Difference between revisions of "Openings on 19 x 19"
(5-5 obtuse corner theory) |
(convert acute corner joseki to hexboard) |
||
| Line 65: | Line 65: | ||
Corner joseki on 19×19 can be quite involved. Here's a sampler for inspiration. | Corner joseki on 19×19 can be quite involved. Here's a sampler for inspiration. | ||
| − | |||
| − | |||
===5-4 acute corner=== | ===5-4 acute corner=== | ||
| − | * | + | * KataHex's favorite 5-4 joseki is the following: |
| − | + | <hexboard size="8x8" | |
| + | coords="hide" | ||
| + | edges="bottom right" | ||
| + | contents="R 1:e4 B 2:e5 R 3:d5 B 4:e3" | ||
| + | /> | ||
| − | * | + | 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. |
| + | |||
| + | * Here's an extended variation that is also quite common. | ||
| + | |||
| + | <hexboard size="8x8" | ||
| + | coords="hide" | ||
| + | edges="bottom right" | ||
| + | contents="R 1:e4 B 2:e5 R 3:d5 B 4:e3 R 5:f3 B 6:d6 R 7:c6" | ||
| + | /> | ||
===6-5 acute corner=== | ===6-5 acute corner=== | ||
| − | * | + | * A relatively simple joseki where Blue gets a 4th row ladder escape: |
| − | + | <hexboard size="8x9" | |
| + | coords="hide" | ||
| + | edges="bottom right" | ||
| + | contents="R 1:e3 B 2:e5 R 3:f5 B 4:f4 R 5:d5 B 6:d6 R 7:c6" | ||
| + | /> | ||
| − | + | * A much longer variation: | |
| − | + | <hexboard size="8x11" | |
| + | coords="hide" | ||
| + | edges="bottom right" | ||
| + | contents="R 1:g3 B 2:g5 R 3:h5 B 4:g6 R 5:i6 B 6:h7 R 7:i7 B 8:h4 R 9:i2 B 10:h6 | ||
| + | R 11:f5 B 12:f4 R 13:g4 B 14:e7 R 15:d6 B 16:e5 R 17:e6 | ||
| + | E *:(b7 c8)" | ||
| + | /> | ||
| − | Red 11 is a good minimaxing move, but he can only play it after Blue 10, | + | 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. |
| + | |||
| + | * Here's another complex joseki. Red has a long group connected to the bottom, while Blue gets a 2nd row ladder escape and a few hexes of territory, including the option of playing at one of (*) sometime in the future. Note also that Red 13 is unable to escape 3rd row ladders, which could come in handy for Blue, since Red 13 is already halfway towards the obtuse corner on a 19×19 board. | ||
| + | |||
| + | <hexboard size="8x13" | ||
| + | coords="hide" | ||
| + | edges="bottom right" | ||
| + | contents="R 1:i3 B 2:i4 R 3:j3 B 4:j4 R 5:h4 B 6:g6 R 7:f5 B 8:g4 R 9:g5 B 10:e7 | ||
| + | R 11:k2 B 12:j5 R 13:d6 B 14:e5 R 15:e6 | ||
| + | E *:(b7 c8)" | ||
| + | /> | ||
| + | |||
| + | 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 (*): | ||
| + | |||
| + | <hexboard size="8x13" | ||
| + | coords="hide" | ||
| + | edges="bottom right" | ||
| + | contents="R 1:i3 B 2:i4 R 3:j3 B 4:j4 R 5:h4 B 6:g6 R 7:f5 B 8:g4 R 9:k2 B *:f7" | ||
| + | /> | ||
===7-6 acute corner=== | ===7-6 acute corner=== | ||
| − | + | 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: | |
| + | |||
| + | <hexboard size="8x10" | ||
| + | coords="hide" | ||
| + | edges="bottom right" | ||
| + | contents="R 1:e2 B 2:e4 R 3:f4 B 4:e5 R 5:g5 B 6:g6 R 7:i6 B 8:h7 R 9:f6" | ||
| + | /> | ||
==Obtuse corner theory== | ==Obtuse corner theory== | ||
Revision as of 03:09, 1 April 2023
19×19 is the most popular of the "large" board sizes. This board size offers a lot of room for strategic freedom (unlike 11×11 or 13×13), 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.
The advice in this guide is heavily influenced by hzy's KataHex bot, the strongest known (and easily superhuman) bot as of March 2023.
Contents
Differences from smaller boards
- While 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 18×18 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 common example.
- There is a lot more room to ignore your opponent's threats and play elsewhere in the early opening. Moves are less forcing, and there's a much larger variety of different strategies you can try.
- On smaller boards, the game becomes quite tactical after the opening, and playing well often means playing stones that "work well" with existing stones near the corner. On 19×19, there is room to start a local fight near the middle of the board, relatively far away from existing stones.
Common human mistakes
- 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
- Corner and edge moves: In the absence of other stones nearby, Red would do well to play in one of the following spots:
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.
- 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:
KataHex prefers A the most often on a relatively empty board.
- If Blue plays near the middle of her 5th row:
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.
- If Blue plays near the middle of her 6th row:
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.
