HexWiki - User contributions [en]

Territory

2011-01-28T08:38:16Z

Turing: reverted spam

The '''territory''' of a [[player]] is usually meant to signify the part of the [[board]] that the player ''controls''. One way to define it is to say that it is the set of [[Hex (board element)|hexes]] occupied by the player, plus those adjacent to cells occupied by the player.

However, it is often better to consider it in a looser sense. For example, if [[Red (player)|Red]] has an [[outpost]] on the [[fourth row]], which can be used as a [[Ladder escape]], it makes sense to consider the area between this and the [[edge]] as Red's territory.

{{stub}}
[[category:strategy]]

Sixth row template problem

2009-02-23T17:27:48Z

Turing: /* ... answering "Yes" */ fixed typo

As of January 2009 the following problem, initially stated by javerberg and wccanard in the LG forum, is still [[open problems|open]]:

Is there a one stone sixth row [[template]] that uses no stones higher than the sixth row?

More generally, it is still unknown whether one stone edge templates that use no cell higher than the initial stone) can be found for all heights. Such [[Edge templates with one stone|templates]] have been found for sizes up to 5 but none above. Answering with "No" to the former question answers the latter.

== Description ==

Is there a number m such that the game on the board of width m designed as follows, with Blue's turn to play, is won by Red ?

<hex> R7 C11
1:HHHHHVHHHHH
2:_____V_____
</hex>

== Generalisation ==

The general problem of knowing if there is n such that there is no one stone edge template on the n^th row<math>n^th</math> is also referred to as the n-th row template problem.

One of the way to prove if there is such an n is to prove if there is such n-1 for which an (n-1)-row-template with one defender stone originaly placed next to attacker stone in the same row. Of course if such template exists n-row-template is still not proven to exist.

Here is an example for n = 7
<hex> R8 C11
1:HHHHHVHHHHH
2:+++++V+++++
3:____HV_____
</hex>

For now it seems like there is no solution for above example.

== Possible paths to answer ==
===By "hand"...===
====...answering "Yes" ====
This would involve placing a stone on the 6th row of a sufficiently wide board, and showing how to always connect to the bottom. (Note this does not necessarily identify the minimal template needed.)

See [[defending against intrusions in template VI1]] for complete proof.
====6th row template====
<hex>
R7 C14 Q0
1:BBBBBBBBBRBBBBB
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
Sa4 Sb4 Sc4 Sd4 Sn4
Sa5 Sb5
Sa6
</hex>

====...answering "No" ====
This would involve showing how to connect (in the diagram above) the Blue stones to the right (plus Blue stones on the far right edge) to Blue stones on the left (plus Blue stones on the far left edge), no matter how wide the board is.

=== Computer Aided demonstration ... ===
==== ... answering "Yes" ====
Such a proof would use the computer to find the template and its [[carrier]]. Afterwards it should be easy to manually check that every Blue intrusion does not prevent Red from connecting to bottom.

==== ... answering "No" ====
TODO

== See Also ==
* [[Theory]]
* [[User:Wccanard|Wccanard]]

== External link ==

* The [http://www.littlegolem.net/jsp/forum/topic2.jsp?forum=50&topic=339 thread] were the names were associated.

[[category:theory]]
[[category:templates]]

Advanced (strategy guide)

2008-12-11T12:24:50Z

Turing: /* Template Vb */ fixed typo

== Advanced edge templates ==
=== Template IVc ===

<hex>R4 C4 Q1 1:BBRR 2:B_+_ 3:B**_ 4:_+__</hex>

This is a two-piece template and is useful for squeezing edge connections and ladder escapes into relatively small regions. Also, many players are unaware of it. Red's main threats are the two-chained connections via b3 or c3 (marked '*'). So the only strong defense is playing at c2 or b4 (marked '+').

==== Solution to intrusion at b4 ====

<hex>R4 C4 Q1 1:BBRR 2:B 3:B MH Mb4 Md3 Md2 Mb3</hex>

If Blue intrudes at b4, Red responds with d3, which is connected to the edge, so the blue move on d2 is forced.
Now b3 is a double threat for connecting either to the edge or to the forcing move at d3.
It is also possible to reverse the order of Red2 and Red4.

==== Solution to intrusion at c2 ====

<hex>R4 C4 Q1 1:BBRR 2:B 3:B MH Mc2 Mb3 Mb2 Md2 Mc4 Mc3</hex>

If Blue intrudes at c2, then Red responds with b3; b3 is connected to the edge via template II and threatens a direct connection via b2. So b2 by Blue is forced. Then Red plays at d2. Red threatens to extend d2 to template II at c3 and d3, and threatens to two-chain from d2 to the edge at c4. The only hex that is in the overlap of all these threats is c4 thus, Blue is forced to play at c4. Then Red plays at c3 completing the connection.

=== [[Defending_against_intrusions_in_template_1-Va|Template Va]] ===

<hex>R6 C10 Q1 1:BBBBBBRRBB 2:BBBBB_R_BB 3:BBBB_____B 4:BB 5:B +f4 +d6 +f6</hex>

If Blue intrudes in the template at any hex besides the three marked '+', Red makes a move that reduces the situation to a closer template.

Note that template Va occurs in a mirror-image form (in the mirror image form, the three hexes on the 5th row (from the bottom) are shifted over 1 hex to the G, H, and I columns). It may seem that this template is very strong because it reaches 5 rows into the board but it rarely occurs because of the huge size of the template; the template requires 31 empty hexes and 10 hexes along an edge — the entire edge on the 10x10 board!

Furthermore, the large perimeter makes it more vulnerable to encroaching adjacent plays and forcing moves. Additionally, template area surrounds the 5th row piece on both "shoulders" so that non-overlapping plays from the 5th row piece can occur in only two directions.

=== Template Vb ===

<hex>R6 C10 Q1 1:BBBBBBRBBB 2:BBBBBRRBBB 3:BBBB___BBB 4:BBB_____BB 5:BB______BB 6:B_______BB +f3 +e5</hex>

If the horizontal player Blue intrudes in the template at any hex besides the two marked '+', Red makes a move that reduces the situation to a closer template.

==== Solution to the intrusion at f3 ====

There are several solutions but the simplest is to respond with g3. Blue's only play to stop the immediate connection is f5. Then Red plays e4 yielding

<hex>R6 C10 Q1 1:BBBBBBRBBB 2:BBBBBRRBBB 3:BBBB___BBB 4:BBB_____BB 5:BB______BB 6:B_______BB MB Mf3 Mg3 Mf5 Me4</hex>

The e4 piece is connected to the bottom via a 3rd row template and e4 is connected to the other group of red pieces through e3 and f4. Thus, the connection is complete.

==== Solution to the intrusion at e5 ====

Red's best response is g4. This piece is connected to the bottom via a 3rd row template and hence Blue must block at g3. Red then plays e4 yielding

<hex>R6 C10 Q1 1:BBBBBBRBBB 2:BBBBBRRBBB 3:BBBB___BBB 4:BBB_____BB 5:BB______BB 6:B_______BB MB Me5 Mg4 Mg3 Me4</hex>

The e4 piece threatens to connect to the bottom in two non-overlapping ways, to d5 and to g4 (through f4). Hence the connection is unstoppable.

Unlike template Va, this template is not a rare occurrence and many hex players are not familiar with it.

== Advanced templates as ladder escapes ==

Templates IVc and Vb are valid escapes for row 2, row 3, and row 4 ladders. Template Va is not a valid ladder escape.

Exception: Template Vb is not valid for 3rd and 4th row ladders coming from the right side in the above diagram if the Horizontal player has a piece at h3. For the horizontal player to defeat the 3rd row ladder in this case, connecting to h3 must provide a strong threat that the vertical player needs to respond to.

Note: The unique way to win with template Vb and a 2nd row ladder is as follows. As soon as your head ladder piece intrudes on the template, your very next move must be to two-chain up to the 3rd row (this is true no matter which side of the template you are entering from). Then you break off the ladder (this piece will be connected to the edge via a smaller edge template).

== The minimax principle ==
(See also the page [[Minimax]])

Suppose you have multiple ways of establishing/maintaining a connection to an edge. A move that maintains as strong a connection as possible is not preferable to other connection moves because you only need to get some connection; you don't win extra points by connecting more strongly.

In fact it is generally better to play a move that maintains as ''weak'' a connection as possible; the reason being that such a piece may help you extend the connection towards the opposite edge. This principle is sometimes called "mini-maxing."

