Openings on 19 x 19 - Revision history

Hexanna: more edits on specific openings

2024-08-17T14:44:30Z

more edits on specific openings

Hexanna: add more detail to a few specific openings

2024-08-17T05:00:02Z

add more detail to a few specific openings

Hexanna: update with newest katahex net

2024-08-17T03:27:54Z

update with newest katahex net

Selinger: Link to KataHex

2023-11-18T14:54:46Z

Link to KataHex

Hexanna at 22:24, 11 April 2023

2023-04-11T22:24:12Z

Hexanna at 14:33, 6 April 2023

2023-04-06T14:33:41Z

Hexanna: elaborate on initial stones; hopefully this wraps up the article, save for relatively minor edits

2023-04-04T04:32:59Z

elaborate on initial stones; hopefully this wraps up the article, save for relatively minor edits

Hexanna: convert acute corner joseki to hexboard

2023-04-01T03:09:34Z

convert acute corner joseki to hexboard

Hexanna: 5-5 obtuse corner theory

2023-03-30T04:48:08Z

5-5 obtuse corner theory

Hexanna: reorganize

2023-03-30T01:12:50Z

reorganize

@@ Line 94: / Line 94: @@
 * A well-played game between equally matched players should "use" almost the whole board. In particular, large templates like [[edge template VI1a]] rarely matter on 19&times;19. Many players are tempted to play a stone in the middle of their 6th row, because such a stone is connected. However, the opponent has good responses intruding into the template (see above).
-* Suppose Red has played the 5-4 opening. It turns out that a [https://hexworld.org/board/#19nc1,d5g3:pd4 decent response by Blue] is playing at 3-7 (from Red's perspective), partially due to the threat of Blue 4-4 as a followup. This would imply that, had Blue ''first'' played at 3-7 before Red played in the corner, Red should not respond with 5-4, because that would make Blue's 3-7 (which was placed first) unnecessarily effective. Red should instead play a move that works well against Blue's stone. It turns out that the [https://hexworld.org/board/#19nc1,:pg3d4 4-4 corner] is such a move. This is an important concept &mdash; you don't want to play a move close to your opponent's, if that would make your opponent's stone efficiently placed relative to yours.
+* Suppose Red has played the 5-4 opening. It turns out that a [https://hexworld.org/board/#19nc1,d5g3:pd4 decent response by Blue] is playing at 3-7 (from Red's perspective), partially due to the threat of Blue 4-4 as a follow-up. This would imply that, had Blue ''first'' played at 3-7 before Red played in the corner, Red should not respond with 5-4, because that would make Blue's 3-7 (which was placed first) unnecessarily effective. Red should instead play a move that works well against Blue's stone. It turns out that the [https://hexworld.org/board/#19nc1,:pg3d4 4-4 corner] is such a move. This is an important concept &mdash; you don't want to play a move close to your opponent's, if that would make your opponent's stone efficiently placed relative to yours.
 * Here's another [https://hexworld.org/board/#19nc1,e4d4d5 example]. Red accidentally played the 4-5 corner move instead of 5-4. Blue should not play 4-4, because then Red could play 5-4, and he would be in the same position that he would've been, had he played the first move correctly (via the Red 5-4, Blue 4-4, Red 4-5 joseki). Blue essentially let Red out of his mistake. A better move for Blue here is simply to tenuki.
@@ Line 421: / Line 421: @@
    />
-'''F:''' Somewhat common in human games, this move shares a lot of similarities with '''E'''. The move itself is usually a slight inaccuracy, but Red's best reply is again to connect directly. Blue 3 is a possible followup.
+'''F:''' Somewhat common in human games, this move shares a lot of similarities with '''E'''. The move itself is usually a slight inaccuracy, but Red's best reply is again to connect directly. Blue 3 is a possible follow-up.
 <hexboard size="8x8"
@@ Line 429: / Line 429: @@
    />
-In practice, many players in Red's position don't connect directly, because it looks too naive. However, if Red plays elsewhere on move 2, Blue's followup at (*) is often pretty strong.
+In practice, many players in Red's position don't connect directly, because it looks too naive. However, if Red plays elsewhere on move 2, Blue's follow-up at (*) is often pretty strong.