- If Blue plays close to the center, Red would do well to block at a distance, rather than using an adjacent or near block.
- 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 19×19. 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 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 4-4 corner is such a move. This is an important concept — 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 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.
Acute corner theory
Corner joseki on 19×19 can be quite involved. Here's a sampler for inspiration.
5-4 acute corner
- 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 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.
- Here's an extended variation that is also quite common.
6-5 acute corner
- A relatively simple joseki where Blue gets a 4th row ladder escape:
- A much longer variation:
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.
- Here's another complex joseki. Red has a long group connected to the bottom, while Blue gets a 2nd row ladder escape and a few hexes of territory, including the option of playing at one of (*) sometime in the future. Note also that Red 13 is unable to escape 3rd row ladders, which could come in handy for Blue, since Red 13 is already halfway towards the obtuse corner on a 19×19 board.
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 (*):
7-6 acute corner
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
4-4 obtuse corner
It's highly instructive to go through the many possible Blue responses to Red 4-4 in the obtuse corner.
A: KataHex's favorite response on 19×19 by far. Blue's move 3 gives her a 3rd row ladder escape in the form of edge template III2a.
Unless Red's acute corner is free, Red usually connects directly to the bottom with move 4. This may be counterintuitive since it goes against the principle of minimaxing, but most Red attempts to minimax allow Blue to gain territory. For instance, if Red plays at 4 below, Blue gets move 7 for free, and the result is favorable to Blue.
If the acute corner is free, Red can play an alternative joseki on move 4:
This joseki is quite tactical. After Blue's move 3, Red has a third row ladder from the obtuse corner, even if he plays elsewhere, but no ladder escape. Instead of connecting outright, Red plays 4 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 5. Note that Blue deliberately chooses the 3-7 point, which works well against Red's 4.
After Red responds at 6, Blue has several reasonable options. Blue can push the ladder defensively, which Red can't escape outright because of Blue 5, but eventually Red can climb or carry out a complex switchback with the help of 4 and 6 (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.
B: Interestingly, this move is relatively common on 11×11 but not 13×13. 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 (*):
C: This move is often effective on smaller boards when Blue has a ladder escape at her acute corner. However, the acute corner is much farther away on 19×19, and Blue's 5th row ladder is much less threatening, so Blue gains less from playing this move. Red, who is defending the ladder, usually pushes the ladder by playing at (*) below, or he jumps a couple hexes forward on the 3rd or 5th row (either immediately or after pushing a few times), indicated by (+):
D: This blocking move is common on 13×13 but less so on 19×19. Blue's idea, if Red ignores the threat, is to follow up with this move 2, which is quite strong since it neutralizes Red's 4-4 stone significantly:
Indeed, Red usually responds to the threat, and the following sequence is a common joseki on 13×13:
Red 6 is often at one of (*), (+), or (-). The move (*) allows Red to gain territory, while (+) creates a capped flank that blocks Blue 3rd row ladders under Red's 4-4 stone. It's not obvious to me why, but KataHex tends to think Red is slightly better after this sequence on 19×19, so Blue usually doesn't play D in the first place.
E: Usually not the best move for Blue. Depending on local tactics, Red should either tenuki, or play one of (*):
F: This 4-2 obtuse corner block is strong on small boards like 11×11, but it's rarely a good move on 19×19, whether as the first stone in the obtuse corner, or in response to 4-4. There are exceptions — the 4-2 move works well in combination with a "middle of third row" opening stone, for example. Red would do well to connect directly with 2:
G: This block is a "surprise weapon" of sorts — it's a weak move on an empty board, but for local tactical reasons it can be very strong. The standard example is with the q2 opening, where an unsuspecting Blue who plays 4-4 in response is faced with an unpleasant surprise (more on that later).
Move G is also a threat if Blue already has a stone in either of (*) below.
If G is played, Red should consider blocking the 3rd row ladder at a, or minimaxing at b.
H: Another "surprise weapon," arguably even more so. Anecdotally, when KataHex thinks H is the best move in a position, it rarely assigns a high policy to the move, only liking the move after some search. In other words, KataHex's policy "intuition" rarely considers the move a top choice, or even top 10, until it realizes that the move works tactically in the particular situation.
This 2-2 obtuse corner move typically works as an unusual minimaxing move, providing ladder escapes for Blue while simultaneously blocking Red and threatening a move like (*).
I: This move is sometimes played on 13×13, but it rarely works on 19×19. The standard joseki is favorable to Red, probably because Blue 1 and 5 function mainly as a ladder escape blocker, and ladders/ladder escapes are themselves less important on 19×19.
J: Like many other Blue responses, this is a bad move in isolation. Red's 4-4 is already connected to the bottom via edge template IV1d, so Blue attempts to block are futile unless she gets useful territory in exchange (like with A), but the territory gained by J is not nearly as good. However, this move can become useful if there are other blue stones present.
K: Also a weak response. Can you see why?
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.
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.
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.
A: A common move on 13×13 that also works well on 19×19. Red's usual response is to connect directly.
It might be tempting for Red to minimax on move 2, but a minimaxing move is usually no better than the simple bridge here. Red could also play the 3-3 obtuse corner on move 2:
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.
B: Strong reply that's seen on both 13×13 and 19×19. Red has a few responses worth discussing:
If Red plays the 3-3 obtuse corner (*), Blue responds at (+) and the position simply transposes to the sequence mentioned in the discussion of move A.
More commonly, Red plays at (+) instead. After Blue 3, Red has three reasonable options at a, b, or c:
Finally, Red could play at (-), but this is a very common mistake in human games. Presumably, Red is trying to minimax with this move, but it allows Blue to connect to the left on move 3, which in turn is very powerful because of the forcing sequence (moves 4-14) that allows Blue to gain a lot of territory with bridge intrusions.
Note that Blue 3 is necessary for the sequence to be forcing, because without that stone, Red can defend the Blue 4th row ladder starting from 1 on the left side. With Blue 3 in place, Red is forced to connect on the right side at any cost. If Red tries something different, like playing near the acute corner on move 4, then Blue's simple response at (*) is devastating:
Even if the long undermining sequence isn't obvious, the local placement of Blue stones 1 and 3 — the 2-2 obtuse corner and a bridge move away — 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 13×13, but KataHex plays it frequently on 19×19. 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 (*).
D: The usual joseki ends after Red 2, but Blue could continue with (*):
E: Red should come out ahead if he responds correctly to this move, but it can be tricky. For starters, Red should connect directly instead of attempting to minimax. Blue's move 3 threatens to hold Red to a 2nd row ladder, which can get pretty tactical. Red can attempt a cornering move if he doesn't have a ladder escape in the acute corner, and Blue can choose to tenuki instead of defending the ladder.
Red 2 is essentially forced. If Red plays a different move 2, whether locally or elsewhere, it helps to know that Blue likely has a strong response. For instance, if Red chooses to tenuki or play move 2 at any of the following, then Blue 3 at the 4-4 obtuse corner is a strong local reply:
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.
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.
G: As mentioned earlier, the 4-2 obtuse corner is a standard block on 13×13, but it's less effective on 19×19. Red's usual reply is at (*) or (+). Either move has the ability to hold Blue to a 3rd row ladder.
The tradeoff is that (+) is stronger towards the top, but it potentially allows Blue to play a different joseki:
H: Red could respond at either of (*), though other responses are possible.
I: Somewhat weak move. Red should play at 2 with the idea of undermining Blue's stone, though there are many possible sequences.
J: Red has several possible responses. The moves marked (*) seem more common, but the moves marked (+) can also work.
The first move
See Swap_rule#Size_19 for a swap map.
We'll now go through the general strategy of specific first moves. For simplicity, everything will be from Red's point of view, assuming Blue doesn't swap. Unlike the guides for smaller board sizes, we won't think too hard about ladder escapes or switchbacks, and instead we will just mention some brief notes for some selected openings.
Acute corner openings
The stone in the acute corner affects which moves are locally efficient for Red and Blue.
c2
On 13×13, b5 or c6, marked with (*) below, are common Red moves that combine well with c2. On 19×19, these moves are a bit too close to the corner. Playing a bit further along the b5-c6 diagonal, such as A or B below, is often a better move:
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.
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.
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 plays at A or C, Blue often peeps in Red's bridge, as follows. Red typically responds at one of the hexes marked (*) or elsewhere, instead of defending the bridge.
a10–a15
Some of the fairer openings in this category are a10, a14, a15. Blue's best response to a10–a15 in the obtuse corner is usually 4-4, but there's no rush to play it:
On 19×19, a15 is weaker than it looks, because the 4-2 obtuse corner, marked (*) below, is less potent for Red than on smaller boards:
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.
Obtuse corner openings
There are several openings that affect play in the obtuse corner, but they are quite different from each other so we'll consider them separately.
a19
A common joseki for Red is to play at 1, which is basically the 4-4 opening shifted up one row. Blue often responds at 2, and Red has a couple good responses marked (*):
My subjective opinion is that this is the most beginner-friendly opening:
- A beginner who opens with Red c2 could accidentally play b3 instead, or alternatively his opponent who wishes to swap Red c2 could implement swap-pieces incorrectly and replace it with Blue c2 instead of b3. Though a19 should technically be swapped to s1 under the swap-pieces convention, it doesn't really matter.
- Aesthetically, a19 retains the "most" symmetry of any fair opening. Beginners who don't want to think about the swap rule could play Hex without swap, where Red must open in an obtuse corner, and such a ruleset would be quite elegant and still balanced, even on large boards.
- For beginners who don't want to learn too much opening theory, "obtuse corner" is easy to remember and a good Schelling point. It's relatively likely that other beginners who look at the swap map and just want to try a random opening will pick a19 or s1.
q2
If Red opens q2, the most important advice for Blue is to refrain from playing 4-4 in the nearby obtuse corner, because of Red's strong response:
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.
Third and fourth row openings
According to KataHex, the fairest openings in this category are e3 (mentioned above), n3, and p3.
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.
Third row openings, especially those near an obtuse corner (except p3), tend to combine well with the 4-2 obtuse corner move:
