-3 (right). These reductions overlap at points A and B .

There are two intrusion points common to all these reductions. The responses to these intrusion points are detailed in Diagram 182. Note the similarities to Template C-4.

A 1 2 4 3 Reset board to initial state Next move Previous move
B 2 4 3 1 Reset board to initial state Next move Previous move

Diagram 182

Responses to intrusions at A and B .

5.3 Switchbacks

Consider the position in Diagram 183. The white stone A is connected to the northeast with Template A-4, and a ladder is about to form on the b-file. But B cannot serve as a second-row ladder escape, so how is White to win?

B A 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 183

White to move and win.

Even though B can’t serve as second-row ladder escape, White can still use it to win the game. First she runs the ladder up the edge and then breaks with b2 (Diagram 184).

B 11 10 9 8 7 6 5 4 3 2 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 184

White ladders and breaks.

After the forced response b3 White can now run a “ladder” back in the opposite direction, with each move a forcing move, finally connecting at d5 (Diagram 185). This technique is called a switchback. Notice how each White move of the final sequence threatens to connect to White’s second-row stones, making Black’s responses forced.

13 12 14 15 16 17 18 19 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 185

White connects with a switchback.

A fourth-row stone can also switchback a third-row ladder. We can see the approach in Diagram 186, with Black using Template A-3. The resulting switchback returns along the fifth row.

1 Reset board to initial state Next move Previous move Last move First move
7 5 3 6 4 2 Reset board to initial state Next move Previous move Last move First move

Diagram 186

Third-to-fifth-row switchback.

Note that if White yields the third-row ladder to the second row, Black can use the second-to-fourth-row switchback, as in Diagram 187, to connect back to the initial stone.

12 10 11 2 4 6 9 8 3 1 5 7 Reset board to initial state Next move Previous move Last move First move

Diagram 187

If White yields, Black uses a different switchback.

In Diagram 98 we saw that a3 (or it’s equivalents) can’t serve as a third-row ladder escape. It can, however, be used to start a switchback. In Diagram 188 we can see that White has forced a third-row ladder along the northeast edge. This group is connected to the southwest edge through bridges to A (which itself is connected by Template A-3). Notice how B on k13 for White is equivalent to a3 for Black in Diagram 98. Notice also that at no point could Black yield the ladder to the second row because B is a second-row ladder escape.

A B 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 188

White to move.

From this position White can start the switchback. White starts with j12 (Diagram 189). The k13–j12 group is connected to the northeast ( Template M-4a). After k10 White gets the switchback and goes on to finish the game: i11 j10 i10 j9 i9 j8 h8, and White is connected by either C or D . Had Black played k11, White first secures a second-row ladder escape before beginning the switchback with l10 k10 i11 etc.

C D 9 8 7 6 5 4 2 3 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 189

White connects by way of either C or D .

It’s important to note here how critical the timing is. White needs to play no earlier or later in the ladder sequence, or else it won’t work.

Not all switchbacks will eventually reconnect so easily as seen in these examples. Nevertheless, they can often result in a long line of stones parallel to your edge which are connected to it. This effectively gives you a new “edge” closer to the center of the board, which is easier to connect to.

5.4 Folding under

In some cases one ladder will fold under another. In Diagram 190, Black can ladder along the fourth row to the right. A can’t escape a fourth-row ladder, but it can escape a ladder on the second or third row, so White cannot yield.

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

Diagram 190

Black to move.

Nonetheless, Black proceeds (Diagram 191). After i10, Black’s combined threats ( B , C with Template A-3, and D with Template B-3) will force White to block at D , the only point where all three threats overlap.

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

Diagram 191

After the block, Black can squeeze through the bottleneck and play a second-row ladder towards the escape at E , folding under the fourth-row ladder (Diagram 192).

Naturally, this can only occur with ladders on the fourth or higher rows.

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

Diagram 192

Black’s ladders back beneath the fourth-row ladder.