 '''G:''' As mentioned earlier, the 4-2 obtuse corner is a standard block on 13&times;13, but it's less effective on 19&times;19. Red's usual reply is at (*) or (+). Either move has the ability to hold Blue to a 3rd row ladder.
@@ Line 497: / Line 497: @@
 ====e3====
-KataHex thinks e3 is one of the fairest openings with the swap rule, with a 47% win rate for Red if Blue doesn't swap. A good local response for Blue is f6. This is because e3 cuts just enough into Blue's edge to make the usual corner move f5 a bad move, due to Red d6:
+KataHex thinks e3 is one of the fairest openings with the swap rule, with a 47% win rate for Red if Blue doesn't swap. A good local response for Blue is f6:
 <hexboard size="7x7"
@@ Line 507: / Line 515: @@
 ===First column openings===
-If Red starts with a move near the middle of his first column, like a10, a good followup for Red is to play one of the hexes marked A or B, or sometimes C (or both). These moves combine very efficiently with the opening stone to split up Blue's edge. KataHex nearly always plays one of these in the early opening.
+If Red starts with a move near the middle of his first column, like a10, a good follow-up for Red is to play one or more of the hexes marked A/B/C. These "bridging" moves combine very efficiently with the opening stone to split up Blue's edge. KataHex nearly always plays one of these in the early opening.
 <hexboard size="7x5"
@@ Line 513: / Line 521: @@
    edges="left"
    contents="R a4 E A:b5 B:c6 C:b2"
    />
@@ Line 533: / Line 533: @@
    />
-If Red plays a13 or a14, Blue could also respond with the 3-3 obtuse corner. This is the only place I've seen the 3-3 move (in an empty corner) come up "naturally", and it's an interesting way to test an opponent who's normally more familiar with 4-4 and 5-5 joseki.
+Normally, if Blue plays the obtuse corner on one of her edges, it's a mistake to also play the acute corner on the same edge (and vice versa) if Red hasn't intruded on her edge, because that is overplaying one side of the board. However, if Red plays a move like a10&ndash;a15, this is no longer true, and playing both corners on the same edge is a good counter to Red's "bridging" strategy:
 If Red plays a15 and Blue responds with 4-4, Red must be careful not to play move 5 below, because Blue 6 is very strong in the presence of Red 1 and 5, and it makes the a15 stone nearly useless.
@@ Line 545: / Line 553: @@
 ====a16====
-a16 is also a relatively fair opening. Blue usually responds with the 2-2 obtuse corner, but she doesn't have to play it immediately. Surprisingly, KataHex thinks Blue 1 below is a strong follow-up move and seems to prefer it over the more "obvious" move (*):
+If Red plays a16, Blue's most common local response is the 2-2 obtuse corner. Usually, both players tenuki after this, but if Red tries to split up Blue's edge above the a16 stone, Blue can respond at (*):
 <hexboard size="5x5"
    coords="hide"
    edges="bottom left"
-   contents="R a2 B b4 1:c5 E *:d3"
+   contents="R a2 B 1:b4 E *:d3"
    />
-If Blue instead waits for Red to play 1 as follows, then Blue 2 is a strong response.
+Blue also doesn't have to play the 2-2 obtuse corner immediately. If she waits and Red tries the "bridging" strategy with Red 1, then Blue 2 is a strong response.
 <hexboard size="7x5"
@@ Line 595: / Line 611: @@
 ====b17====
-For the adventurous, while b17 should be swapped, it is weaker than it looks and quite playable. It's not overly strong, because Blue can play b18, either immediately or later. I consider it the obtuse-corner analog of b4, which is surprisingly weak because of the threat of Blue c2. Similarly to the a16 opening, (*) is remarkably a strong follow-up move for Blue.
+For the adventurous, while b17 should be swapped, it is weaker than it looks and quite playable. It's not overly strong, because Blue can play b18, either immediately or later. I consider it the obtuse-corner analog of b4, which is surprisingly weak because of the threat of Blue c2. Similarly to the a16 opening, Blue can optionally play the tricky follow-up move (*) in the early opening.
 <hexboard size="5x5"

