User talk:Fjan2ej57w

Hello :D

Here is the way to make a hex board:

 [<][hexboard size=]["3x4"]
 [visible=]["][area(][a3,d3,d1,c1] 
 [)"]//set bondary by vertex
 [edges=]["][bottom]["]//colouring the bottom only
 [coords=]["][none]["]//not showing numbers
 [contents=]["][R c1]["]
 [/>]

then I will get a ziggurat:

 [<][hexboard size=]["6x7"]
 [coords="none"]
 [egdes="bottom"]  
 [visible=]["] 
 [area(a6,g6,g4,f5,e4,d5,c4,b5,a4)]["]
 [contents="R f5 d5 b5"]
 [/>]

a longer rampart :p

some questions about hex

1.Is there a 2nd row ladder escape template that contains only empty cells? (It's equivalent to ask that given enough space, is a 2nd row ladder able to connect itself to the edge. 2.find templates that escape ladders on both sides,e.g.,Edge template II escapes 2nd and 3rd row ladders on both size at the same time. 3.is it possible to get a switchback from a 3rd row ladder? 4.Does single stone 8th row edge template exist? Is there a better way to analyze such templates? 5.is it possible to totally surround a single stone on an infinite board? I.e., to make the group coming from that stone remain bounded. 6.Find the ways to prolong a losing game as much as possible.(or shorten a winning game as much as possible) 7.Which leads to the question that how much space of an empty board would be filled if both sides play optimally.(I guess if n(approaching infinity) is the length of the board, then the game(with or without swap)would end in n^(3/2)•k moves, where k is a constant depending on whether the swap rule is used or not) 8.Bridge ladders are common in actual games, so there must be some conclusions about it, comparing such "interior" bridges to an interval of edge. 9.there is the concept of capture. And it can be used to determine the shape of an edge template. https://www.hexwiki.net/index.php/Theorems_about_templates more complicated and frequently occurring conditions of capturing and their corresponding strategy may be very helpful.

independent subgames

In some cases, a game is seperated into two or more independent subgames, just like the example above. In order to win, the only way for red is to connect his group to both sides. On the other hand, if red fails to connect his group to either side, blue is able to connect within that region instead. The board is actually seperated into two independent parts by red stones parallel to his own edge. No matter what happens in one part, the other part won't be affected at all.(except that the question of who would play first in a certain region) The upper part:

And the lower part:

Sometimes, the board would be seperated into more than two independent parts. The position below is one example:

Now the board is seperated into at least 3 independent parts: 1.

2.

3.

Blue will achieve the final victory if and only if she wins 1 or both 2 and 3. On the other hand, red will win if and only if he wins 1 and either 2 or 3.

It actually doesn't matter what's the relative position of these subgames or how they are interconnected in the original board. What We really care is their logical relationships, that is, the winning condition for both players.

These examples looks more or less artificial, but the phenomen of independent subgames actually occurs quite often in actual game play. By merely identifying such patterns, a game would be much easier to analyze in some cases. The following are some examples with subgames having more vague boundaries.

some thoughts about hex

Beginners are too eager to push ladders. From the attacker's pespective, this seems to oversimplify the game since a ladder could be used in potentially different ways. And for the defender, it's generally better to play elsewhere until the ladder becomes threatening enough. The opponent may get inappropriate advantages from any kind of overreaction.

As shown above, after red's c2, blue didn't swap and played d8. It's not good in general to handle the ladder in such early stage of the game. By defending this ladder, red has actually assumed the solid connection between d8 and the right edge. On the other hand, by pushing the ladder, blue has not only assumed this, but also that he gets a 2nd row ladder escape on the top, which is currently not the case.

Finding all 2nd row ladder escapes may be at least as hard as finding all 3rd row ladder escapes. Consider the following position with blue to move:

Red's ladder stone marked "↑" is already connected to the top edge. The connection is not shown, but it does not use any space on the 2nd and 3rd row, nor any space within the carrier of the potential ladder escape template. Notice that red has a 2nd row ladder at first, and could get a 3rd row ladder to the right of that blue stone in the middle:

That means for any 3rd row ladder escape template,we could simply add the pattern below to the left and get a 2nd row ladder escape template:

For example, the following is a 3rd row ladder escape template in the artical Theory of ladder escapes:

then we could add that pattern to it and get a 2nd row ladder escape template:

It may not be minimum(even though I suspect is)But there must exist one minimum 2nd row ladder escape template coming from this.

So this naturally generates an injective map from the collection of all 3rd row ladder escape template to the collection of all 2nd row ladder escape template.

lolololololololol seperate line lolololololololol

To actually "learn" a josiki, we have to know every possible moving sequence within that region before that corner is completely settled. But this is not possible. Fortunately, with some simple reasoning, It's possible to make the right choice most of the time. A josiki is played when both sides think it's good to make that exchange, the following is an example:

It's generally not good for red to tenuki after blue 6 c4,

because blue would otherwise get an additional 2nd row(but not 3rd row) ladder escape. This is already adequate to connect 4-4 obstue corner stone from any distance away. After red 7, b6(Which is almost forcing for blue) blue no longer get any kind of ladder escapes. The right side of this josiki, namely the moves after red 9 e3 could be delayed, and blue may retain it as a threat. According to Hexanna's talk page, switchbacks, climbing, or ladder creation templates may not the first thing to consider at the beginning. In my opinion, that is because ladders are at most a family of statements about virtual connections within that narrow region along one flat edge. Ladders are too "subtle" compaired to the whole board of complex strategy. Let alone there are still countless undecided areas. The ladder creation template one could design with delicacy may become useless in the end. ladder escapes are an "unexpected" outcome of a josiki that will take effect after a very long time, or just serve as a threat to be exchanged into other connections in the midgame.