5.5 J9 ladder escape

It’s very important to understand how a stone on the fifth row can be used to escape second- and third-row ladders. Along the southeast of the board, j9 is the closest to the acute corner a black stone on the fifth row can lie and still serve as a second-row ladder escape. Along the other edges, d5 plays an equivalent role for Black, as do i10 and e4 for White. These moves are popular during the game’s opening phase.

Diagram 193 shows a black stone on j9 with a second-row ladder and the minimal ladder escape shaded.

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

Diagram 193

j9 ladder escape.

Black approaches j9 with the sequence in Diagram 194, jumping twice. Note that moves and are not frequently played, however I’ve included them to show that Black still connects even if they are. From this position Black threatens to play either Template A-3 (Diagram 195a) or Template A-4 (Diagram 195b) on his tenth move. Black’s threats overlap at the six points labeled A–F so White will need to play at one of these for her ninth move.

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

Diagram 194

Black’s approach to j9.

A B C D E F 10 b c d e f g h i j k l m 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

(a)

A B C D E F 10 b c d e f g h i j k l m 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

(b)

Diagram 195

Black’s threats for move 10. White will have to play move 9 at one of the labeled hexes.

Black’s responses are shown in Diagram 196. Diagram 196g shows Black’s response if White attempts to intrude into the bridge on move 5. It may seem difficult to remember seven different lines, but line (a) involves a common ladder-escape fork which any experienced player should be able to recognize, and there is a common theme running through lines (c), (d), (f) and (g). Each of these involves placing a stone on the 12th row connected to the bottom of the board, and then using a series of forced moves to go over and around it.

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

(a) ladder-escape fork.

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

(b) Trapezoid and Template A-3.

12 11 13 14 10 9 b c d e f g h i j k l m 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

(c) Template A-3.

12 11 13 14 10 15 16 9 b c d e f g h i j k l m 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

(d) Forced move sequence.

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

(e) Fork. Black plays either i12 or k10.

12 11 13 14 10 15 16 9 b c d e f g h i j k l m 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

(f) Forced move sequence.

12 14 6 13 15 16 5 8 11 10 17 18 9 7 b c d e f g h i j k l m 9 10 11 12 13 Reset board to initial state Next move Previous move Last move First move

(g) Alternative move 5 by White. Black uses a forced move sequence.

Diagram 196

Responses to White’s attempts to block.

Next we consider the third-row ladder. The first thing to note here is that f10 is part of the ladder-escape template for third-row ladders, and must be unoccupied by White. Now, if White never yields, the ladder will eventually reach f11 as in Diagram 197, and from this point Black’s approach will be identical to that of Diagram 194. White may attempt to yield the ladder to the second row instead. However, should she yield to d13 (or earlier) Black can respond with d12 c13 f11 and the situation will again be that of Diagram 194. Therefore the only new consideration for the third-row ladder is that of White yielding to e13 (Diagram 198). We can see Black’s response in the diagram, using Template A-4. Note how Black requires f10 here. If f10 isn’t free, this is the approach White should use to block.

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

Diagram 197

White doesn’t push the third-row ladder.

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

Diagram 198

White yields to e13.

5.6 Parallel ladders

Reset board to initial state Next move Previous move

Diagram 199

Start of a parallel ladder. Black to move.

Consider the situation in Diagram 199 with Black to move. Clearly Black can start a second-row ladder. But the threat of this second-row ladder allows Black to push a fourth-row ladder from which White cannot yield (Diagram 200). Black can push this ladder as far as he likes.

1 3 5 2 4 6 Reset board to initial state Next move Previous move

Diagram 200

Black can push the fourth-row ladder as far as he likes.

Why can’t White yield here? Because if she does, Black can create a ladder escape for the second-row ladder by intruding into the bridge as in Diagram 201.

1 3 2 6 5 4 Reset board to initial state Next move Previous move

Diagram 201

White cannot yield.

This opens up tactical possibilities. There are many variations possible. In Diagram 202 Black makes use of the parallel ladder approach to play the ladder-escape fork , connecting by the ladder or the bridge.