The idea behind the term is that you are playing a move that maintains a minimal connectivity in one direction while building up (i.e. maximizing) your strength in the other direction. I'll illustrate this with a couple of positions from my games. (Note that this principle applies equally well when establishing/maintaining a connection to ''a group of pieces''.)

=== Example 1 ===
<hex>R10 C10 Q1 Ma3 Mf5 Mc6</hex>

My opponent, Blue played the minimax move f4. This move maintains a minimal strength connection to the left while building up strength to the right; in fact the f4-f5 group is almost connected to the right edge via template Vb. I responded with my own minimax move d5 (d6 is the other minimax option) yielding the following position.

<hex>R10 C10 Q1 Va3 Hf5 Vc6 MH M4f4 Md5</hex>

d5 maintains a minimal strength connection to the bottom while maximizing my strength to the top. (d6 would have maintained a minimal strength connection to the top while maximizing my strength to the bottom.) A move that is even stronger towards the top, such as d4, would be a mistake. My opponent could then block at the bottom with c7, which is connected to the left edge via a 3rd row template and which threatens to link up with the central group. If I try to stop the connection to the central group with e6, my opponent responds with d5 yielding the following position.

<hex>R10 C10 Q1 Va3 Hf5 Vc6 Hf4 M5d4 Mc7 Me6 Md5</hex>

d5 is connected to the central group via a 2-chain and the combined threats c5 and d6 guarantee a connection to the left edge (a7 is defeated by c5, b5, b6, a6, b7, a8, b9). I would be in dire straits as the central pair f4-f5 is almost connected to the right edge.

Now back to the game; after my minimax move d5, I can safely meet c7 with e6. Yielding

<hex>R10 C10 Q1 Va3 Hf5 Vc6 Hf4 Vd5 MH M6c7 Me6</hex>

In fact, the c7, e6 sequence occurred in the actual game. I eventually won after a close hard fought battle.

=== Example 2 ===
<hex>R10 C10 Q1 Va3 Vc6 Vb8 Vc8 Vd8 Ve8 Vg6 Vg7 Vg8 Hf5 Hf7 Hf8 He9 Hd9 Hc9 Hb9 Hd7</hex>

In this position, I was the vertical player and was expecting f6 to which h4 would give me an excellent position (with best play, this position would in fact be winning though this is not obvious). Instead my opponent played the excellent minimax move f4. This move fights in both directions and is in fact a killer move. I can't block the f4-f5 pair from the right due to the forking ladder escape at h9. Thus, I must meekly submit to the forcing sequence f6, e7, e6, d5 yielding

<hex>R10 C10 Q1 Va3 Vc6 Vb8 Vc8 Vd8 Ve8 Vg6 Vg7 Vg8 Hf5 Hf7 Hf8 He9 Hd9 Hc9 Hb9 Hd7 MH Mf4 Mf6 Me7 Me6 Md5</hex>

The game is over. The f4-f5 pair is connected to d5 which in turn threatens to connect to left in two non-overlapping ways, c5 (a 3rd row template) and d6, hence the pair is connected to the left. If I try to block at the right, the best I can do is yield a ladder (e.g. h4, h3, j2, i3 and H has a second row ladder) and then the forking ladder escape at h9 wins the game.

=== Example 3 ===
In the next example, I am the horizontal player and it is my move.

<hex>C10 R10 Q1 Va3 Vb5 Vb8 Vc7 Vd6 Vd5 Vf4 Hc6 Hc5 Hd4 He4 He5 Hf5</hex>

Most hex players would probably connect to the left side with a7 (or b6 or b7). Despite its apparent necessity, this move actually loses (against best play). Instead I played the winning minimax move d3! By adding a second non-overlapping connection threat to the left, my group of pieces maintains a connection to the left. And despite its modest appearance, d3 also helps out on the right and in fact guarantees a winning connection from f5 to the right by defeating one of the main potential blocking plays.

<hex>C10 R10 Q1 Va3 Vb5 Vb8 Vc7 Vd6 Vd5 Vf4 Hc6 Hc5 Hd4 He4 He5 Hf5 MH Md3</hex>

E.g. suppose V tries to block the f5 piece from the right as follows.

<hex>C10 R10 Q1 Va3 Vb5 Vb8 Vc7 Vd6 Vd5 Vf4 Hc6 Hc5 Hd4 He4 He5 Hf5 Hd3 M2g5 Mg4 Mi3 Mi2</hex>

4 at h4 would also be possible. Now I have a forced winning ladder down row 2, completing the win.

<hex>C10 R10 Q1 Va3 Vb5 Vb8 Vc7 Vd6 Vd5 Vf4 Hc6 Hc5 Hd4 He4 He5 Hf5 Hd3 Vg5 Hg4 Vi3 Hi2 Mh3 Mh2 Mg3 Mg2 Mf3 Mf2 Me3 Me2</hex>

This line clearly shows the usefullness of d3. If I hadn't played d3 (playing a7 instead, for instance), the vertical player could continue d3, d2, a4! and eventually winning with best play (considerable deep analysis is needed to show this).

<hex>C10 R10 Q1 Va3 Vb5 Vb8 Vc7 Vd6 Vd5 Vf4 Hc6 Hc5 Hd4 He4 He5 Hf5 Ha7 Vg5 Hg4 Vi3 Hi2 Vh3 Hh2 Vg3 Hg2 Mf3 Mf2 Me3 Me2 Md3 Md2 Ma4</hex>

Minimax moves are not always "parallel" moves. The principle of maintaining a minimal amount of connectivity in one direction while maximizing your strength in the opposite direction is more general than that.

=== Example 4 ===
The final example from a game of mine illustrates non-parallel mini-max moves. I was the vertical player and opened with 1. a3 and my opponent responded with 1... e4 yielding the following position.

<hex>C10 R10 Q1 Va3 He4</hex>

I played the minimax move 2. f5 yielding

<hex>C10 R10 Q1 Va3 He4 Vf5</hex>

By connecting as far away as possible from the top, I increase my strength towards the bottom. (i.e. I am maintaining a minimal strength connection to the top while maximizing my strength towards the bottom). Before playing such a move, I have to verify that my opponent can't stop me from reaching the top. I could meet the attempted block with 2...g4 or 2...h2 by getting a third row ladder (2...g4 3.f4 g2 4.f3, etc. or 2...h2 3.g3 g2 4.f3, etc.), laddering down to e3, and then playing b4 (how to play a third row to a3 is described in a later section). I would be happy with such a line. My opponent however played the excellent e3. This move takes away the ladder, hence forcing me to reconnect to the top, while at the same time increasing his strength to the left.

<hex>C10 R10 Q1 Va3 He4 Vf5 He3</hex>

Here I played the minimax move g4. g4 has the potential to help block my opponent from going across the bottom of the board (e.g. Blue e7, Red f7, Blue f6, Red h5 and now g4 is helping out) or equivalently helps me to connect downwards on the right. I.e. g4 maintains a minimal strength connection towards the top while maximizing my strength towards the bottom. Note that a stronger move towards the top such as g3 does not have the same potential to help out towards the bottom. This potential may seem remote but in fact I would not have won the game without it! The rest of the game does not illustrate minimaxing but it is instructive nevertheless.

'''See [[Glenn_C._Rhoads_vs._unknown]]'''

== Special situations, tricks, etc. ==

=== Reconnecting edge template IIIa after an intrusion ===

<hex>R4 C10 Q1 Ve2 Hd3 Pf2 Se3</hex>

In this diagram, suppose you are Red and Blue has just played d3 intruding upon the third row template connecting your e2 to the bottom. Most hex players would reconnect with e3 without giving it much if any thought, yet there are three distinct ways to reconnect and there is often a reason for preferring one over the other.

A second way for Red to reconnect is to play f2 — the hex f2 and the empty hexes g2,e3,f3,g3,d4,e4,f4, and g4 form edge template IIIa; hence f2 has an unbreakable connection to the bottom and f2 is connected to e2.

The potential advantage of reconnecting with f2 over e3 is that it is easier to connect other pieces to the the group e2-f2 than to the group e2-e3 (e.g. h1 is a two-chain away from f2 but is not a two-chain away from either e2 nor e3). The extra connection possibilities can make a critical difference. For example, consider the following position with Red to move.

<hex>R9 C9 Q1 Vg2 Vf3 Ve4 Vd5 Vd6 Vh3 Vh4 Vf7 Hi4 Hc6 Hb8 Hc8 He6 Hf6 Hg6</hex>

Red can win by laddering 1. d7 d8 2. e7. Suppose instead Red plays 1.h5 intruding on the g6 edge template. If Blue reconnects with h6, then Red would have nothing else to do except play the winning line. So Blue reconnects with g7 making the win tougher. (Red could still win by d7, d8, e7, e9, f8, f9, h8! — a forking ladder escape which decides the issue).

Now suppose that Red again intrudes on the edge template with 2. h6. Now the game continues 2...g8 (again reconnecting by playing parallel to the edge) 3. h7 (persistent) h8, 4. d7 d8, 5. e7 e9! and now Blue has an unbreakable winning chain at the bottom. By reconnecting with the parallel moves instead of the direct reconnection, Blue's group had a new way to connect to the left and this extra possibility turned a defeat into a win.

So is it always better to reconnect with the parallel move? No!! Sometimes the parallel reconnection can lose the game while the simple direct connection wins! The potential weakness of the parallel reconnection is that your opponent might then be able to use a double threat to defeat the edge connection. For example, consider the following position with Red to move.

<hex>R9 C9 Q1 Vh3 Vg2 Vf3 Ve4 Vd5 Vd6 Hc6 Hb8 Hc8 He6 Hg5 Hi3</hex>

With best play Blue wins, so Red tries 1. h4. If Blue responds with the direct reconnection h5, then the win is assured and Red may as well resign. Suppose instead that Blue reconnects with 1... g6. Then Red can respond with 2.h7! — this forking ladder escape is a killer. Red now has two disjoint winning threats, laddering from d7 to h7 and play i5 (This double two-chain cutoff threat occurs in situations besides cutting off third row edge templates. It is well worth being familiar with this idea.). Blue cannot stop them both so Red wins.

But this doesn't exhaust the reconnection possibilities. There is a third way to reconnect; a way that most players don't seem to discover.

<hex>R4 C10 Q1 Ve2 Hd3</hex>

Again starting at the initial position in this section, Red's e2 piece is connected to the bottom via edge template IIIa and Blue intrudes upon it with d3. In addition to e3 and f2, Red can reconnect with the surprising f1!

<hex>R4 C10 Q1 Ve2 Hd3 Vf1</hex>

Red is threatening to connect e2-f1 to the bottom with e3. If Blue tries to block this with e3, then Red can reconnect by playing g2. g2 is connected to the bottom via template IIIa (Blue's e9 piece is just outside of this template) and h3 connects to f1 via a two-chain.

But what if Blue blocks with e4 instead of e3? (note the e4 is within the g2 piece's edge template). Then Red can still reconnect by playing as follows. 1. e3 d4 (forced) 2. g3 f3 (forced again) 3.g2 ending up with the following position.

<hex>R4 C10 Q1 Ve2 Hd3 Vf1 MH Me4 Me3 Md4 Mg3 Mf3 Mg2</hex>

How does this method compare to the previous two? Compared to the parallel reconnection, it is quite a bit more susceptible to forking plays and plays that encroach upon the increased area that is needed to reconnect, but by playing away from the edge, you have even more potential to connect the edge group towards the opposite edge. Sometimes the extra connection possibilities generated by playing away from the edge is exactly what is needed.

For example consider the beautiful solution to the following position (I wish I could take the credit for its discovery but the original over the board play was found by Tom239 on _Playsite_ (he was at the orange level at the time!). The position below is a slight modification of one constructed by Kevin O'Gorman, the maintainer of the Ohex data base).

<hex>R10 C10 Q1 Va2 Va3 Va4 Va5 Va6 Va7 Va8 Va9 Ha10 Hb2 Hb3 Hb4 Hb5 Hb6 Hb7 Hb8 Vc6 Hc7 Vd5 Hd6 Vd7 Ve4 He5 Vf3 Hf4 Vg2 Hg3 Vh1 Hh2 Hi2</hex>

It is Red's move. To win, Red must connect his a9 piece to bottom. To do this, Red must make some ladder escape that additionally must somehow use the d7 piece to threaten another way to connect to the ladder. This looks impossible but yet there is a way. Red can win by starting with 1.b9 b10 2.c9 c10 3.f8!!

<hex>R10 C10 Q1 Va2 Va3 Va4 Va5 Va6 Va7 Va8 Va9 Ha10 Hb2 Hb3 Hb4 Hb5 Hb6 Hb7 Hb8 Vc6 Hc7 Vd5 Hd6 Vd7 Ve4 He5 Vf3 Hf4 Vg2 Hg3 Vh1 Hh2 Hi2 Mb9 Mb10 Mc9 Mc10 Mf8</hex>

This brilliant move is the only way to win. 3.g7 is defeated only by 3...d9 and 3.d9 d10 4.g7 is defeated only by 4...f8 (it takes a ''lot'' of analysis to demonstrate these claims). Blue's only good attempt is to intrude on the edge template with 3... e9. But Red can defeat this by reconnecting with 4.g7! (this is what Red had in mind when playing 3.f8!!)

<hex>R10 C10 Q1 Va2 Va3 Va4 Va5 Va6 Va7 Va8 Va9 Ha10 Hb2 Hb3 Hb4 Hb5 Hb6 Hb7 Hb8 Vc6 Hc7 Vd5 Hd6 Vd7 Ve4 He5 Vf3 Hf4 Vg2 Hg3 Vh1 Hh2 Hi2 Vb9 Hb10 Vc9 Hc10 Vf8 MH Me9 Mg7</hex>

Now f8-g7 has an unbreakable connection to the bottom and Red threatens two distinct ways of connecting this group back to the group containing c9; Red threatens f6, double two-chaining between d7 and g7, and Red threatens e8 two-chaining to c9. Blue's only possible defense is the forcing move 4...d8. This interferes with the immediate connection threat between c9 and f8, and it prepares to meet the f6 threat with c8 cutting off d7 from c9. But this move is still not sufficient because after 4...d8, Red can win with 5.d9 d10 (forced) 6.e8.

In practice, you can think of the parallel reconnection as your "standard" response (more often than not, it is the correct choice). But if the potential threat to cut off the parallel play from the edge is serious, then go with the direct reconnection. The "away" reconnection entails a substantially increased risk of being cut off from the edge but if you can see that it will be safe or if you need the stronger connection possibilities towards the opposite edge, then go with the "away" connection.

=== Third row ladder to a3 and its symmetric analogues ===
(See also the page [[a3 escape trick]])

The following position is from one of my games.

<hex>R10 C10 Q1 Hg2 Vi2 He3 Hg3 Hb4 Hc4 He4 Vf4 Vg4 Vb5 Vc5 Ve6 Vf6 Hh10</hex>

I am Blue and it is my move. Red's e6-f6(-f4-g4) group is connected to bottom via template Vb. Red's i2 piece is connected to the top via edge template II. In order to stop these two groups from connecting to each and completing a win, I must start laddering down column H. So I ladder down to h6 forcing Red to follow down column I to i6 yielding the following position.

<hex>R10 C10 Q1 Hg2 Vi2 He3 Hg3 Hb4 Hc4 He4 Vf4 Vg4 Vb5 Vc5 Ve6 Vf6 Hh10 Hh3 Vi3 Hh4 Vi4 Hh5 Vi5 Hh6 Vi6</hex>

My h10 piece is ''not'' a valid ladder escape. If I ladder all the way down to h10, then Red follows down to i8 and his response to h9 is not i9 but j9!

<hex>R10 C10 Q1 Hg2 Vi2 He3 Hg3 Hb4 Hc4 He4 Vf4 Vg4 Vb5 Vc5 Ve6 Vf6 Hh10 Hh3 Vi3 Hh4 Vi4 Hh5 Vi5 Hh6 Vi6 Hh7 Vi7 Hh8 Vi8 Hh9 Vj9</hex>

Red has a winning chain on the right side. You might think I could win by instead laddering down one more hex, and then double two-chain to the h10 piece yielding the following position.

<hex>R10 C10 Q1 Hg2 Vi2 He3 Hg3 Hb4 Hc4 He4 Vf4 Vg4 Vb5 Vc5 Ve6 Vf6 Hh10 Hh3 Vi3 Hh4 Vi4 Hh5 Vi5 Hh6 Vi6 Hh7 Vi7 Hg9</hex>

This may appear to settle the matter in my favor but in actuality, Red has a winning position! Red can win by 1. h8 (h9 also works but h8 is slightly more deceptive). If I respond by saving the link, i.e. by 1...g8, then Red wins by playing 2.h9 g10 (forced) 3. j9.

<hex>R10 C10 Q1 Hg2 Vi2 He3 Hg3 Hb4 Hc4 He4 Vf4 Vg4 Vb5 Vc5 Ve6 Vf6 Hh10 Hh3 Vi3 Hh4 Vi4 Hh5 Vi5 Hh6 Vi6 Hh7 Vi7 Hg9 Vh8 Hg8 Vh9 Hg10 Vj9</hex>

Red has an unbreakable winning chain down the right. Instead it is better for me to respond to Red's 1.h8 with 1...h9. My g9-h9-h10 group is now solidly connected to the right but Red can continue 2.g8 and I cannot stop g8 from connecting to the bottom because of the help provided by Red's e6-f6 pieces (work it out!)

In the initial position I cannot afford to ladder down any farther than g6. If I ladder down one more hex, I lose against best play no matter what. If there are no other pieces in the area, as is the case here, then the strongest way to play it is to ladder down one hex short of the hex that could double two-chain to the "almost-escape" piece, and then two chain up from the almost-escape piece which in our present case yields the following position.

<hex>R10 C10 Q1 Hg2 Vi2 He3 Hg3 Hb4 Hc4 He4 Vf4 Vg4 Vb5 Vc5 Ve6 Vf6 Hh10 Hh3 Vi3 Hh4 Vi4 Hh5 Vi5 Hh6 Vi6 Hg9</hex>

Red has three tries to stop the connection between the h6 and g9 pieces.

* g8 is defeated by continuing the ladder down (try it!).
* h7 and h8 are best met by f8 (double two-chaining in the same direction).
* Meeting the play h8 with g8 (connecting up to h6) doesn't work for the same reason that laddering down to h7 and double two-chaining to h10 doesn't work (work it out and you should see what I mean).

Also, note that Red's attempt h9 is of no consequence. Against h9 you should save the link with g10 and then again meet either h7 or h8 with f8.

In the actual game my opponent played h7 and I responded with f8. f8 threatens to connect with with h6 through g7. So my opponent played g7 to which I responded with f7. Again this threatens a winning connection from f7 to h6 through g6. So my opponent played g6 and I responded with c9 with a winning position.

<hex>R10 C10 Q1 Hg2 Vi2 He3 Hg3 Hb4 Hc4 He4 Vf4 Vg4 Vb5 Vc5 Ve6 Vf6 Hh10 Hh3 Vi3 Hh4 Vi4 Hh5 Vi5 Hh6 Vi6 Hg9 Vh7 Hf8 Vg7 Hf7 Vg6 Hc9</hex>

Further play no longer concerns the topic under discussion but the remaining moves were d9, e7, d7, d8, b9, c8, a8, b8, a9, b7, a7, d6, resigns. My opponent doesn't need to see g8, f9, h9, g10, j9, i8

The key play of two-chaining up from the escape piece is also useful in another common type of third row ladder position. For example, consider the following position with the vertical player to move.

<hex>R10 C10 Q1 He2 Vi2 Va3 Hf3 Hc4 Vd4 He4 Hf4 Vh4 Vi4 Vc5 Hd5 Hf5 Hh5 Vi5 Vc6 Hf6 Hg6 Hi6 Vc7 Hd7 He7 Vf7 Hg7 Vh7 Vc8 Vd8 Ve8 Hg8 Hh8 Hb9 Vc9</hex>

Red has a chain running from the bottom at c9 up to d4. The only way Red can win is to connect this group to the top. Red can ladder d3, c3, b3 but as we saw earlier, the a3 piece is not a valid ladder escape. But Red can still win by two-chaining from a3 to b4.

<hex>R10 C10 Q1 He2 Vi2 Va3 Hf3 Hc4 Vd4 He4 Hf4 Vh4 Vi4 Vc5 Hd5 Hf5 Hh5 Vi5 Vc6 Hf6 Hg6 Hi6 Vc7 Hd7 He7 Vf7 Hg7 Vh7 Vc8 Vd8 Ve8 Hg8 Hh8 Hb9 Vc9 Vb4</hex>

This threatens a winning connection to c5 through b5. If Blue blocks this with b5, then Red plays the ladder because now the pair a3-b4 are a valid ladder escape. If instead Blue blocks off the ladder with say c3, then Red wins with the line b5, b3, a4 (forced), b1, d2!

<hex>R10 C10 Q1 He2 Vi2 Va3 Hf3 Hc4 Vd4 He4 Hf4 Vh4 Vi4 Vc5 Hd5 Hf5 Hh5 Vi5 Vc6 Hf6 Hg6 Hi6 Vc7 Hd7 He7 Vf7 Hg7 Vh7 Vc8 Vd8 Ve8 Hg8 Hh8 Hb9 Vc9 Vb4 Hc3 Vb5 Hb3 Va4 Hb1 Vd2</hex>

d2 is a forking ladder escape; it threatens d3 and it provides an escape to the 2nd row ladder starting with b2. Blue cannot stop both winning threats with a single move, thus Red wins.

a3/j8 is a common opening move. If you frequently play it or play against somebody who does, then you will run into these 3rd row ladder situations and hence, it will be beneficial to learn how to play them.

=== The parallel ladder trick ===
(See also the page [[Parallel ladder]])

Consider the following position with Red to play.

<hex>R10 C10 Q1 Hc1 Vd2 Vd3 He3 Vf3 Vd4 Ve4 Hf4 Hg4 Ve5 Vc6 Vd6 He6 Hi6 Hc7 Vd7 Ha8 Hb8 Vc8 Hd8 Hb10</hex>

All of Red's pieces form a connected group. This group is connected to the top. At the bottom, Red has a second row ladder with no possible escape on the left. The potential escapes on the right are inadequate. For example, suppose Red ladders to f9. Then tries to escape with 5.h9 g9 6.h8 g8 7.h7 f7.

<hex>R10 C10 Q1 Hc1 Vd2 Vd3 He3 Vf3 Vd4 Ve4 Hf4 Hg4 Ve5 Vc6 Vd6 He6 Hi6 Hc7 Vd7 Ha8 Hb8 Vc8 Hd8 Hb10 Vc9 Hc10 Vd9 Hd10 Ve9 He10 Vf9 Hf10 Vh9 Hg9 Vh8 Hg8 Vh7 Hf7</hex>

Now Red's only reasonable try is 8.g7 f8. Now 9.g6 loses to 9...f5 and 9.h5 loses to the forcing sequence 9...g6 10.h6 h4 11.g5 f5. All the other escape attempts likewise fail. Is Red done for?

No! Red can create a sufficient escape by making use of a parallel ladder. In the original position Red plays 1.e7. How can Blue stop Red from connecting to the bottom? d9 lets Red two-chain from e7 to f8 connecting to the bottom; e9 and e10 allow d9 which is connected to the bottom and threatens to connect to Red's big group through c9 and e8; d10 loses to e8, f9 (forced), c10; hence, Blue is forced to play the parallel ladder move 1...e8. It is simplest for Red to repeat this and ladder to f7 forcing the 2...f8 response.

<hex>R10 C10 Q1 Hc1 Vd2 Vd3 He3 Vf3 Vd4 Ve4 Hf4 Hg4 Ve5 Vc6 Vd6 He6 Hi6 Hc7 Vd7 Ha8 Hb8 Vc8 Hd8 Hb10 Ve7 He8 Vf7 Hf8</hex>

Now Red now goes back to the second row ladder and tries to escape. What have we gained by preceding this with the parallel ladder moves? When trying to escape, the threat to connect to d7-e7-f7 is stronger than the previous weak threat to connect to d7. This extra threat will let us push our escape chain farther up the board and in this case, just far enough to win the game.

Red's winning sequence is long but rather simple because every one of Blue's replies is forced. As before, Red ladders to f9 and escapes with 7. h9. Play continues 7...g9 8.h8 g8 9.h7 g7 10.h6 g6 11.h5. Red is threatening to play g5 with the double winning threats f5 and f6. But if Blue blocks this, say with 11...g5, then Red continues 12.i3 i2 13.h3 and 14.g3 completes the win.

I have managed to pull this trick off from one row farther back; i.e. with ladders on row 3 and 5 but this occurs far less frequently and you have to examine some additional defensive possibilities. Consider the following position.

<hex>R10 C10 Q1 Vd5 He5 Vd6 Ve6 Hb7 Vc7 Hd7 Hb9</hex>

Red has just played e6 trying the parallel ladder trick. With the closer ladder on row 2, we saw that Blue was forced to respond with the parallel ladder play e7. But here Blue has two additional possibilities e8 and c9 (the only other possibility where Red doesn't have a way to force his group to connect to the bottom is c10. But Red can respond with f8 and now Blue has nothing better than e7, g6).

e8 yields a second row ladder after d8, e7, c8, c10, d9. The play c9 also leads to a second row ladder after the likely f7, f8, e8 (d9 is met by e7) d10. In the latter case, Red could again try the parallel ladder trick by playing g7. Of course, the existence of other pieces in the area can change the possibilities.