It's also good to know what would happen near a josiki when the game is close to an end. consider a simplier Joseki, blue tenuki after red 5 d3:

red 5 is connected to the top edge, but some weak points would be created if he also need the same group to serve as a ladder escape.

See also Near ladder escape. If any of the space required are occupied by blue, red would be in trouble. And if red do trys to connect like that, blue could in some cases intrude into the cells marked"*" to get a 2nd row ladder escape as well as some territory.

One game that I played against myself some time ago

2025.03.8

This game was played on 11x11. Moves may not be perfect but I could explain some basic strategies and some thoughts during the play. Hope that would be helpful to new players. :D

The end game looks like this, red resign after blue 34.e3:

Let's start from the beginning. Red played c2 as the first move and blue responded at d8:

c2 is quite balanced, but it's still too weak to be swapped. If blue plays the obtuse corner d8, the future use of this stone would become very limited———It only serves as a 3rd row ladder escape. On the other hand, d8(sometimes also called the 4-4 obtuse corner) Is pretty strong. At such an early stage, we don't even need to worry about it's connection to the left edge, and it's better to treat it as if it's already connected(until it's not :p). And it's already blocking the opponent's edge very well, while constantly threatening to proceed to the middle(f7, f6, g7, etc.).

After blue 2.d8, red played the acute corner move at 3.h7:

Notice how this move is "one row upper" from the long diagonal, and how this is useful for the potential bridge ladder:

It blocks opponent's edge as much as possible, while keeping the desired connection. If red had got one row further, this "imaginary" bridge ladder would not function anymore.

After that, blue intruded at 3.h9 and a common joseki occurred:

I don't want to go in details about this, because there are articles on this site specifically for josekis, like this one: Josekis.

The only thing that matters is the outcome. After the exchange, blue got 12.g8 and 14.e10, which would be useful later. Red also got 9.j6 and solidified the connection from h7 to the bottom edge. And it's still blue's turn to move. "He" played another 4-4 and red intruded at j3, hoping to use the c2 piece on the left:

Notice how 17.j3 is immediately forcing for blue. It generates a 3rd row ladder for red and eventually connects to the top with the help of c2(shown as coloured area). And It's also threatening to bridge to h7(shown as "*"):

Since red's 17 is sufficiently connected to the top edge, blue chose to play tidily at h3, forcing red to respond at 19.j2. (See also: Tidiness.):

This exchange is——in most cases——good for blue. The additional piece 18.h3 would help blue to connect to the left edge. On the other hand, red only got what he almost deserved in the first place, making his moves repetitive. For example, 19.j2 indeed serves as a 2nd row ladder escape, but c2 already did the job.

After that, blue has very few choice to avoid an immediate lose. 20.j4 is one of such. After this move, red cut at i4 and blue blocked red at h6, forming a bottleneck in the middle (See also: Bottleneck.) :

Moves like 20 and 22 are very efficient combination to block your opponent, especially when 22 is very far away from his goal of connection. In this game, it punished the weak point red had left at i6. In fact, 22 is virtually connected to the right edge. Red is unable to prevent this connection. For example, like this:

The blue stone 8 and 10, which seem to have been "eaten" by red earlier finally revealed their effect.

Since the outcome is clear for both sides, and neither red nor blue would benefit from the above sequence, red tenuki and tried to block on left half of the board:

Let's view this position again. Blue now has successfully cut red on the right. If red continues pushing at h5, this would only help blue. And even if red wisely tenuki as in the actual game, blue is already too strong! I mean, look at the board, there are blue stones everywhere, but the only stone for red that seem to have some effect is c2. The position for red doesn't look good at first glance, but it's still not hopeless. Blue still has much weakness in the lower part, as well as the cutting point at h5.

So after red 23.c6, blue fixed at g7, leaving almost no chance for red to going through the gap between 2.d8 and 22.h6(or use it as a threat) (Actually I'm not so sure about g7, but it seems quite ok for blue.):

Now, the problem for red is that c6 is a bit too far away from the top edge, and also very hard to connect to the bottom. In many cases, b5 is better, because it combines well with c2, providing huge ladder escapes on the left. I'm not saying c6 is not playable, actually it also combines well with c2, if we count the bridge ladders:

Blue has the following way to block c6, and the blue sequence would combine well with 18.h3, which formes a two—gap.(as we could see later in the actual game):

Within this region, red is unable to connect, because c2 doesn't escape 4th row ladders. Conversly, blue could get a 2nd row ladder starting from the cell marked "+"

So after blue 24, red tried to block at b9, as a desperate attempt.

After that, blue tidied up the game by generously giving red the connection he wanted on the bottom:

Notice what blue get from this exchange, and how well they combine with the groups in the right half of the board. At this point, many weakness of blue that I mentioned earlier disappears automatically. By playing like that, blue controlled the center. Many empty cells are almost captured(See also:Captured cell.)The current position could be roughly viewed like this:

The area shaded blue could be viwed as the "territory" of blue, though they are not actually captured within this region. The cell marked "*" are two hopeful ways that red could use as a threat. Unfortunately, all possible attack of red eventually fall into the "bottleness pit" of blue territory below.

After that, blue has to return to the top and block red in the way mentioned above:

That's when red resigned.(Actually that's when I thought red should resign XD)

There are eventually two moves available for red now(marked below as "*" and "+"), all other moves are relatively easy to check :

If red played at "*" blue eventually has to respond at e4, after which red has many choices, but most of them are obvious. for example, like this:

If red played at "+" blue could respond at f4, then the most complicated sequence may be like that: