Little Golem#1 · hexanna
17 Oct 2021
I want to see if some of the less-played opening moves in Hex are actually viable (especially on larger boards). In this post I’m focused on openings on the b column. The discussion and coordinates here focus on 13x13 for simplicity (but when I say the b11 opening, I really mean the 3-2 obtuse corner opening in general), but I would love any input from stronger players on whether any of what I’ve written makes sense. :)
Acute corner openings:
First, let’s talk about b1 and b2 to get a point of reference:
b1 is really weak (almost as weak as a1):
• It captures a1
• It’s a second-row ladder escape
• It barely cuts into White’s edge, so White has to play e5 as her 5-4 acute corner opening instead of e4
b2 is pretty fair, worth about half a move since White is relatively indifferent about swapping:
• It captures 5 hexes in the corner
• It’s a second- and third-row ladder escape
• It cuts slightly into White’s edge, so White has to play e6 as her 5-4 point instead of e4
b3 is much too strong, I think worth nearly a full move, since it’s often played anyways in joseki (such as in response to White d3). As an opening:
• It’s a second-, third-, and fourth-row ladder escape
• It cuts into White’s edge, and White has to move three rows over if she wants to play in that corner.
b4 is the first interesting option. I think it’s weaker than b3, and it’s probably stronger than a5, though this isn’t totally obvious to me, because b4 doesn’t actually capture the hexes a4 and a5. I wonder if it’s playable on larger boards like 19x19.
• Like a4, it can be used as a 2nd-to-4th row and a 3rd-to-5th row switchback
• It cuts into White’s edge about as much as a4 does
• However, unlike a4, White has room for Template A-3 in the corner. What would be an appropriate joseki in this case? I doubt the examples here really represent optimal play in the corner.
◦ https://www.trmph.com/hex/board#13,b4c2d3f2e1
◦ https://www.trmph.com/hex/board#13,b4c2c3d2
Obtuse corner openings:
When I say b12 for example, I really mean “the 2-2 obtuse corner on any size board.”
b13 is really weak, possibly even weaker than a1:
• It’s a second-row ladder escape
• It doesn’t cut into White’s edge at all, and White can still play the 4-4 or 5-5 obtuse corner as usual
b12 is much too strong, also worth nearly a full move just like b3:
• It’s a second- and third-row ladder escape
• It’s on the short diagonal and cuts a bit into White’s edge, which means White would have to play the 4-5 obtuse corner off the short diagonal
Next up is b10, we’ll look at b11 later. Now b10 looks too strong and worth nearly a full move, as it’s often a good move in response to a 5-5 obtuse corner move, and it’s even a viable first move in the obtuse corner, in some cases.
• It cuts well into White’s edge, and White can’t even fit Template A-3 in the obtuse corner
b11 is a tricky move to evaluate, I’m quite interested in others’ opinions on how strong it is. My personal guess is that it’s about as strong as a move like a4 (and should be swapped), but not as strong as a5 or a12.
• Like b10, it doesn’t provide any direct ladder escapes for Black, and its primary purpose appears to be blocking White’s edge, though it’s not as effective as b10 in doing so.
Finally, we can consider b9. My guess is that this move is far too strong, because it can combine very well with b12, leaving no room for Template A-3 in between.
Some other random questions I have:
• In my experience, the trapezoid and crescent are both very common interior templates (they have the same carrier and also seem to come up equally often). However, the 3-stone wheel template seems much rarer, appearing even less than the span and parallelogram, and usually when it does appear, only two of the stones actually matter in making the connection (I wouldn’t consider these occurrences as true wheels unless all 3 stones are tactically necessary). Why? Is there some sense in which the wheel is a less “efficient” template?
◦ The only example I have on hand is https://littlegolem.net/jsp/game/game.jsp?gid=2269620&nmove=14 where the wheel allows for the ladder-escape fork i11. Another wheel is formed later in the game, https://littlegolem.net/jsp/game/game.jsp?gid=2269620&nmove=21 but I don’t really count this because at this point, the f5 stone doesn’t matter anymore in making the connection.
• A fun one: say for the first move, Black has another possible move, which consists of putting a stone in each acute corner (so a1 and m13 on a 13x13 board), which White has the option to swap. How strong is this “move”? My intuition says White should in fact swap, because you get a second-row ladder escape in both corners, which sounds stronger than a move like c2, which just gives you a second- and third-row ladder escape in a single corner. Would you rather play against (a1+m13) or a “normal” strong move like a4?