For whom who understand The parallel ladder trick !
This trick is useful only for ladder 2nd and 4th!

Consider the following position with Red to play and win. Red's has winning position even wiht a blue stones in h5 from the beginning.
<hex>R10 C10 Q1
Hc1
Vd2
Vd3 He3 Vf3
Vd4 Ve4 Hf4 Hg4
Ve5 Hh5
Vc6 Vd6 He6 Hi6
Hc7 Vd7
Ha8 Hb8 Vc8 Hd8

Hb10 </hex>

[[parallel ladder#A parallel ladder trick puzzle|The solution is 1.f8]]

== See also ==
* [[Basic (strategy guide)]]
* [[Intermediate (strategy guide)]]

[[category:Advanced Strategy]]

A3 opening

2008-11-07T00:16:55Z

Turing: /* External link */

{{wrongtitle|title=a3 opening}}

== Common answers ==

<hex>R13 C13 Q1 N:on
Ra3 Pg7</hex>

Most players answer here g7 (+ hexa) because the center is said to be important. There other possibilities though: i10 and j11.

These two moves are good too because of [[template Va]] (i10) and [[template IVa]] (j11), hence Blue is connected to right edge and makes it harder for Red to link to Bottom edge.

=== Second move: i10 ===
<hex>R13 C13 Q1 N:on
Ra3 Bi10
Sm4
Sl5 Sm5
Sk6 Sl6 Sm6
Sk7 Sl7 Sm7
Sj8 Sk8 Sl8 Sm8
Si9 Sj9 Sk9 Sl9 Sm9
Sj10 Pk10 Sl10 Sm10
Si11 Sj11 Sk11 Sl11 Sm11
Sj12 Sk12 Sl12 Sm12
Sk13 Sl13 Sm13
</hex>

k10 is then a frequent move for Red, because it intrudes Blue template and creates one template at the same time. Moreover it may prove useful later as a [[ladder escape]].
=== Second move: j11 ===
<hex>R13 C13 Q1 N:on
Ra3 Bj11
Sm7
Sl8 Sm8
Sk9 Sl9 Sm9
Sk10 Sl10 Sm10
Sk11 Sl11 Sm11
Sj12 Sk12 Sl12 Sm12
Sk13 Sl13 Sm13
</hex>

== See also ==

[[a3 escape trick]]

==External link==

There used to be a very good website by [http://www.f.kth.se/~rydh/Hex/openings.html J. Rydh on openings], but it seems to have disappeared. It can be seen through the [http://web.archive.org/web/20070710205655/http://www.f.kth.se/~rydh/Hex/openings.html Internet Archive], however.

{{stub}}
[[category:opening]]

Main Page

2008-03-27T14:23:19Z

Turing: fixed typo

[[Hex]] is a [[connection game]] invented in the 1940s and popularised in recent years on game sites on the web. With simple [[Rules_(Hex)|rules]] and much inherent [[strategy]], it makes for a game which an increasing audience finds interesting and stimulating.

[[Image:Hexposition02.jpg|thumb|250px|A Hex game]]
Depending on your interest, some good pages to start exploring this site are:

* a description of the [[rules]] of Hex
* some [[History of Hex|historical]] background
* a strategy guide consisting of 3 levels: [[Basic (strategy guide)|basic]], [[Intermediate (strategy guide)|intermediate]], and [[Advanced (strategy guide)|advanced]]
* the [[strategy]] page has links to specific strategy topics
* Pick up an article in the list of [[Special:Allpages|all articles]], or select a [[Special:Categories|category]] you wish to get informed about
* information on [[computer Hex]]
* information on [[online playing]]
* ideas for [[physical hex sets]]
* information on [[Tournaments]]
* some [[variants using the same equipment]]
* [[Commented games]] to learn from
* Tips for [[Typesetting Hex]]

History of Hex

2008-03-01T18:24:06Z

Turing: /* Recent History */ word choice

== Early History ==
The game was first invented by the Danish mathematician [[Piet Hein]]. The first article describing the game, which Piet Hein called Polygon, appeared in the Danish newspaper [http://en.wikipedia.org/wiki/Politiken Politiken] on 26 December [http://en.wikipedia.org/wiki/1942 1942] but the game was introduced to an association of math students at [http://mydatapages.com/university_of_copenhagen.html The University of Copenhagen] called [[The Parenthesis]] during a lecture on conditions for good games.

In [http://en.wikipedia.org/wiki/1948 1948] the game was discovered independently by the mathematican [[John Nash]]. Nash's fellow players at first called the game Nash. According to [[Martin Gardner]], some of the [http://en.wikipedia.org/wiki/Princeton_University Princeton University] students also referred to the game as John, because it was often played on the hexagonal tiles of bathroom floors. However, this story is, according to [[Jack van Rijswijck]], unfortunately apocryphal. In [http://en.wikipedia.org/wiki/1952 1952] [[Parker Brothers]] marketed a version. They called their version "Hex" and the name stuck.

== Recent History ==
The first book devoted to Hex and only Hex is available since 2000. [[Hex Strategy Making the Right Connections]], by [[Cameron Browne]].

As of 2008, Poland dominates the game of Hex.

''Here we could add something about the development of the different online communities.''

== Hex and Go ==
Hex has many similarities to the game Go.
One similarity is that both have a wiki dedicated to them, and each wiki has a page pointing to the opposite wiki: [[Go]] and [http://senseis.xmp.net/?Hex Sensei's library: Hex].

[http://senseis.xmp.net/?OtherGamesConsideredUnprogrammable Sensei's library: other games considered unprogrammable] lists other games similar to Go and Hex.

== See also ==
[[History of computer Hex]]

[[Tournaments]]

==References==
* Browne, Cameron (2000). Hex Strategy Making the Right Connection. A K Peters, Ltd. ISBN 1-56881-117-9.

User talk:Halladba

2008-02-11T14:25:47Z

Turing:

Hi Halladba, I see you asked Gregorio about the hex tournament. Here it is the link:

http://spainhex.blogspot.com/

you can find participants and classifications. Gregorio will add more sometime :)

I really liked your page on Y corner templates. — [[User:Turing|turing]]

Variants using the same equipment

2008-01-29T07:29:10Z

Turing: moved atoll here

''Adapted with permission from Cameron Browne's PBeM Help files.''

== Chameleon ==

Chameleon was discovered by Randy Cox in early November 2003, then independently rediscovered mid November 2003 by Bill Taylor after an idea by Cameron Browne. Interestingly, there is a good reason for the proximity of these independent discoveries, as both were motivated by the upcoming deadline for the 2003 Shared Pieces game design competition.

The game was originally called Goofy Hex then Funky Hex by Randy, but was first made public under the name Chameleon and that has stuck. This name refers to the fact that players tend to change colours based on their environment; the fact that Bill's eyes pop out when he sees a good move has nothing to do with it.

=== Rules ===

Two players, Vert and Horz, take turns placing either a red piece or a blue piece on the board.

Vert wins by completing either a chain of red pieces or a chain of blue pieces between the top and bottom board edges. Horz wins by completing either a chain of red pieces or a chain of blue pieces between the left and right board edges.

If a move results in a connecting chain for both players, then the mover wins.

=== Examples ===

A win by Horz:

<hex>R7 C7 Q1 Vc5 Hd4 Hc4 Hb5 Ha5 Hd5 Ve2 Hc2 He5 Hf4 Hg4 Vd7 He7 Vf7</hex>

A win by Vert:

<hex>R7 C7 Q1 Vc5 Hd4 Hc4 Hb5 Ha5 Hd5 Hc3 Ve2 Hc2 He5 Hf4 He6 Vd1 Hc1 Vd7 He7 Vf7</hex>

A win by the last mover:

<hex>R7 C7 Q1 Vc5 Hd4 Hc4 Hb5 Hb6 Va6 Ha7 Hd5 Hg1 Ve2 Hc2 He5 He3 Hf2 Vd7 He7 Vf7</hex>

=== Notes ===

Playing Chameleon is a constant tightrope act. In most connection games, each player can concentrate fully on pushing their connection as hard as possible. However in Chameleon players must keep their connections strong only in their direction or risk having them stolen. Players must consider the implications of each move very carefully.

Chameleon has a similar feel to Jade but with clearer goals.

One of the most interesting aspects of Chameleon is that it inherently solves the first move advantage problem which plagues most connection games. While opening in the centre is a winning move in Hex, it is a death sentence in Chameleon. The first player's best opening move is well away from the centre and any opponent's edge.

Chameleon should be played on larger boards. Games smaller than 10x10 tend to degenerate into a race after only a few moves.

==Bidding Hex==

By James Hutchings.

Both players start with 100 'gold'.

At the start of each turn, both players gain 1 gold for each piece they have on the board.

Initially, a hex is chosen randomly.

Both players choose an amount to bid for this hex. Players don't see each other's bids until both players have bid. The minimum bid is 0, the maximum is the amount of gold they have at the time.

If the two bids are the same, both players lose gold equal to the amount they bid, and the hex is left empty.

If there is a higher bid, the player who bids higher loses an amount of gold equal to their bid, and places one of their pieces on the hex.

If one player bid at least twice as much as the other, the higher bidder may choose the hex which is subject to bidding next turn, after players receive their gold. If neither player bid twice as much as the other, the next hex is chosen randomly.

== Atoll ==

A generalized form of Hex created by Mark Steere. See [http://www.marksteeregames.com/Atoll_rules.pdf the rule sheet] for more information.

[[category : Other games]]

Variants using the same equipment

2008-01-29T07:24:40Z

Turing: removed jade -- feel free to add it again with information

Main Page

2008-01-29T07:23:53Z

Turing: moved the info on Atoll to separate page

[[Hex]] is a [[connection game]] invented in the 1940s and popularised in recent years on game sites on the web. With simple [[Rules_(Hex)|rules]] and much inherent [[strategy]], it makes for a game which an increasing audience finds interesting and stimulating.

[[Image:Hexposition02.jpg|thumb|250px|A Hex game]]
Depending on your interest, some good pages to start exploring this site are:

* a description of the [[rules]] of Hex
* some [[History of Hex|historic]] background
* a strategy guide consisting of 3 levels: [[Basic (strategy guide)|basic]], [[Intermediate (strategy guide)|intermediate]], and [[Advanced (strategy guide)|advanced]]
* the [[strategy]] page has links to specific strategy topics
* a list of [[Special:Allpages|all articles]]
* information on [[computer Hex]]
* information on [[online playing]]
* ideas for [[physical hex sets]]
* information on [[Tournaments]]
* some [[variants using the same equipment]]
* [[Commented games]] to learn from
* Tips for [[Typesetting Hex]]

Multiple threats

2007-09-30T11:51:04Z

Turing: short explanation

Threatening to do two different attacks with one move. Often the opponent will only be able to defend against one of the attacks, or defend only partially against both.

{{stub}}

Connection game

2007-08-12T13:10:03Z

Turing: reverted spam

A '''connection game''' is a [[game]] where the goal is to use the [[Piece (general)|piece]]s to create a connection between some parts of the [[Board (general)|board]]. The first connection game was [[Hex]], which was invented in [http://en.wikipedia.org/wiki/1942 1942], after which several other connection games have been created.

== Timeline ==

;[[Hex]] ([[Piet Hein]] [http://en.wikipedia.org/wiki/1942 1942] and [[John Nash]] [http://en.wikipedia.org/wiki/1948 1948])
:The original connection game. Played on a [[rhombic hex grid]].
;[[Y]] ([[Craige Schenstead]] and [[Charles Titus]], [http://en.wikipedia.org/wiki/1950s 1950s])
:Played on a [[triangluar grid of hexagons]]
;[[Twixt]] ([[Alex Randolph]], [http://en.wikipedia.org/wiki/1960s 1960s])
:Played on a [[square grid]] of holes into which the players place [[peg]]s. The pegs can be connected via [[Bridge (general)|bridges]].
;[[Havannah]] ([[Christian Freeling]], [http://en.wikipedia.org/wiki/1980 1980])
;[http://www.di.fc.ul.pt/~jpn/gv/quax.htm Quax] (Bill Taylor?, 2000?)
:Played on a square grid with the possibility of diagonal connections.
;[[Onyx]] ([[Larry Back]], [http://en.wikipedia.org/wiki/2000 2000])
:Played on an original grid consisting of both triangles and squares. It is the first connection game with a [[capturing rule]].
;[[Gonnect]] ([[João Pedro Neto]], [http://en.wikipedia.org/wiki/2000 2000])
:This game is simply [[Go]], but with a different goal, namely to create a connection between any two opposite sides.
;[[Unlur]] ([[Jorge Gómez Arrausi]], [http://en.wikipedia.org/wiki/2001 2001])
:Played on a [[hexagonal hex grid]]. Unique in the way that the players have [[different objectives]].

== References ==

;[[Cameron Browne]], [http://www.amazon.com/Connection-Games-Variations-Cameron-Browne/dp/1568812248/ref=pd_bbs_sr_1/104-1532904-9846317?ie=UTF8&s=books&qid=1177663469&sr=8-1 "Connection Games: Variations on a Theme"]

Intermediate (strategy guide)

2007-08-12T13:09:24Z

Turing: reverted spam

''Adapted with permission from Glenn C. Rhoads strategy guide.''

== Loose connections ==
''(See also the article [[Loose connection]])''

[[Adjacent move]]s provide a guaranteed connection but cover little ground. [[Bridge|Two-bridges]] cover twice the distance and are almost as strong. The next best connection when even more distance is required is called the '''loose connection''' — a [[Hex (board element)|hex]] that is a two-bridge plus an adjacent step away.

<hex>R4 C5 Vb2 Sc2 Sc3 Vd3</hex>

The [[piece]]s of the loose connection [[threat]]en to connect via a two-bridge plus an adjacent step [[Multiple threats|in two different ways]] — by playing at either of the marked hexes. Also, the two marked hexes are the only ones that are in the [[overlap]] of the two [[Template|connection patterns]]. Thus, to break a loose connection, one must play in one of the marked hexes.

Another connection pattern that is useful to be aware of is two pieces in the same row or column that are three hexes apart.

<hex>R5 C6 Sd2 Vb3 Pc3 Pd3 Ve3 Sc4</hex>

The pieces threaten to connect via 2 two-bridge steps in two different ways, namely by playing at piece at one of the hexes marked with a *. There are two hexes that are in the overlap between these two connection threats and a move played in either of them breaks the immediate connection (these two hexes are marked with a +). This connection pattern is not as strong as the loose connection.

== The useless triangle ==
''(See also the article [[Useless triangle]])''

When a piece's neighboring hexes are [[occupied hex|filled]] by the [[opponent]] such that that piece has only two empty neighboring hexes that are also [[adjacent]] to each other, then the piece is said to lie in a "'''useless triangle'''."

<hex>R7 C7 Q1 Vc5 Hd4 Hc4 Hb5 Hd5 Vd7 He7 Vf7</hex>

In the above diagram, the red piece at c5 and the [[empty hex]]es b6 and c6 form a useless triangle. The blue piece at e7 and the empty hexes e6 and f6 also form a useless triangle. The important point is that unless the piece in a useless triangle is in that player's [[First row|border row]], the piece has effectively been removed from the game — that is, it cannot have any effect on the rest of the game regardless of the rest of the position.

== Minimal edge templates ==
(See also the page [[Edge templates]])

An '''edge template''' is a pattern of empty hexes that will allow a piece to be [[Connection|connected]] to the [[edge]] even if the opponent has the next move. Just as the two-bridge is a useful connection pattern to know, so are minimal edge templates — the ones of the smallest size. (The templates are numbered according to row of the [[connecting piece]]).

=== [[Template I]] ===

Trivially, a piece on an edge row is connected to the edge.

<hex>R3 C3 Vb3</hex>

=== [[Template II]] ===

<hex>R3 C3 Vb2 Sa3 Sb3</hex>

If the opponent plays inside the template, [[Red (player)|Red]] plays the other move in the template restoring the connection to the edge.

For templates farther away, the general strategy to apply when the opponent intrudes on the template is to make a move in the template that reduces to a smaller and closer template.

=== [[Template IIIa]] ===
''(Also called [[Ziggurat]])''

<hex>R4 C4 Q1 Vc2 Sb3 Sd3</hex>

If the opponent intrudes on the template, then Red plays at one of the two marked points achieving [[template II]]. Since the b3 template and the two-chain/d3 template combination don't overlap, the opponent cannot stop both. (This template exists in a mirror image form with the red piece at d2).

=== [[Template IIIb]] ===

<hex>R4 C5 Vd2 Sb3 Se3 Pc4</hex>

The [[Hex (board element)|hex]] marked with an '+' can be occupied by the opponent! If the opponent intrudes on the template, then Red two-chains to either of the marked hexes and in either case forms [[template II]]. Since the two-chain/template II combinations don't [[overlap]] with each other, the opponent cannot stop both.

=== [[Template IVa]] ===

<hex>R5 C7 Q1 Ve2 Sd3 Se3 Sf3 PD5</hex>

If the opponent intrudes on the template, Red plays to one of hexes marked with '*' forming [[template IIIa]]. The one exception is if the opponent plays at d5, then Red plays to e3 and connects via [[template IIIb]]. (This template has a mirror image form with the red piece at f2.)

=== [[Template IVb]] ===

<hex>R5 C8 Vf2 Sd3 Sg3 Pe4</hex>

The hex marked with a '+' can be occupied by the opponent! If the opponent intrudes on the template, Red two-chains to one of the marked hexes forming [[template IIIa]].

== Forming ladders ==
''(See also the article [[Ladder]])''

A '''ladder''' occurs when one player tries to force a connection to an edge but is kept a constant distance away by the opponent, resulting in a sequence of moves parallel to the edge. The following is an example with Red to play.

<hex>R9 C9 Q1 Ve3 Vd4 Vd5 Vc6 Vc7 Hb8 Hb9 Hd7 He6 Hf6</hex>

Suppose Red plays c8 which forces c9 in reply. Now Red can play the following forcing sequence. d8, d9, e8, e9, f8, f9, etc. A sequence of such plays parallel to an edge is called a ladder. Note that the [[Blue (player)|Blue]]'s responses are forced. If Red blindly continues the ladder all the way to end, then he will simply lose (Blue will get pieces in row 9 from b9 through i9). There is no good reason to ever force a ladder all the way through to end, it only helps your opponent.

=== Ladder escapes ===
''(See also the article [[Ladder escape]])''

Consider the same position as before but suppose Red has an additional piece at h8.

<hex>R9 C9 Q1 Ve3 Vd4 Vd5 Vc6 Vc7 Hb8 Hb9 Hd7 He6 Hf6 Vh8</hex>

This additional piece forms a '''ladder escape''' which allows Red to jump a move ahead of the ladder and win the game. The piece at h2 is called the "[[escape piece]]." Red should now play along the ladder as before, forcing Blue's response at each step. After c8, c9, d8, d9, e8, e9, f8, f9, g8 Red is connected to the bottom.

<hex>R9 C9 Q1 Ve3 Vd4 Vd5 Vc6 Vc7 Hb8 Hb9 Hd7 He6 Hf6 Vh8 Vc8 Hc9 Vd8 Hd9 Ve8 He9 Vf8 Hf9 Vg8</hex>

In general, for a ladder escape to be successful, it should be safely connected to the edge and not interfere with the ladder's [[Projected ladder path|projected path]].

=== Ladder escape templates ===
''(See also the article [[Ladder escape templates]])

* [[Second row|Row-2]] ladders: All of the [[edge template]]s described earlier are valid.
* [[Third row|Row-3]] ladders: Templates [[Template II|II]], [[Template IIIa|IIIa]], and [[Template IVa|IVa]] are valid.
* [[Fourth row|Row-4]] ladders: [[Template IIIa]] is valid. Also [[template IVa]] is valid if you can double two-bridge to the [[escape piece]] as follows.

<hex>R6 C9 Vb3 Vc3 Vd3 Sf2 Vg3 Ha4 Hb4 Hc4 Hd4</hex>

Red can jump ahead to the escape template by playing at the marked hex.

=== The ladder escape fork ===
''(See also the article [[Ladder escape fork]])''

If you are forced onto a ladder and no convenient escape is present, then you must create one. The best way is to play one of the valid ladder escape templates that threatens another strong connection. Such a move is called a '''ladder escape fork'''. For an example, see the first example in the upcoming section "forcing moves." The first forcing move is a ladder escape fork played just prior to the formation of the ladder (and a very short ladder at that). A ladder escape fork is frequently a [[killer move]].

=== Foiling ladder escapes ===
''(See also the article [[Foiling ladder escapes]])''

In order to successfully stop a ladder escape, you must either block the [[projected ladder path]] from connecting to the escape piece or intrude on the ladder escape template. To successfully stop a ladder escape fork, you need to do both with a single move and almost always with a move that is [[Adjacent move|adjacent]] to the escape piece. The following is an example of foiling a ladder escape fork.

<hex>R9 C9 Q1 Vg3 Vf4 Vf5 Vg5 Vh6 Vh7 Vd7 Hc6 Hd6 He7 Hf7 Hg7 Hi7 Hg9 Sc7 Sb8 Sc8 Sd8 Sa9 Sb9 Sc9 Sd9</hex>

Red has just played a forking ladder escape at d7. This piece is connected to the edge via template IIIa as shown by the marked hexes. Red is threatening to create an unbeatable chain by playing at E6 and the edge template is a valid ladder escape for the row-2 ladder starting G8, F9, F8, etc. To stop this, Blue needs to play a move that blocks the ladder path from connecting to the escape piece and that also intrudes on the escape template. Blue can achieve both aims by playing at D8 (which is adjacent to the escape piece). Red responds by playing C8 re-establishing the connection to the edge (there is nothing better). Now Blue continues by playing E6 blocking the forking path obtaining a [[win|winning position]].

<hex>R9 C9 Q1 Vg3 Vf4 Vf5 Vg5 Vh6 Vh7 Vd7 Ve6 Hc6 Hd6 Hd8 He6 He7 Hf7 Hg7 Hi7 Hg9 Vc8</hex>

Consider the same initial position but with Blue's piece on e7 removed.

<hex>R9 C9 Q1 Vg3 Vf4 Vf5 Vg5 Vh6 Vh7 Vd7 Hc6 Hd6 Hf7 Hg7 Hi7 Hg9 Sc7 Sb8 Sc8 Sd8 Sa9 Sb9 Sc9 Sd9</hex>

This change may look inconsequential but now Blue cannot foil the forking ladder escape. Suppose the play goes d8, c8, e6 as before.

<hex>R9 C9 Q1 Vg3 Vf4 Vf5 Vg5 Vh6 Vh7 Vd7 Ve6 Hc6 Hd6 Hd8 He6 Hf7 Hg7 Hi7 Hg9 Vc8</hex>

Now Red can ladder up to E8 by the sequence G8, F9, F8, E9, E8 achieving the following position.

<hex>R9 C9 Q1 Vg3 Vf4 Vf5 Vg5 Vh6 Vh7 Vd7 Ve6 Hc6 Hd6 Hd8 He6 Hf7 Hg7 Hi7 Hg9 Vg8 Hf9 Vf8 He9 Ve8 Vc8</hex>

Now if Blue stops the e8 piece from connecting to the [[Bottom edge|bottom]] by playing d9, Red responds by playing e7 connecting to the bottom anyway. This example illustrates that a potential foiling move that leaves vulnerable points is unlikely to succeed against a forking ladder escape. The proper handling of ladders and ladder escapes is a complex matter and it is where many games are won or lost.

=== Pre-ladder formations ===

It's important to recognize situations in which a ladder is about to form or which could be formed. Such recognition allows you to play pieces that also serve as ladder escapes before the ladder occurs. It also allows you to play defensive moves that also block potential ladder paths prior to the existence of the ladder. By far the most common pre-ladder formation is the following "[[Bottleneck]] formation."

<hex>R5 C7 Q1 Hd3 Ve3 Hf3 Hd5</hex>

Red can now form a ladder by playing e4, e5, f4, f5, etc. or by playing d4, c5, c4, b5, etc. Such formations typically occur due to blocking a player from directly connecting to an edge as in the following example.

<hex>R5 C7 Q1 Vg1 Ve2 Hf3</hex>

In order to block Red from connecting to the bottom edge, Blue plays d3 creating a [[bottleneck]]. Red responds with e3 squeezing through and then Blue blocks with d5 completing the formation in the previous diagram.

The other common pre-ladder formation occurs when the defender is blocking the connection to an edge via a classic block as in the following diagram.

<hex>R5 C7 Q1 Ve1 Hd4</hex>

Red can form a ladder by playing d3, c4 and then laddering either to the left or right (c3, b4, b3, a4 or e3, e4, f3, f4, etc.)

== Forcing moves ==
''(See also the article [[Forcing move]])''

'''Forcing moves''' are moves that make a threat that your opponent must reply to on their next turn. Common forcing moves include playing in one of the [[Empty hex|open hexes]] in a two-chain (threatening to break the link), intrusion into an edge template, or threatening an immediate strong connection or win. Consider the following position with the [[vertical player]] to move.

