Openings on 13 x 13

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Hex Openings

-- Adapted with permission, from content originally created by Jonatan Rydh, recovered from https://web.archive.org/web/20070214100026/http://www.nada.kth.se/~rydh/Hex/openings.html. --

Note that Jonathan Rydh compiled the statistics in 2007 (or before), and that current win percentages, etc., may have changed.

Introduction

I will in this page consider some usual hex openings for 13x13 board. The observations are based on around 10.000 correspondence games played by beginners as well as experts. As is the common case, the swap rule will be utilized. This rule says that after the first stone has been placed, the second player may switch side if he wants. This is to remove the big advantage one has for playing first. Everything on this page should be taken with a grain of salt. It is based on actual played games which may be a beginner against another beginner. This is why for example only 81% of the games which started G7 is won. (or lost if you take in the fact of the swap rule.) That being said there might be some useful info to ponder upon. Just don't complain to me if your game is lost because you followed any of my advice...

The first move

The first move should, because of the swap rule, not be too good nor too bad. It now happens that most hexes on the board are too good to start with so the number of good first moves are quite limited. The following diagram shows the number of wins in percent. The first stone to be placed is black. Since the board looks the same rotated 180° it only consider half the board. The hexes which lack numbers are very seldom played but not necessarily bad moves. (Although a hex somewhere near the center is definitely a bad move.) Typically a good start move has a number around 50. If it is higher we would swap it and if less we would not. The most common moves played are A3, B2 and A2, in that order, all in the acute corner of the board. Other moves to consider is C2, D2, E2, A11, A12 and other moves along the A column.

(See the discussion on the LittleGolem forums [|Hex 13x13 Openings] for more current statistics)

As a general principle one can say it's not too bad to swap all moves but A1, B1, ... , L1. However if A3, B2, A2 etc. is winning or not has not been proved and it's much of personal preference whether to swap or not. The strength of having a stone on for example A2 is of course it's function as a ladder escape. A2 and B2 and other stones on second row can be used as second and third row ladder escapes and A3 can be used as second row ladder escape and will help getting down third and fourth rows as well. Personally, I don't swap A3 and B2 as much as I used to. It seems getting the strategically important positions as quick as possible is more important than having the first stone.

The second move

After the swap phase is finished, it's time to make the first really important move. We now assume you connecting from left to right. Typically your opponent has a stone in either A2, A3 or B2 (marked as 1 in the diagram below).

Most now play the middle hex, G7 (marked as 2 in the diagram below). Statistically this seems to be a bad move, as more than half of the games are lost after this move. No matter where the first stone is placed, the best responses to G7 seems to be K10 or J9 (marked as 3 in the diagram below) which usually end up with a win. However if your opponent responds with a move like H7, F7 or I6 (marked as * in the diagram below) you are quite well off with your middle stone.

abcdefghijklm12345678910111213111233

It should be stressed though that many strong players play G7 and do well. Statistically it doesn't seem so but it's very hard to tell with statistics.

A good alternative to G7 is I10 or J11. For the horizontal player these moves are equivalent with the previous mentioned vertical player's K10 and J9. One reason these are good as both second and third moves are the one-stone templates:

Template Va
Template IVa

In other words, this stone is connected downwards with a strong connection. It's quite optimally placed, further down would be too far from the centre and further up would be too far from the edge thus not connected. In another way of seeing it, J9 for the vertical player lies pretty much in the center of the right half triangle of the board. It can be used as a ladder escape from the left and is dangerous upwards.

Another idea as second move is to block the opponent's first stone by playing in the top acute corner (assuming he played there). This should be done in a similar manner as above. A template should exactly match into the space right of the opponent's stone. If it is at A3, the typical block move should be D6, as shown in the diagram below.

abcdefghijklm1234567891011121312

Similarly if red's first move is at A2 blue may play at D5.

abcdefghijklm1234567891011121312

For a response to red's first move of B2, the block would go at E6.

abcdefghijklm1234567891011121312

A warning should be made: do not use the usual third row template in this purpose as this is too weak a threat. For example the response C4 of B2 usually ends up bad. If a block in this manner is a good idea or not is up to discussion, it seems it's better than playing in the center but not quite as strong as playing I10 or J11.

The move A3

It's not a bad idea to swap A3. The main reason being the following templates:

Template 4o
Template 5s

The A3 stone is the the one on the left. The pattern probably generalizes to bigger dimensions as well but I haven't checked this. The point being that it can be used quite effectively to "jump up" when having a ladder on third row.

So how do you respond if you find yourself playing against A3? The following table shows the nine most common answers sorted by their rate of winning the game in the end. Ideas what to play and not to play as third move are collected in the third and fourth column. These are sorted in win percent from left to right (and in case of bad response, from worse to less worse). Note that the most common response which is G7 (the middle square) is rather far down the list. Good responses typically lies in the opposite acute corner along the diagonal.

1.A3
Win rate
Good response
Bad Response
I10
72.5%
I9, K10
G7, F8, G8, H8, G9, H9, G10, H10
I9
65.9%
F8
H9, F10, G7
J11
63.8%
F8, F9
J10
D6
62.2%
H6, F7, K10
G7, H7, E6, F6, F8, G8
C2
52.1%
J9, H6
G7, F8
J10
50.4%
J9, F9, G7
H9
G7
46.7%
I8, J9, K10, I7
K6, D9, I6, F8, F7, H7, J6
F8
45.4%
K10, I8, J9, H8
G7, E8, G8, H7, I7
H6
44.0%
K10, J9, E7, F7
F6

The move B2

The second most common move is B2 with around equal strength and possibilities as A3. The big advantage of B2 is that in contrary to A3 it's a solid third row ladder escape. The disadvantage lies perhaps in the vertically direction where A3 probably is slight stronger. It's not entirely true though, three very useful templates in this corner are:

Template 5j
Template 5c
Template 5L

The two leftmost can also be used with A2 as well as B2. The third cannot and but it is basically the same template as the one to the left.

Responses of B2 is quite similar to A3 with a few exceptions: D6 are now a bad idea, instead E6 and D5 takes it's place. Best moves still seem to lie in the opposite acute corner.

1.B2
Win rate
Good response
Bad Response
I10
86.4%
E9?, D11?
G7
I9
76.5%
G7?, F8?
F9, I9, H6
J11
68.1%
G10?
G7, I10, H9
E6
66.7%
G7
F6, G6, H6, F8
D5
61.1%
G6?, D6?
H6, G7
F7
56.4%
H7
I6
F8
53.3%
I7, H8
E8, G7, H7
G7
49.7%
K10, J9, J7
F7,H7, D9, I6, G9, E8, D8
C3
28.6%
G7, K10, J9
D3
G6
21.1%
G7, E7, H6
I5
C4
9.1%
G7, A4, E5
-

The move A2

This move is probably the weakest of the three but still good as second and third row ladder escapes as well the two leftmost templates above. This is why I think it still very well can be swapped. What to respond to I10 I'm not sure though.

1.A2
Win rate
Good response
Bad Response
I10
81.5%
F8?, F9?
G7, G8, G9, H9, H10
E6
62.2%
K10, J9, G9
G6, H5, H6, F6, G6
J11
61.5%
G10?, E10?
G7, H5, H6, F6, G6
G7
48.7%
K10, J9, G9
E7, E8, D8, H7, I7
F7
38.7%
K10, H7, C8
G7
F8
38.7%
H8, G8
G7, E8
B3
18.5%
G7, C3, D4, F5
-

Other moves

Following is a list of other less commonly encountered moves and possible responses. What isn't yet considered are moves along the middle A row. It seems these kinds of moves requires quite different strategy to tackle.

1.C2
Win rate
Good response
Bad Response
J11
70.0%
?
F9, F10
E6
65.7%
K10, F8, H8
F6, H7
G7
42.2%
E7, H7, I6
E8
F8
36.0%
H8, I8, J9, K10
G8
1.D2
Win rate
Good response
Bad Response
J11
66.7%
F10?
-
G7
57.4%
K10, J7, J6, D8, D7
E8, F7, E7, D9, I6, G9
F8
36.0%
H8, H7, I8
E8
1.E2
Win rate
Good response
Bad Response
G7
70%
I7
H7, F7, E8, G6, D8, D9
F8
55.6%
H8, K10
H7, E8
1.A11
Win rate
Good response
Bad Response
H6
87.5%
F6?
G6, E6, E7
D3
69.2%
G5?, J9?
G7
G7
44.7%
F5?, E6?
D7
C10
10.0%
E9, F8, G7
-
1.A12
Win rate
Good response
Bad Response
F8
87.5%
J8?
J9, H7, H8, F7, E8
E4
75.0%
H6?
F5, G5, H4, I4
G7
44.3%
D5?
K10

Fourth, fifth move...

This is where the tough part comes... to actually play Hex :-) One thing important in early games seems to be to cover ground placing far apart from both your own and your opponent's stones rather than building small chains. Another common strategy seems to be to build walls in the same direction as your edge (see figure). These builds in both directions and can be seen as a half-move in both direction. It also hinders the opponent a little to get around from both sides. These walls can extend quite long, I've seen five or six in a row.