Strategic advice from KataHex - Revision history

Hexanna: fix typo

2026-02-20T01:44:31Z

fix typo

Hexanna: typo

2025-12-18T04:31:32Z

typo

Hexanna: more formatting/compress spacing

2025-12-13T14:25:24Z

more formatting/compress spacing

Show changes

Hexanna: /* Joseki */ replace hexworld with diagrams, "fix" formatting

2025-12-13T14:16:55Z

‎Joseki: replace hexworld with diagrams, "fix" formatting

Hexanna: remove a useless pattern; grammar

2025-11-29T22:41:09Z

remove a useless pattern; grammar

Hexanna: /* Cuts */ small copyedit

2025-11-27T13:07:00Z

‎Cuts: small copyedit

Hexanna: elaborate on allow-cuts

2025-11-27T02:18:39Z

elaborate on allow-cuts

Hexanna: fix intro, move over "Big picture, and some meta-points" (moving the tl;dr to the front)

2025-11-27T01:56:02Z

fix intro, move over "Big picture, and some meta-points" (moving the tl;dr to the front)

Hexanna: some terminology on cuts

2025-11-27T01:49:09Z

some terminology on cuts

Hexanna: remove some less useful parts

2025-11-10T00:55:33Z

remove some less useful parts

@@ Line 79: / Line 79: @@
 ** In [https://littlegolem.net/jsp/game/game.jsp?gid=2369954&nmove=26 this game] ([https://hexworld.org/board/#15n,a7:sd12k12l4h2g2h1c4d3c3d2c2c5d4c14b14c13b13c12b12c11b11c10b10d6 HexWorld link]), what should Black play on move 27? White is threatening to connect 26 back to the 16&ndash;24 group if Black isn't careful. Black's obvious options are to play at c8 and c9. Which option is better?
 ** A tempting answer is c8 because it appears to connect more closely to the top. However, note that White's stone on move 14 functions exactly like an opening a3 stone. For example, it can escape 2nd but not 3rd row ladders. If Black plays c8, White can play the [[A3 escape trick]], as shown in [https://hexworld.org/board/#15n,a7:sd12k12l4h2g2h1c4d3c3d2c2c5d4c14b14c13b13c12b12c11b11c10b10d6c8e7d8e8d9e9 this continuation]. This sequence allows White to "make the most" of stone 14, and Black shouldn't allow it. Better for Black is 27. c9, which doesn't allow White to carry out a 3rd-to-5th row switchback. Indeed, KataHex evaluates c9 as 97% to win for Black and c8 as only 30%.
-** Consider [https://hexworld.org/board/#13n,c2d10c11c10b11e6b10d8l4l3c8d5b5d6h7h6j5i6k7 this position] (which is based on [https://www.littlegolem.net/jsp/game/game.jsp?gid=2369782 this game]). Where should White play in the lower-right acute corner? Black had just played at the "3-7" point from White's perspective; as mentioned in the 19&times;19 opening guide, a strong response to 3-7 is 4-4 (at j10) instead of the usual 5-4 (at j9). A player who is short on time can play j10 without thinking too hard. As it turns out, KataHex thinks j10 is the best move, evaluating it as 91% for White, whereas j9 is only around 50%.
+** Consider [https://hexworld.org/board/#13n,c2d10c11c10b11e6b10d8l4l3c8d5b5d6h7h6j5i6k7 this position] (which is based on [https://www.littlegolem.net/jsp/game/game.jsp?gid=2369782 this game]). Where should White play in the lower-right acute corner? Black had just played at the "3-7" point from White's perspective; as mentioned in the 19&times;19 opening guide, a strong response to 3-7 is 4-4 (at j10) instead of the usual 5-4 (at i10). A player who is short on time can play j10 without thinking too hard. As it turns out, KataHex thinks j10 is the best move, evaluating it as 91% for White, whereas j9 is only around 50%.
 * Sometimes, you know you have a completely winning position after your opponent blunders very early in the game. Your goal is to preserve that win until the end of the game. Don't overextend yourself and try to win too "quickly", possibly making suboptimal moves in the process. Even when KataHex plays itself with a significant handicap (like playing without swap), a significant fraction of the board seems necessary to carry out the win, assuming strong defense. I prefer taking my time to "fill the board" by focusing on playing moves at least as good as my opponent's, instead of worrying about connecting in as few moves as possible.