Reset board to initial state Next move Previous move
1 3 5 2 4 6 7 Reset board to initial state Next move Previous move

Diagram 202

Black uses the parallel ladder approach to connect.

5.7 “Tom’s move”

In Diagram 203 (adapted from a real game) it is White’s turn to move. The A B group is connected to the southwest via C , and is also connected to D by a Parallelogram. White needs to connect D to the northwest. How should she proceed?

D A C B 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 203

White to move.

White begins with j7 k7 k6 m5 l6 m6 (Diagram 204). Now she plays what has come to be known as “Tom’s move” (evidently discovered by someone named Tom): k9. This move threatens to escape the second-row ladder, but if Black blocks the ladder at l7 White responds with j8 connecting anyway. Black’s only reasonable response here is l8 (m7 can be defeated with l8, as can anything further down, such as l9 l8). White now finishes the job with l7 m7 j10: the group is connected to the northeast by Template E-4, and is connected to by either i9 (double bridge) or k8. Seeing that these threats don’t overlap, Black resigns.

4 3 5 6 1 2 9 10 8 7 11 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 204

White uses “Tom’s move”.

Diagram 205 shows what is required to execute Tom’s move. We need the two connected stones and enough empty space to complete the move. Since the area is rather large, it is helpful to count out four bridge moves from the fourth-row stone as in the diagram.

4 3 2 1 Reset board to initial state Next move Previous move

Diagram 205

Minimal area needed to execute Tom’s move.

There are many ways to get the two stones on the left, some of these are shown in Diagram 206.

2 1 6 4 3 5 Reset board to initial state Next move Previous move Last move First move

(a) Lone stone on the fourth row.

6 2 4 1 3 5 Reset board to initial state Next move Previous move Last move First move

(b) From below.

2 4 6 1 3 5 14 8 10 12 7 9 11 13 Reset board to initial state Next move Previous move Last move First move

(c) Parallel ladders.

Diagram 206

Some approaches to Tom’s move.

Tom’s move gives rise to Template H-4, shown in Diagram 207.

Reset board to initial state Next move Previous move Last move First move

Diagram 207

Template H-4.

5.8 More complex switchbacks

A lone stone on the fifth row can be used to obtain a second-to-fourth-row switchback. Diagram 208 shows the approach. is connected to the bottom with Template D-4.

12 14 15 13 2 4 6 8 11 10 1 3 5 7 9 Reset board to initial state Next move Previous move Last move First move

Diagram 208

This same fifth-row stone can also be used to obtain a third-to-fifth-row switchback. If White doesn’t yield the ladder, Black’s approach is straightforward, as in Diagram 209. But if White attempts to yield to the second row, things go much worse for her: Black can apply the above second-to-fourth-row switchback to connect, as in Diagram 210.

2 4 6 8 11 10 1 3 5 7 9 Reset board to initial state Next move Previous move Last move First move

Diagram 209

18 16 14 12 17 15 13 2 4 6 8 11 10 3 1 5 7 9 Reset board to initial state Next move Previous move Last move First move

Diagram 210

If White yields, Black can connect.

A 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 211

Black to move.

Let’s see this put to use in an actual game. In Diagram 211 Black’s central group cannot be stopped from connecting to the northwest. But what about the southeast? Black can use A to get a switchback and win. Black starts a ladder with c12 c13 d12 d13 and jumps to the third row with f11 (Diagram 212). White cannot yield the third-row ladder as discussed above. Black breaks the third-row ladder a few moves later with j11. After i11, Black begins the switchback and jumps again on move 17: j9 i10 i9 h10 h8. Now Black has a double threat and White is finished.

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

Diagram 212

Black uses a switchback.

As a result of the above discussion, structures with two stones on the fifth row, like the one shown in Diagram 213, can be very powerful. The two stones can be any distance apart as long as there are at least two empty hexes between them. If either of these stones is connected to the other side of the board, it can be connected to the bottom using the techniques described in this section.