@@ Line 493: / Line 493: @@
 ====b4====
-Under the right circumstances, Blue c2 (followed by Red tenuki) can be a good local response, though this happens less in the early opening.
+Under the right circumstances, Blue c2 (followed by Red tenuki) can be a good local response, though KataHex seems to prefer Blue e5 or f6 in the early opening.
 ====e3====
-KataHex thinks e3 is one of the fairest openings with the swap rule, with a 47% win rate for Red if Blue doesn't swap.
+KataHex thinks e3 is one of the fairest openings with the swap rule, with a 47% win rate for Red if Blue doesn't swap. A good local response for Blue is f6. This is because e3 cuts just enough into Blue's edge to make the usual corner move f5 a bad move, due to Red d6:
 ===First column openings===
@@ Line 519: / Line 525: @@
 ====a10&ndash;a15====
-Some of the fairer openings in this category are a10, a14, a15. Blue's best response to a10&ndash;a15 in the obtuse corner is usually 4-4, but there's no rush to play it:
+In this category, a10 and a13&ndash;a15 are relatively balanced opening moves; a11&ndash;a12 are too strong and should be swapped. Blue's best response to a10&ndash;a15 in the obtuse corner is usually 4-4, but there's no rush to play it:
 <hexboard size="7x6"
@@ Line 527: / Line 533: @@
    />
-On 19&times;19, a15 is weaker than it looks, because the 4-2 obtuse corner, marked (*) below, is less potent for Red than on smaller boards:
+If Red plays a13 or a14, Blue could also respond with the 3-3 obtuse corner. This is the only place I've seen the 3-3 move (in an empty corner) come up "naturally", and it's an interesting way to test an opponent who's normally more familiar with 4-4 and 5-5 joseki.
 <hexboard size="6x5"
    coords="hide"
    edges="bottom left"
-   contents="R a2 E *:b3"
+   contents="R 1:a2 B 2:d3 R 3:c4 B 4:c3 R 5:b4 B 6:b3"
    />
 ====a16====
-a16 is also a relatively fair opening. Blue usually responds with the 2-2 obtuse corner, but she doesn't have to play it immediately. If Blue instead waits for Red to play 1 as follows, then Blue 2 is a strong response.
+a16 is also a relatively fair opening. Blue usually responds with the 2-2 obtuse corner, but she doesn't have to play it immediately. Surprisingly, KataHex thinks Blue 1 below is a strong follow-up move and seems to prefer it over the more "obvious" move (*):
 <hexboard size="7x5"
@@ Line 579: / Line 595: @@
 ====b17====
-For the adventurous, while b17 should be swapped, it is weaker than it looks and quite playable. It's not overly strong, because Blue can play b18, either immediately or later. I consider it the obtuse-corner analog of b4, which is surprisingly weak because of the threat of Blue c2.
+For the adventurous, while b17 should be swapped, it is weaker than it looks and quite playable. It's not overly strong, because Blue can play b18, either immediately or later. I consider it the obtuse-corner analog of b4, which is surprisingly weak because of the threat of Blue c2. Similarly to the a16 opening, (*) is remarkably a strong follow-up move for Blue.
 <hexboard size="5x5"
    coords="hide"
    edges="bottom left"
-   contents="R b3 B 1:b4"
+   contents="R b3 B 1:b4 E *:c5"
    />