@@ Line 81: / Line 81: @@
 ** Consider [https://hexworld.org/board/#13n,c2d10c11c10b11e6b10d8l4l3c8d5b5d6h7h6j5i6k7 this position] (which is based on [https://www.littlegolem.net/jsp/game/game.jsp?gid=2369782 this game]). Where should White play in the lower-right acute corner? Black had just played at the "3-7" point from White's perspective; as mentioned in the 19&times;19 opening guide, a strong response to 3-7 is 4-4 (at j10) instead of the usual 5-4 (at j9). A player who is short on time can play j10 without thinking too hard. As it turns out, KataHex thinks j10 is the best move, evaluating it as 91% for White, whereas j9 is only around 50%.
-* Sometimes, you know you have a completely winning position after your opponent blunders very early in the game. Your goal is to preserve that win until the end of the game. Don't overextend yourself and try to win too "quickly", possibly making possibly suboptimal moves in the process. Even when KataHex plays itself with a significant handicap (like playing without swap), a significant fraction of the board seems necessary to carry out the win, assuming strong defense. I prefer taking my time to "fill the board" by focusing on playing moves at least as good as my opponent's, instead of worrying about connecting in as few moves as possible.
+* Sometimes, you know you have a completely winning position after your opponent blunders very early in the game. Your goal is to preserve that win until the end of the game. Don't overextend yourself and try to win too "quickly", possibly making suboptimal moves in the process. Even when KataHex plays itself with a significant handicap (like playing without swap), a significant fraction of the board seems necessary to carry out the win, assuming strong defense. I prefer taking my time to "fill the board" by focusing on playing moves at least as good as my opponent's, instead of worrying about connecting in as few moves as possible.
 ==Local patterns==

@@ Line 303: / Line 303: @@
 * The 4-3 corner move is almost always a mistake compared to the 5-4, even on 11&times;11. If your opponent plays 4-3, 90% of the time the best local reply is 3-3. If 4-3 is played, here are some common sequences:
-<hexboard size="5x7"
+: <hexboard size="5x7" float="inline" coords="hide" edges="bottom right" contents="R 1:e2 B 2:e3 R 3:d3"
-  coords="hide"
+/> <hexboard size="5x7" float="inline" coords="hide" edges="bottom right" contents="R 1:e2 B 2:e3 R 3:f2 B 4:f3 R 5:d3 E a:b4 b:c5"
-  edges="bottom right"
+/>
-  contents="R 1:e2 B 2:e3 R 3:d3"
+: In the second joseki, Blue should play either (a) or (b), or she can defer the question until later. On larger boards with no nearby stones, (b) is often better.
-  />
-−
 <hexboard size="5x7"
-  coords="hide"
-  edges="bottom right"
-  contents="R 1:e2 B 2:e3 R 3:f2 B 4:f3 R 5:d3 E a:b4 b:c5"
-  />
-−
 In the second joseki, Blue should play either (a) or (b), or she can defer the question until later. On larger boards with no nearby stones, (b) is often better.
-−
 * If your opponent plays the 5-4 joseki, a reasonable choice is to always play the 4-4 "high intrusion." KataHex prefers the 4-4 response by far, especially on 13&times;13 and larger. It's easily the "safest" choice, and many strong players have recently shown a clear preference for 4-4.
+* In this often-played joseki, Red 7 is a mistake because of the territory Blue gets after move 8:
-* In [https://hexworld.org/board/#14nc1,k10k11l10l12m11m12j11i13h12g14f13g12g13 this often-played joseki], Red 7 is a mistake because of the territory Blue gets after move 8.
+: <hexboard size="6x10" float="inline" edges="bottom right" coords="none" contents="R 1:g2 B 2:g3 R 3:h2 B 4:h4 R 5:i3 B 6:i4 R 7:f3 B 8:e5 R 9:d4 B 10:c6 R 11:b5 B 12:c4 R 13:c5" />
-** If the obtuse corner on Red's same edge is empty, a more principled response for Red is to play in that corner, like [https://hexworld.org/board/#14c1,k10k11l10l12d11 this].
+:* If the obtuse corner on Red's same edge is empty, a more principled response for Red is to play in that corner, like this:
-** If the obtuse corner is already occupied by Blue, then Red should still respond in the obtuse corner. One reasonable option (among others) is [https://hexworld.org/board/#14c1,:pd11k10k11l10l12e11 this].
+:: <hexboard size="6x14" float="inline" edges="bottom left right" coords="none" contents="R 1:k2 B 2:k3 R 3:l2 B 4:l4 R 5:d3" />
+:* If the obtuse corner is already occupied by Blue, then Red should still respond in the obtuse corner. One reasonable option (among others) is this:
 * See more discussion of acute corner joseki at [[Openings_on_19_x_19#Acute_corner_theory]]. For the obtuse corner, see [[Openings_on_19_x_19#Obtuse_corner_theory]] which covers responses to the 4-4 and 5-5 obtuse corner in great detail. Most of this is applicable to 13&times;13 and larger, and not just 19&times;19.

