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?

Welcome to hex! I hope you reach the top soon, we're in need of new semi-serious players! :)

B11 is weaker than B10 and B12 but it's still very strong on 13x13. You can experiment with A12 to get a feeling of how it works because A12 already wins comfortably on 13x13. For B9, it's similar. You can play A9 and A10 instead of B9 to get a feeling of the problem. B9 should be weaker than B11 but it should comfortably win.

https://www.hexwiki.net/index.php/Interior_template

You're right, “wheel” (and “diamond”) happen less because they're less “efficient”. For the “wheel” you need 3 stones, and a lot of space, to cover only a small distance. The “hammock” happens but only at high level.

On the white side, A4, A7, A8, A10 and A13 are the playable options according to humans and also according to bots (but I don't remember exactly what the bots reported, maybe you can find in old forum posts). On the black side the playable choices are C2, F3, G3, H3 and K2. On larger boards there should be more choices.

Thanks lazyplayer, that was very helpful! I'll maybe try a7 or a8 in a couple games to see how that plays out. Why do you think b9 is weaker than b11?

The bot percentages are in the thread https://littlegolem.net/jsp/forum/topic2.jsp?forum=50&topic=739. Interestingly leela_bot thinks a4 is really strong, and j3 might be as playable as k2, just on the strong side rather than the weak side. I wonder if there's a more recent version or a swap map for larger boards, but that's wishful thinking :)

I've personally never viewed A4 as playable. Top players sometimes say that it is, but I think they are crazy… I happily swap A4 even on 19x19, and on smaller boards it feels even stronger. A3 is, if anything, more playable (A3 is weak, weaker than A2 even, but A4 is incredibly strong).

I believe 1.B1 has been proven to be a losing move, just as 1.A1 has, on any size grid.

In the proof for A1, it is shown that B2 is strictly better than A1, meaning that if A1 is winning, 1.B2 must also be winning. Then using strategy stealing, a contradiction is reached.

Similarly, the initial move C3 can be shown to be strictly better than B1, so if B1 is winning then C3 must also be winning. Again, a strategy stealing argument leads to a contradiction. Hey, I'm convinced.

hexanna, simply because white can at some stage play C11 against B9!

shalev, A4 is for the more daring people. :D

shalev, for example on 8x8 it loses: https://www.hexwiki.net/index.php/Small_boards

It would be nice for someone to “import” leela and gzero “swap maps” on hexwiki…

That's funny you mention it because I was reading this thread yesterday and decided to put leela's map on hexwiki: https://www.hexwiki.net/index.php/Swap_rule

I've just checked out the hexwiki map by leela and I was astounded that f3 to j3 are considered playable… with the exception of i3!!!

I believe there is a lot of random error involved.

I would like to experiment with j3 because on one hand it can be countered by l2, on the other hand it's really blocking white j4 ideas.

g3 is logically the weakest of them because of the e4 and f2 relation and also being least blocking on the right side, but another astounding fact would be if that g3 is really more playable than a13 even!!! Ha! I've indeed struggled playing against a13, but g3 I considered basically a joke for a serious game.