@@ Line 3: / Line 3: @@
 An average well-played game lasts about 72-90 moves before one side resigns, or 20-25% of the board, though it varies considerably from game to game. This article covers opening strategy that is most relevant in the first 10-30 moves of the game. Some of it is specific to 19&times;19, but much of it is applicable to other large board sizes.
-The advice in this guide is heavily influenced by [[KataHex]], the strongest known (and easily superhuman) bot as of March 2023.
+The advice in this guide is heavily influenced by [[KataHex]], the strongest known (and easily superhuman) bot as of 2024.
 ==Differences from smaller boards==
-* While [[corner move|corner moves]] are still good moves, playing near the middle of your opponent's 4th to 6th rows is often just as good. This starts to become true for boards 18&times;18 and larger.
+* While [[corner move|corner moves]] are still good moves, playing near the middle of your opponent's 4th to 6th rows is often just as good. This starts to become true for boards 17&times;17 and larger.
 * Ladders are somewhat less threatening, since the defender has more options on a large board. Human games often have long ladders across a side of the board, but it's usually a mistake for the defending side to keep pushing the ladder. Often, it's best for the defender to jump, allowing their opponent to connect in exchange for territory. Here is an illustrative example, where Red's opening stone c2 serves as a ladder escape for his 3rd row ladder. Instead of continuing to defend the ladder, Blue jumps ahead on move 9, gaining a useful stone that could combine well with Blue 1 via (*).
@@ Line 70: / Line 70: @@
    coords="hide"
    edges="left"
-   contents="B d4 E A:f3 B:e4 C:e5"
+   contents="B d4 E A:e5 B:e4 C:f3 D:f2"
    />
-KataHex prefers A the most often on a relatively empty board.
+KataHex usually prefers A or C, though B or D are also good options. It's useful to think of these 4 responses as 2 sets of 2 moves a bridge apart (one set is A/C and one set is B/D). A/C are strong when combined &mdash; Red could very well play both moves &mdash; and similarly, B/D are strong when combined.
 * If Blue plays near the middle of her 5th row:
@@ Line 78: / Line 78: @@
    coords="hide"
    edges="left"
-   contents="B e4 E A:g3 B:f4 C:f5 D:d6 E:c5 F:d3 *:f2"
+   contents="B e4 E A:g3 B:f5 C:d6 D:c5 E:d3 *:f2"
    />
-KataHex usually prefers A or E, though B/C/D/F are also common. The move marked (*) is usually less good, because Blue can respond at A.
+KataHex usually prefers A or D, though B/C/E are also common. Note that all of these moves are a bridge away from the blue stone. The move marked (*) is usually less good, because Blue can respond at A.
 * If Blue plays near the middle of her 6th row:
@@ Line 86: / Line 86: @@
    coords="hide"
    edges="left"
-   contents="B f4 E A:h3 B:e6 C:d5 D:e3 *:(g2 g5) +:g4"
+   contents="B f4 E A:h3 B:e6 C:d5 D:e3 *:(g2 g5)"
    />
-Here, all of A/B/C/D are often good choices. The moves marked (*) are usually worse because Blue can respond at A. The move marked (+) is also worse, and Blue usually does well to tenuki.
+Here, all of A/B/C/D are often good choices. The moves marked (*) are usually worse because Blue can respond at A.
 * If Blue plays close to the center, Red would do well to block at a distance, rather than using an adjacent or near block.
@@ Line 324: / Line 324: @@
 ===5-5 obtuse corner===
-The 5-5 corner opening is common in human games. Strictly speaking, KataHex thinks 5-5 is a slightly worse move than 4-4, and it typically assigns the 4-4 a slightly higher win percentage (around 3-4%). Note that this is miniscule, and comparable to "1/25th of a stone" or "Blue's advantage when she swaps the (very fair) a19 obtuse corner opening." That is to say, you should not be discouraged at all from playing the 5-5 opening.
+The 5-5 corner opening is common in human games. Strictly speaking, KataHex thinks 5-5 is a slightly worse move than 4-4, and it typically assigns the 4-4 a slightly higher win percentage. However, the difference isn't really meaningful for human games, and you should not be discouraged at all from playing the 5-5 opening.
 Let's walk through some possible Blue responses to Red 5-5 in the obtuse corner. The sequences are more complex and varied than in the 4-4 opening, so we won't have room to cover every possibility, but hopefully the general ideas are clear.
@@ Line 347: / Line 347: @@
    coords="hide"
    edges="bottom left"
-   contents="R e4 B 1:f5 R 2:c6 B 3:d6 R 4:d4 B 5:c5 R 6:e6 E *:g6"
+   contents="R e4 B 1:f5 R 2:c6 B 3:d6 R 4:e6"
    />
-Blue should probably tenuki or play at (*) after Red 6, instead of defending her bridge. Moves 4 and 5 are optional for Red; he could play 6 directly after move 3, followed by Blue tenuki.
+Blue should probably tenuki after Red 4, instead of defending her bridge.
 '''B:''' Strong reply that's seen on both 13&times;13 and 19&times;19. Red has a few responses worth discussing:
@@ Line 389: / Line 389: @@
 Even if the long undermining sequence isn't obvious, the local placement of Blue 1 and 3 &mdash; the 2-2 obtuse corner and a bridge move away &mdash; is very efficient, and it should set off alarm bells. A strong player should intuitively recognize, without calculation, that the local configuration after Blue 3 is quite favorable for Blue.
-'''C:''' Rarely seen on 13&times;13, but KataHex plays it frequently on 19&times;19. Red 2 below is pretty common. Blue's reply is more varied; she can either play elsewhere or respond locally in a few different ways, such as one of (*).
+'''C:''' Rarely seen on 13&times;13, but KataHex plays it occasionally on 19&times;19. Red 2 is a common response. Blue's reply is more varied; she can either play elsewhere or respond locally in a few different ways, such as one of (*).
 <hexboard size="8x8"
@@ Line 497: / Line 497: @@
 ====e3====
-e3 is notable because KataHex thinks it's the fairest opening with the swap rule, with KataHex assigning a 49.2% win percentage for Blue, assuming no swap, after 100k visits.
+KataHex thinks e3 is one of the fairest openings with the swap rule, with a 47% win rate for Red if Blue doesn't swap.
 ===First column openings===
@@ Line 537: / Line 537: @@
 ====a16====
-a16 is also a relatively fair opening. Blue can play 2-2 obtuse corner like on smaller boards, but it's less clearly the best option. The 4-4 obtuse corner also works, and if Blue instead waits for Red to play 1 as follows, then Blue 2 is a strong response.
+a16 is also a relatively fair opening. Blue usually responds with the 2-2 obtuse corner, but she doesn't have to play it immediately. If Blue instead waits for Red to play 1 as follows, then Blue 2 is a strong response.
 <hexboard size="7x5"
@@ Line 589: / Line 589: @@
 ===Third and fourth row openings===
-According to KataHex, the fairest openings in this category are e3 (mentioned above), n3, and p3.
+According to KataHex, the fairest openings in this category are e3 (mentioned above) and n3.
-Openings in the middle of Red's 4th row are surprisingly playable, but most people prefer not to have their opening stone swapped, and playing against a 4th row opening stone can seem daunting, so a 3rd row opening is often preferable. If you strongly prefer having the first stone, or you think your opponent is overly eager to swap, you can play a weaker opening like g3 or h3.
+Openings in the middle of Red's 4th row are surprisingly playable, but most people prefer not to have their opening stone swapped, and playing against a 4th row opening stone can seem daunting, so a 3rd row opening is often preferable. If you strongly prefer having the first stone, or you think your opponent is overly eager to swap, you can play a weaker opening like f3 or g3.
 Third row openings, especially those near an obtuse corner (except p3), tend to combine well with the 4-2 obtuse corner move:

@@ Line 3: / Line 3: @@
 An average well-played game lasts about 72-90 moves before one side resigns, or 20-25% of the board, though it varies considerably from game to game. This article covers opening strategy that is most relevant in the first 10-30 moves of the game. Some of it is specific to 19&times;19, but much of it is applicable to other large board sizes.
-The advice in this guide is heavily influenced by hzy's KataHex bot, the strongest known (and easily superhuman) bot as of March 2023.
+The advice in this guide is heavily influenced by [[KataHex]], the strongest known (and easily superhuman) bot as of March 2023.
 ==Differences from smaller boards==

@@ Line 9: / Line 9: @@
 * While [[corner move|corner moves]] are still good moves, playing near the middle of your opponent's 4th to 6th rows is often just as good. This starts to become true for boards 18&times;18 and larger.
-*  Ladders and ladder escapes are less important. Human games often have long ladders across a side of the board, but it's usually a mistake for the defending side to keep pushing the ladder. Often, it's best for the defender to jump, allowing their opponent to connect in exchange for territory. Here is an illustrative example, where Red's opening stone c2 serves as a ladder escape for his 3rd row ladder. Instead of continuing to defend the ladder, Blue jumps ahead on move 9, gaining a useful stone that could combine well with Blue 1 via (*).
+* Ladders are somewhat less threatening, since the defender has more options on a large board. Human games often have long ladders across a side of the board, but it's usually a mistake for the defending side to keep pushing the ladder. Often, it's best for the defender to jump, allowing their opponent to connect in exchange for territory. Here is an illustrative example, where Red's opening stone c2 serves as a ladder escape for his 3rd row ladder. Instead of continuing to defend the ladder, Blue jumps ahead on move 9, gaining a useful stone that could combine well with Blue 1 via (*).
 <hexboard size="6x19"
@@ Line 384: / Line 384: @@
    coords="hide"
    edges="bottom left right"
-   contents="R e4 B 1:d6 R 2:c5 B 3:b7 R 4:p4 E *:f5"
+   contents="R e4 B 1:d6 R 2:c5 B 3:b7 R 4:p4 B *:f5"
    />

@@ Line 7: / Line 7: @@
 ==Differences from smaller boards==
-* While [[corner move|corner moves]] are still good moves, playing near the middle of your opponent's 5th row is often just as good. This starts to become true for boards 18&times;18 and larger.
+* While [[corner move|corner moves]] are still good moves, playing near the middle of your opponent's 4th to 6th rows is often just as good. This starts to become true for boards 18&times;18 and larger.
-*  Ladders and ladder escapes are less important. Human games often have long ladders across a side of the board, but it's usually a mistake for the defending side to keep pushing the ladder. Often, it's best for the defender to jump, allowing their opponent to connect in exchange for territory. Here is a [https://hexworld.org/board/#19n,c2d16p15o5r4q2q3r2p3p2o3m3o2 common example].
+*  Ladders and ladder escapes are less important. Human games often have long ladders across a side of the board, but it's usually a mistake for the defending side to keep pushing the ladder. Often, it's best for the defender to jump, allowing their opponent to connect in exchange for territory. Here is an illustrative example, where Red's opening stone c2 serves as a ladder escape for his 3rd row ladder. Instead of continuing to defend the ladder, Blue jumps ahead on move 9, gaining a useful stone that could combine well with Blue 1 via (*).
 * There is a lot more room to ignore your opponent's threats and [[tenuki|play elsewhere]] in the early opening. Moves are less forcing, and there's a much larger variety of different strategies you can try.
@@ Line 147: / Line 154: @@
    />
-Red 11 is a good minimaxing move, but he can only play it after Blue 10. If Red plays the move a bit early, Blue has a strong minimaxing reply at the stone marked (*):
+Red 11 is a good minimaxing move, but he can only play it after Blue 10. If Red plays the move a bit too early, Blue has a strong minimaxing reply at the stone marked (*):
 <hexboard size="8x13"
@@ Line 380: / Line 387: @@
    />
-Even if the long undermining sequence isn't obvious, the local placement of Blue stones 1 and 3 &mdash; the 2-2 obtuse corner and a bridge move away &mdash; is very efficient, and it should set off alarm bells. A strong player should intuitively recognize, without calculation, that the local configuration after Blue 3 is quite favorable for Blue.
+Even if the long undermining sequence isn't obvious, the local placement of Blue 1 and 3 &mdash; the 2-2 obtuse corner and a bridge move away &mdash; is very efficient, and it should set off alarm bells. A strong player should intuitively recognize, without calculation, that the local configuration after Blue 3 is quite favorable for Blue.
 '''C:''' Rarely seen on 13&times;13, but KataHex plays it frequently on 19&times;19. Red 2 below is pretty common. Blue's reply is more varied; she can either play elsewhere or respond locally in a few different ways, such as one of (*).

@@ Line 1: / Line 1: @@
 &times;19 is the most popular of the "large" board sizes. This board size offers a lot of room for strategic freedom (unlike 11&times;11 or 13&times;13), but tactics and local play remain highly important.
-An average well-played game lasts about 72-90 moves before one side resigns, or 20-25% of the board, though it varies considerably from game to game.
+An average well-played game lasts about 72-90 moves before one side resigns, or 20-25% of the board, though it varies considerably from game to game. This article covers opening strategy that is most relevant in the first 10-30 moves of the game. Some of it is specific to 19&times;19, but much of it is applicable to other large board sizes.
 The advice in this guide is heavily influenced by hzy's KataHex bot, the strongest known (and easily superhuman) bot as of March 2023.
@@ Line 19: / Line 19: @@
 * Playing too close to your own edge is by far the most common mistake in the opening. There are exceptions where it can be a good idea, like when you're playing a corner move or joseki, or your opponent has intruded heavily into one of your edges, or you're responding to a local tactical situation. However, if your opponent hasn't played near one of your edges, it's almost always a bad idea to play a move closer to that edge than one of your opponent's edges.
-==General principles==
+==Initial stones==
-* Corner and edge moves: In the absence of other stones nearby, Red would do well to play in one of the following spots:
+It's easy to feel lost in the early opening, with so many choices on the wide open board and no clear "best" move. We'll discuss the very first move and swap map later, but let's talk about how to play the first few (non-swapped) stones, from Red's point of view for simplicity. In the absence of other stones nearby, Red would do well to play in one of the hexes shaded red:
 <hexboard size="19x19"
    coords="show"
-   contents="R d5 e6 *:f7 g8 f9 *:e10 *:e11 *:d16 p15 o14 *:n13 m12 n11 *:o10 *:o9 *:p4"
+   contents="S red:(d5--g8 p15--m12 area(d8 g8 h9 j9 g12 d12) area(p12 m12 l11 j11 m8 p8))
    />
-This is far from an exhaustive list; many other moves near the middle of Blue's 4th to 6th rows are often just as good. Of course, the presence of other stones even moderately nearby can influence things. KataHex prefers the spots marked (*) especially often.
+This diagram is a lot to digest, so here's a breakdown:
-* If Blue plays too closely to her edge, Red usually has some good local responses. In particular, if Blue plays near the middle of her 4th row, Red can choose one of the following blocks:
+* If Blue plays too closely to her edge (which is a mistake), Red usually has some good local responses. In particular, if Blue plays near the middle of her 4th row, Red can choose one of the following blocks:
 <hexboard size="7x7"
    coords="hide"
@@ Line 442: / Line 471: @@
 ===Acute corner openings===
 The stone in the acute corner affects which moves are locally efficient for Red and Blue.

@@ Line 65: / Line 65: @@
 Corner joseki on 19&times;19 can be quite involved. Here's a sampler for inspiration.
 ===5-4 acute corner===
-* High intrusion is by far the most common: [https://hexworld.org/board/#19nc1,p15p16o16p14 here]
+* KataHex's favorite 5-4 joseki is the following:
-Blue typically doesn't play 4 if she already occupies the obtuse corner on that side, but in other cases it's often the best move. Other bots like leela_bot also play this joseki often, so even if the benefit of Blue 4 isn't immediately obvious to humans, the move still deserves serious consideration.
+<hexboard size="8x8"
-* An extended version: [https://hexworld.org/board/#19nc1,p15p16o16p14q14o17n17 here]
+Blue typically doesn't play 4 if she already occupies the obtuse corner on that side, but in many cases it's the best move. Other bots like leela_bot also play this joseki often, so even if the benefit of Blue 4 isn't immediately obvious to humans, the move still deserves serious consideration.
 ===6-5 acute corner===
-* Low intrusion by Blue, high intrusion by Red: [https://hexworld.org/board/#19nc1,o14o16p16p15n16n17m17 here]
+* A relatively simple joseki where Blue gets a 4th row ladder escape:
-* A much longer variation: [https://hexworld.org/board/#19nc1,o14o16p16o17q17p18q18p15q13p17n16n15o15m18l17m16m17 here]
+<hexboard size="8x9"
-Blue has a couple ways to gain territory from Red 15, either playing at j18 or k19, but it seems better to defer the [[question]] and wait until one option is clearly preferable.
+* A much longer variation:
-* High intrusion by Blue: [https://hexworld.org/board/#19nc1,o14o15p14p15n15m17l16m15m16k18q13p16j17k16k17 here]
+<hexboard size="8x11"
-Red 11 is a good minimaxing move, but he can only play it after Blue 10, since otherwise Blue has a [https://hexworld.org/board/#19nc1,o14o15p14p15n15m17q13l18 strong minimaxing reply].
+Blue has a couple ways to gain territory from Red 15 by playing at one of (*), but it seems better to defer the [[question]] and wait until one option is clearly preferable.
 ===7-6 acute corner===
-* Here's a standard one that KataHex prefers: [https://hexworld.org/board/#19nc1,n13n15o15n16p16p17r17q18o17 here]
+The possibilities for 7-6 joseki are endless, and there's not much point memorizing lots of different sequences. Instead, it's better to infer patterns from 5-4 and 6-5 corner joseki. We just show one representative example that KataHex likes to play:
 ==Obtuse corner theory==

@@ Line 244: / Line 244: @@
 ===5-5 obtuse corner===
-'''TODO'''
+The 5-5 corner opening is common in human games. Strictly speaking, KataHex thinks 5-5 is a slightly worse move than 4-4, and it typically assigns the 4-4 a slightly higher win percentage (around 3-4%). Note that this is miniscule, and comparable to "1/25th of a stone" or "Blue's advantage when she swaps the (very fair) a19 obtuse corner opening." That is to say, you should not be discouraged at all from playing the 5-5 opening.
 ==The first move==

@@ Line 62: / Line 62: @@
 * Here's another [https://hexworld.org/board/#19nc1,e4d4d5 example]. Red accidentally played the 4-5 corner move instead of 5-4. Blue should not play 4-4, because then Red could play 5-4, and he would be in the same position that he would've been, had he played the first move correctly (via the Red 5-4, Blue 4-4, Red 4-5 joseki). Blue essentially let Red out of his mistake. A better move for Blue here is simply to tenuki.
-==Common joseki==
+==Acute corner theory==
 Corner joseki on 19&times;19 can be quite involved. Here's a sampler for inspiration.
@@ Line 92: / Line 92: @@
 * Here's a standard one that KataHex prefers: [https://hexworld.org/board/#19nc1,n13n15o15n16p16p17r17q18o17 here]
-===4-4 obtuse corner===
+==Obtuse corner theory==
-* KataHex usually responds to the 4-4 obtuse corner by playing 3-3: [https://hexworld.org/board/#19nc1,d16c17d17c18d18 here]
+===4-4 obtuse corner===
-As a (long) aside, it's highly instructive to go through the many possible Blue responses to Red 4-4 in the obtuse corner.
+It's highly instructive to go through the many possible Blue responses to Red 4-4 in the obtuse corner.
 <hexboard size="7x7"
@@ Line 119: / Line 119: @@
    contents="R d4 B 1:c5 R 2:d5 B 3:c6 R 4:e5 B 5:d7 R 6:f6 B 7:f5 R 8:e6"
    />
 '''B:''' Interestingly, this move is relatively common on 11&times;11 but not 13&times;13. The usual purpose of this move is to block Red from playing at (+) below. It appears slightly worse than move '''A''', but it's still very playable. Red has many reasonable responses marked (*):
@@ Line 230: / Line 242: @@
 Red 2 is strong, but that's not the only reason why. It turns out that had Blue played 1 first (before Red played the initial 4-4 stone), then a good Red response would be playing at 4-4. Going back to our general principles, it's a bad idea to play a move that would make your opponent's existing stone unnecessarily well-placed relative to yours, and that's exactly what '''K''' does.
-Okay, that was a long detour &mdash; back to discussing other joseki.
+===5-5 obtuse corner===
-−
-* An alternative if Red's acute corner on the same side is free: [https://hexworld.org/board/#19nc1,d16c17d17c18p15m17q16 here]
-−
-This joseki is quite tactical. After move 4, Red has a third row ladder from the obtuse corner, even if he plays elsewhere, but no ladder escape. Instead of connecting outright, he plays 5 to give himself a ladder escape at a distance. Blue can defend the ladder by pushing for a few turns, but it's a mistake to push all the way to the acute corner where Red can escape the ladder. So, Blue jumps at a distance on move 6. Note that Blue deliberately chooses the 3-7 point mentioned above, which works well against Red's 5.
-After Red responds at 7, Blue has several reasonable options. Blue can push the ladder defensively, which Red can't escape outright because of Blue 6, but eventually Red can climb or carry out a complex switchback with the help of 5 and 7 (neither of which are overly strong for Red). Alternatively, Blue can start a fight in the acute corner for territory or ladder escapes. Since this is a joseki, it represents excellent play by both sides without big mistakes, but the exact best continuation will depend on the surrounding board situation.
+'''TODO'''
 ==The first move==