@@ Line 34: / Line 34: @@
 * How should a game of Hex (on larger boards) broadly feel like?
 ** While the win condition is binary (you either connect or you don't), the actual gameplay feels like a gradual accumulation of tiny advantages and disadvantages. Strong players often "know" they're winning in the middlegame, not because they see an actual way to connect, but because their opponent made some mistakes, however small, along the way. (You rarely know for sure who's winning until the end, and you're ultimately making an educated guess.)
-** In particular, it's usually very hard to tell who's winning just by looking at a position. Contrast that with games like chess, where you can often tell by counting up material and broadly looking at positional factors. In Hex, it's much tractable to tell how good your position is ''relative to a few moves ago.''
+** In particular, it's usually very hard to tell who's winning just by looking at a position. Contrast that with games like chess, where you can often tell by counting up material and broadly looking at positional factors. In Hex, it's much more tractable to tell how good your position is ''relative to a few moves ago.''
 ** Relatedly, there's (almost) no meaningful notion of "long-term strategy" in Hex. If anything, it can be harmful to create a long-term plan and stubbornly stick to it, because the moves you should play often differ greatly depending on your opponent's responses.
 ** Hex strategy is equally what to play and what ''not'' to play. The latter is frequently underemphasized. Each stone is worth a lot, and even one bad move can "undo" 10&ndash;20 good ones. The risk-reward balance strongly favors avoiding mistakes, rather than attempting risky but potentially "brilliant" moves.
@@ Line 254: / Line 254: @@
 * If option 1 is true, you are probably losing anyways, so assume (or hope) option 2 is true. If you opponent overplays region A and underplays region B, it's typically a good idea to focus your play in region B. Why? If you keep playing in region A, you're potentially helping your opponent out of their mistake, by making your opponent less over-connected in region A. For example, your opponent could have a minimaxing move that makes them much stronger in region B, at the "concession" of making them weaker in region A &mdash; but this isn't really a concession because your opponent had strength to spare in region A.
-The discussion so far has been highly abstract. What does efficient play look like in practice? As explained in the "Cuts" section, it's strong to "cut through" your opponent's potential connection, especially in the adjacent cut and bridge cut.
+The discussion so far has been highly abstract. What does efficient play look like in practice? As explained earlier, it's strong to adjacent-cut and bridge-cut through your opponent's stones. The small patterns in the "Capture patterns" section above are also locally efficient for the capturing player. Of course, just as offense and defense are equivalent in Hex, so are playing locally efficient moves and inducing your opponent to play locally ''inefficient'' moves.
-−
-The small patterns in the "Capture patterns" section above are also locally efficient for the capturing player. You should generally play them when given the opportunity, and prevent your opponent from doing the same.
-−
-Just as offense and defense are equivalent in Hex, so are playing locally efficient moves and inducing your opponent to play locally ''inefficient'' moves. Sometimes, locally inefficient patterns arise when one player induces the other to play a bunch of stones close together. Here is an example (which occasionally happens in actual games), where Red is connected but took a lot of stones to connect.
-<hexboard size="3x3"
-  float="inline"
-  edges="none"
-  coords="none"
-  contents="R b1 c1 a3 B a2 R 1:b3 B 2:c2 R 3:b2"
-/>
 In the following examples, P1 and P2 are efficient patterns for Red relative the corresponding edges, while P3 is inefficient. P1 is common when Red opens with a first column opening. P2 requires elaboration: normally Red 1 is a weak move because it's too close to Red's own edge. However, when Red must play on his first 3 rows (because of very limited space), Red 1 or its mirror image at (*) is usually the best, because it prevents Blue from playing there and forming the equivalent of P1 herself. P2 also occurs in theoretical contexts, like [[Template Va#If Blue moves at y:]]. In P3, Red 1 is a tempting (because of [[edge template III1b]]), common, but inefficient move, because Blue's response at one of (*) is usually strong. If Red must play near his own edge, he should instead play as in P2 above.

@@ Line 141: / Line 141: @@
 The (short) bridge cut is strong for the attacker (Red above) because he captures the two hexes marked (*). If Blue allow-cuts, often the damage has already been done even if Red doesn't actually cut through immediately on the next turn. (However, note that this isn't always true; some tactical situations require Red to cut through immediately instead of playing elsewhere.)
-* However, there are situations where Blue should allow-cut. If Red's cutting move comes with concessions, like the move is on his second or third row (and especially if Red already has a stone near his own edge, so cutting through would be overplaying that edge), the pattern is much less favorable to Red.
+* There are situations where Blue ''should'' allow-cut. If Red's cutting move comes with concessions, like the move is on his second or third row (and especially if Red already has a stone near his own edge, so cutting through would be overplaying that edge), the pattern is much less favorable to Red.
-The near cut and long bridge cut are also favorable for the attacker, but much less clearly so &mdash; there are many more "exceptions" where cutting is bad and allow-cutting is fine. On the other hand, the adjacent and short bridge cuts are quite strong, and cutting through is usually the best move (unless doing so involves playing a stone that's too close to your own edge, or some other concession).
+The near cut and long bridge cut are also favorable for the attacker, but much less clearly so &mdash; there are many more "exceptions" where cutting is bad and allow-cutting is fine. On the other hand, the adjacent and short bridge cuts are quite strong, and cutting through is usually the best move (unless doing so involves playing a stone that's too close to your own edge, or another major concession).
 Note that allow-cuts can occur not only ''proactively'' before the attacker plays the cutting move, but also ''retroactively'' after the "cutting" move is played (of course, it's not really a "cutting" move until after the defender allow-cuts). In other words, Blue 1 is considered an allow-cut in both of these examples (proactive on the left and retroactive on the right), and they are equally bad for Blue assuming that Red intends to cut in the proactive case:
@@ Line 161: / Line 161: @@
 />
-In fact, an important way of pruning moves and avoiding blunders is making sure you don't play moves that adjacent or bridge allow-cut, either proactively or retroactively, unless you have a good reason to do so. The retroactive case in particular can be easy to overlook if you're not used to thinking in this way.
+An important way of pruning moves and avoiding blunders is making sure you don't play moves that adjacent or bridge allow-cut, either proactively or retroactively, unless you have a good reason to do so. In particular, the retroactive case can be easy to overlook if you're not used to thinking in this way.
 ===Small patterns===

← Older revision		Revision as of 02:18, 27 November 2025
Line 144:		Line 144:

	The near cut and long bridge cut are also favorable for the attacker, but much less clearly so — there are many more "exceptions" where cutting is bad and allow-cutting is fine. On the other hand, the adjacent and short bridge cuts are quite strong, and cutting through is usually the best move (unless doing so involves playing a stone that's too close to your own edge, or some other concession).		The near cut and long bridge cut are also favorable for the attacker, but much less clearly so — there are many more "exceptions" where cutting is bad and allow-cutting is fine. On the other hand, the adjacent and short bridge cuts are quite strong, and cutting through is usually the best move (unless doing so involves playing a stone that's too close to your own edge, or some other concession).
		+
		+	Note that allow-cuts can occur not only ''proactively'' before the attacker plays the cutting move, but also ''retroactively'' after the "cutting" move is played (of course, it's not really a "cutting" move until after the defender allow-cuts). In other words, Blue 1 is considered an allow-cut in both of these examples (proactive on the left and retroactive on the right), and they are equally bad for Blue assuming that Red intends to cut in the proactive case:
		+	<hexboard size="2x3"
		+	float="inline"
		+	edges="none"
		+	coords="none"
		+	visible="-(a1 c2)"
		+	contents="B a2 1:c1 R b1"
		+	/>
		+	<hexboard size="2x3"
		+	float="inline"
		+	edges="none"
		+	coords="none"
		+	visible="-(a1 c2)"
		+	contents="B a2 1:c1 R b1 b2"
		+	/>
		+
		+	In fact, an important way of pruning moves and avoiding blunders is making sure you don't play moves that adjacent or bridge allow-cut, either proactively or retroactively, unless you have a good reason to do so. The retroactive case in particular can be easy to overlook if you're not used to thinking in this way.

	===Small patterns===		===Small patterns===

@@ Line 1: / Line 1: @@
 ==Introduction==
-Several hex bots have popped up in the last few years. Many are neural nets and adaptations of Go bots like AlphaGo Zero. The most recent (and likely strongest) as of 2024 is [[KataHex]], which is based on the open-source KataGo. These bots have influenced human play in many aspects already; one of the most notable is the bots' preference for the 4-4 obtuse corner over the 5-5. Many old strategy guides have become at least partially (if not mostly) outdated.
+Several hex bots have popped up in the last few years. Many are neural nets and adaptations of Go bots like AlphaGo Zero. The most recent (and likely strongest) as of 2025 is [[KataHex]], which is based on the open-source KataGo. These bots have influenced human play in many aspects already; one of the most notable is the bots' preference for the 4-4 obtuse corner over the 5-5. Many old strategy guides have become partially (if not mostly) outdated.
-This article attempts to bring some strategy advice "up-to-date". There's a lot of random insights; most are a direct result of playing around with KataHex evaluations for hundreds of hours, including analyzing the games of strong players for common mistakes. Since this is strategic advice and not tactics, the advice won't apply 100% of the time, and many players may disagree with some parts. Win percentages and evaluations in this article are based on KataHex net [https://github.com/hzyhhzy/KataGo/releases/tag/Hex_20240812 20240812], which is significantly stronger than previous nets.
+This article attempts to bring some strategy advice "up-to-date". There's a lot of random insights; most are a direct result of playing around with KataHex evaluations for thousands of hours, including analyzing the games of strong players for common mistakes. Since this is strategic advice and not tactics, the advice won't apply 100% of the time, and many players may disagree with some parts. Win percentages and evaluations in this article are based on KataHex net [https://github.com/hzyhhzy/KataGo/releases/tag/Hex_20240812 20240812], which is significantly stronger than previous nets.
-Care has been taken to only draw conclusions when there are multiple examples of KataHex preferring something. However, the main goal of this article is to give actionable advice to make players stronger, and there isn't rigorous proof for basically any of these statements.
+Care has been taken to only draw conclusions when there are multiple examples of KataHex preferring something. However, the main goal is to give actionable advice to make players stronger, and there isn't rigorous proof for basically any of these statements.
-For brevity, nearly every statement should have hedging language like "usually" or "rarely" instead of "always" or "never," but this makes the article really verbose, so I only do it when it seems useful.
+===Big picture, and some meta-points===
 ==General==

@@ Line 68: / Line 68: @@
 ==Local patterns==
-An especially effective way to improve at Hex is to learn and gain intuition about lots of small local patterns. These patterns are small enough that they occur basically everywhere when you play Hex. Knowing the patterns can help you avoid blunders (for example, avoiding moves that allow your opponent an adjacent or bridge cut through your stones) and make good moves when it's otherwise unclear what to play.
+An especially effective way to improve at Hex is to learn and gain intuition about lots of small local patterns. These patterns are small enough that they occur basically everywhere when you play Hex. Knowing the patterns can help you avoid blunders (for example, avoiding adjacent or bridge ''allow-cuts'', as explained below) and make good moves when it's otherwise unclear what to play.
 ===Cuts===
@@ Line 98: / Line 98: @@
    contents="B a1 c3 R 1:b2 S b1 a2 c2 b3"
 />
-Suggested names for brevity (in order): adjacent cut, near cut, short bridge cut (or just bridge cut), long bridge cut.
+Consider the four patterns above. Let's call the patterns '''adjacent cut''', '''near cut''', '''short bridge cut''' (or just '''bridge cut'''), and '''long bridge cut''' respectively. In some sense, Red is "cutting" through two of Blue's stones in each pattern, so Red is the '''attacker''' and Blue is the '''defender'''. We can also use '''cut''' as an attacking verb and '''allow-cut''' as a defending verb. For example, the adjacent cut pattern is favorable for the attacker (Red above), so we can say that it's a good idea to ''adjacent-cut'' through opponent stones, and a bad idea to ''adjacent allow-cut'' (meaning it's a bad idea to play a move that allows your opponent to adjacent-cut through two of your stones).
-Some of these cuts are stronger than others. The adjacent cut and the short bridge cut are perhaps the strongest &mdash; usually cutting through is the best move (unless doing so involves playing a stone that's too close to your own edge, or some other concession), so you can play Red 1 without thinking too hard. The near cut is weaker; there are more cases where Red 1 isn't actually the best move.
+Why is it strong to adjacent-cut (and equivalently, why is it a mistake to adjacent allow-cut)? The most intuitive reason is that if Blue allow-cuts, it takes 3 extra moves for her to connect her two stones, as shown below. In a sense, this makes it unlikely for both stones to be concurrently useful in the final connection &mdash; if one of the stones proves useful, chances are the other one won't be.
-* Why is the adjacent cut above so strong for Red? Blue has to play a lot of moves to reconnect the two blue stones. In practice, Blue will try for a connection elsewhere, and probabilistically, the two blue stones are unlikely to be very useful.
+The near cut and long bridge cut are also favorable for the attacker, but much less clearly so &mdash; there are many more "exceptions" where cutting is bad and allow-cutting is fine. On the other hand, the adjacent and short bridge cuts are quite strong, and cutting through is usually the best move (unless doing so involves playing a stone that's too close to your own edge, or some other concession).
-* The (short) bridge cut is strong for Red because he captures the two hexes marked (*). If Blue allows a bridge cut, often the damage has already been done even if Red doesn't actually cut through immediately on the next turn. (This isn't always true; some tactical situations require Red to cut through immediately instead of playing elsewhere.)
-** However, there are situations where Blue should allow a bridge cut. If Red's cutting move comes with concessions, like the move is on his second or third row (and especially if Red already has a stone near his own edge, so cutting through would be overplaying that edge), the pattern is much less favorable to Red.
 ===Small patterns===

@@ Line 89: / Line 89: @@
    coords="none"
    visible="-(a1 b1 d1 a3 c3 d3)"
-   contents="B a2 d2 R c1 1:b3 E *:(b2 c2)"
+   contents="B a2 d2 R c1 1:b3 S b2 c2 E *:(b2 c2)"
 />
 <hexboard size="3x3"
@@ Line 96: / Line 96: @@
    coords="none"
    visible="-(a3 c1)"
-   contents="B a1 c3 R 1:b2"
+   contents="B a1 c3 R 1:b2 S b1 a2 c2 b3"
 />
-<hexboard size="3x3"
+Suggested names for brevity (in order): adjacent cut, near cut, short bridge cut (or just bridge cut), long bridge cut.
-  float="inline"
-  edges="none"
-  coords="none"
-  visible="-c3"
-  contents="B a1 b3 R 1:c1 E *:(a2 b2)"
-/>
-Suggested names for brevity (in order): adjacent cut, near cut, short bridge cut (or just bridge cut), long bridge cut, skew cut.
 Some of these cuts are stronger than others. The adjacent cut and the short bridge cut are perhaps the strongest &mdash; usually cutting through is the best move (unless doing so involves playing a stone that's too close to your own edge, or some other concession), so you can play Red 1 without thinking too hard. The near cut is weaker; there are more cases where Red 1 isn't actually the best move.
@@ Line 112: / Line 105: @@
 * The (short) bridge cut is strong for Red because he captures the two hexes marked (*). If Blue allows a bridge cut, often the damage has already been done even if Red doesn't actually cut through immediately on the next turn. (This isn't always true; some tactical situations require Red to cut through immediately instead of playing elsewhere.)
 ** However, there are situations where Blue should allow a bridge cut. If Red's cutting move comes with concessions, like the move is on his second or third row (and especially if Red already has a stone near his own edge, so cutting through would be overplaying that edge), the pattern is much less favorable to Red.
 ===Small patterns===
@@ Line 135: / Line 127: @@
    visible="-(a1 b4)"
    contents="B a4 R 1:b1"
 />
@@ Line 155: / Line 133: @@
 * Pattern 2: Blue plays a bridge away from Red's stone. This is often a good move, and Red 1 a bridge away from both stones is also good.
 * Pattern 3: Red 1 is a classic block. This is often fine for Red, and Blue doesn't have an obvious best local response. Blue could tenuki here.
 ===Capture patterns===
@@ Line 171: / Line 147: @@
    coords="hide"
    edges="hide"
-   contents="R c1 c3 b3 B a2 E *:(b2 c2)"
+   contents="R c1 c3 b3 B a2 S b2 c2 E *:(b2 c2)"
    />
@@ Line 179: / Line 155: @@
    edges="hide"
    visible="-a1"
-   contents="R b1 a3 b3 E *:b2 A:a2"
+   contents="R b1 a3 b3 S a2 b2 E *:b2 A:a2"
    />
@@ Line 188: / Line 164: @@
    edges="none"
    visible="-a1"
-   contents="R b1 a3 c3 c1 E *:(c2 b3)"
+   contents="R b1 a3 c3 c1 S a2--c2 b3 E *:(c2 b3)"
    />
 <hexboard size="3x3"
@@ Line 195: / Line 171: @@
    edges="none"
    visible="-a1"
-   contents="R a2 b1 c1 c3 E *:c2"
+   contents="R a2 b1 c1 c3 S b2 c2 a3 b3 E *:c2"
    />
@@ Line 233: / Line 209: @@
 />
-Here are common efficient patterns for Red relative to an edge. P1 is strong because Blue cannot fit a ziggurat between the two red stones. P2 is common when Red opens with a first column opening. P3 requires elaboration: normally Red 1 is a weak move because it's too close to Red's own edge. However, when Red must play on his first 3 rows (because of very limited space), Red 1 or its mirror image at (*) is usually the best, because it prevents Blue from playing there and forming the equivalent of P2 herself. P3 also occurs in theoretical contexts, like [[Template Va#If Blue moves at y:]].
+In the following examples, P1 and P2 are efficient patterns for Red relative the corresponding edges, while P3 is inefficient. P1 is common when Red opens with a first column opening. P2 requires elaboration: normally Red 1 is a weak move because it's too close to Red's own edge. However, when Red must play on his first 3 rows (because of very limited space), Red 1 or its mirror image at (*) is usually the best, because it prevents Blue from playing there and forming the equivalent of P1 herself. P2 also occurs in theoretical contexts, like [[Template Va#If Blue moves at y:]]. In P3, Red 1 is a tempting (because of [[edge template III1b]]), common, but inefficient move, because Blue's response at one of (*) is usually strong. If Red must play near his own edge, he should instead play as in P2 above.
-P1: <hexboard size="6x2"
+P1: <hexboard size="3x2"
-  float="inline"
-  edges="left"
-  coords="none"
-  contents="R b5 1:b2"
-/>
 P2: <hexboard size="3x2"
    float="inline"
    edges="left"
@@ Line 246: / Line 216: @@
    contents="R a2 1:b3"
 />
-P3: <hexboard size="2x6"
+P2: <hexboard size="2x6"
    float="inline"
    edges="bottom"
@@ Line 252: / Line 222: @@
    contents="B c2 R 1:e1 E *:b1"
 />
+P3: <hexboard size="3x5"
-In the following example, Red 1 is a tempting (because of [[edge template III1b]]), common, but inefficient move, because Blue's response at one of (*) is usually strong. If Red must play near his own edge, he should instead play as in P3 above.
 <hexboard size="3x5"
    float="inline"
    edges="bottom"
@@ Line 307: / Line 275: @@
 ** If the obtuse corner on Red's same edge is empty, a more principled response for Red is to play in that corner, like [https://hexworld.org/board/#14c1,k10k11l10l12d11 this].
 ** If the obtuse corner is already occupied by Blue, then Red should still respond in the obtuse corner. One reasonable option (among others) is [https://hexworld.org/board/#14c1,:pd11k10k11l10l12e11 this].
 * See more discussion of acute corner joseki at [[Openings_on_19_x_19#Acute_corner_theory]]. For the obtuse corner, see [[Openings_on_19_x_19#Obtuse_corner_theory]] which covers responses to the 4-4 and 5-5 obtuse corner in great detail. Most of this is applicable to 13&times;13 and larger, and not just 19&times;19.