<hex>R9 C9 Q1 Vg3 Vg4 Vf5 Vh5 Hc7 Hd8 Hf7 Hh7</hex>

At first glance, the position looks bad for Red, but Red can win by making a couple of forcing moves. He plays at e8 threatening to play at e7 on his next turn which would create an unbeatable winning chain. Blue has little choice but to stop this threat by playing e7 (there is nothing better). The move e8 is a forcing move.

The forcing nature of the move allows Red to place a piece on the other side of Blue's line without giving Blue any time to do anything constructive. The e8 piece on the other side is connected to the bottom and is of critical importance.

Red continues by playing another forcing move at g7. The only move that stops this piece from immediately connecting to the bottom edge is f9. But after f9, Red completes the win by playing at f8.

<hex>R9 C9 Q1 Vg3 Vg4 Vf5 Vh5 Hc7 Hd8 Hf7 Hh7 Ve8 He7 Vg7 Hf9 Vf8</hex>

The group of red pieces near the bottom are connected to the bottom edge. These pieces are connected via two-chains to the [[group]] g3-g4-f5 which is in turn connected to the top edge via edge [[template IIIa]].

(Note: the two forcing moves could just as easily be played in the reverse order. That is Red plays g7, Blue is forced to respond with f9, and then Red plays e8 which threatens to form an unbeatable chain in two distinct ways.)

In general terms, you have three options when responding to a forcing move in a [[Bridge|two-chain]].

# [[Saving a connection|Save]] the link by playing the other move in the two-chain.
# [[Ignoring a threat|Play elsewhere]] (e.g. playing another move may give another way of meeting the threat thus rendering it harmless)
# [[Counterthreat|Respond]] with a forcing move of your own.

=== Breaking edge templates via forcing moves ===

Forcing moves are also the only way to successfully defeat an edge template. This is done by making a [[template intrusion]] that is also a more threatening forcing move. After the opponent responds to the greater threat, you can play another move within the template and destroy the connection to the edge. For example, consider the following position with the vertical player to move.

<hex>R9 C9 Q1 Hc3 Hd3 He3 Hf2 Hg1 Hg3 Vd7 Ve6 Ve5 Ve4 Vf3 Vh5 Si1 Si2 Si3 Si4 Sh2 Sh3 Sh4 Sg4</hex>

The piece on g3 is connected to the right edge via [[template IIIa]] indicated by the '*'s. Red's best move is to play at h2. This intrudes on the edge template, is connected to the top via edge [[template II]], and threatens to complete an unbeatable chain by playing at g2 next turn. Blue can stop this threat only by playing at g2. Then Red Plays i3 breaking Blue's connection to the right.

<hex>R9 C9 Q1 Hc3 Hd3 He3 Hf2 Hg1 Hg3 Vd7 Ve6 Ve5 Ve4 Vf3 Vh5 Vh2 Hg2 Vi3</hex>

=== Using forcing moves to steal territory ===
''(See also the article [[Stealing territory]])''

I'll define '''territory''' to be the number of empty hexes adjacent to your pieces. By playing a forcing move in one of the empty hexes in a two-chain, a player can steal territory at no cost.

<hex>R5 C5 Hc2 Hb4 Vd2 Vd3 Sb3</hex>

In this position, Blue has two more hexes of territory than Red (9 vs. 7 [[adjacent hex]]es). Suppose Red makes the forcing move at the indicated hex and Blue saves the link.

<hex>R5 C5 Hc2 Hb4 Vd2 Vd3 Vb3 Hc3</hex>

Now Red has two more hexes of territory; i.e. Red has stolen 4 hexes of territory without disturbing either player's connections. Significantly, the additional territory is on the other side of Blue's connection where it may potentially be used for a future threat. The additional territory can't hurt and sometimes it makes a crucial difference.

A forcing move is [[Irrelevant move|harmless]] if it gains no territory for the opponent. You should not be worried at all about leaving harmless forcing moves available for your opponent. When you have more than one way of completing a connection with a two-bridge, e.g. when completing the loose connection described previously, you should consider which forcing move is least valuable for your opponent. Consider the following position with Red to play.

<hex>R5 C6 Q1 Vd2 He3 Hb4 Vd4 Hb5</hex>

Red wants to connect the d4 piece to the d2 piece. There are three distinct moves that accomplish this, d3, c4 (two-chaining to d2), and c3 (two-chaining to d4).

There is not much to be said about d3; it [[Direct connection|directly connects]] without altering anything else. c4 connects but gives a potentially useful forcing move to Blue. Blue can respond with c3 and suppose Red saves the connection with d3. Now Blue has gained a free hex of territory, the hex c2 is now directly adjacent to the c3/b4/b5 group when it wasn't previously. Hence, c4 is worse than d3.

Now consider the last remaining possibility c3. This leaves two forcing moves for Blue but both of them are completely harmless! If after c3, Blue plays one of the forcing moves c4 or d3, then Red can save the link and Blue will not have gained any territory at all — any empty hexes adjacent to the forcing piece were already adjacent to Blue's existing pieces. Hence, c3 is just as safe as d3 but significantly, c3 ''gains'' one hex! — b3 is now adjacent to Red's d2/b3 group when it wasn't before. Thus, c3 is better than d3 and is the best of three choices.

== Using edge templates to block your opponent ==

If your opponent has not completed an [[edge template]] but is threatening to do so in multiple ways, then the only defensive moves that stop the immediate threatened connections are those in the overlap between all threatened template connections. Suppose you are trying to stop the vertical player from connecting to the [[bottom edge]] in the following example.

<hex>R5 C6 Q1 Ve2 Hf3</hex>

The vertical player has not formed an edge template but is threatening to do so in the following four different ways.

{|
| <hex>R5 C6 Q1 Ve2 Hf3 Sd3 Se3 Sd4 Sc5 Sd5</hex> || <hex>R5 C6 Q1 Ve2 Hf3 Sd3 Se3 Sc4 Sd4 Se4 Sb5 Sc5 Sd5 Se5</hex>
|-
| <center>''Two-chain to [[template II]] at d4''</center> || <center>''Adjacent move to [[template IIIa]] at d3 and e3''</center>
|-
| <hex>R5 C6 Q1 Ve2 Hf3 Sc3 Sd3 Sb4 Sc4 Sd4 Sa5 Sb5 Sc5 Sd5</hex> || <hex>R5 C6 Q1 Ve2 Hf3 Sc3 Sd3 Se3 Sb4 Sc4 Sd4 Se4 Sa5 Sb5 Sd5 Se5</hex>
|-
| <center>''Adjacent move to template IIIa at d3'' || <center>''Adjacent move to [[template IIIb]] at d3''</center>
|}

The only three [[Hex (board element)|hexes]] in the overlap among all these edge templates are marked on the following diagram. To stop the immediate connection, the horizontal player must play at one of them.

<hex>R5 C6 Q1 Ve2 Hf3 Sd3 Sd4 Sd5</hex>

== On connectivity ==

=== Overlapping connections ===
''(See also the article [[Overlapping connections]])''

One should be alert to the situations where various connections, edge templates, and potential connections overlap at some hex(es). Consider the following position with Blue to move.

<hex>R11 C11 Vj2 Vi4 Vj5 Vi7 Vi9 Vh9 Vg9 Vf9 Se9 Ve8 Vd10 Hg7 Hf7 He6 Hc7 Hc9 He10 Hf10 Hg10 Hh10 Hi10</hex>

At first glance, it appears that Red has an unbreakable winning path. j2 cannot be stopped from connecting to the [[Top edge|top]], j2 is connected the [[group]] f9-g9-h9-i9 through a series of unbreakable two-chains, this group is connected to e8 via a two-chain, e8 is connected to d10 via another two-chain, and d10 cannot be stopped from connecting to the [[Bottom edge|bottom]].

Appearances are deceiving; it is Blue that has a forced win! The [[Weakest link|flaw]] in Red's formation is that the two-chain from f9 to e8 and the two-chain from e8 to d10 [[overlap]] at the hex marked by a '*' in the diagram (e9). Blue should play at e9. By playing in the overlap, Blue is threatening to break ''both'' two-chains containing this hex. Red cannot save them both.

If Red responds with f8, then Blue plays d9 breaking the two-chain and establishing an unbeatable chain. If Red saves the other link by responding with d9, then Blue breaks through with f8 again establishing an unbeatable chain.

=== Disjoint steps ===

When a piece can be connected to a group of pieces in one move in two non-overlapping ways, then they can be thought of as already connected to the group. Consider the following position.

<hex>R5 C5 Q1 Vc2 Vd2 Vb3 Hc3 Ha5 Hd4</hex>

Red's three pieces are connected to the top. How can Red extend this connection downward? By playing at c4! The piece at c4 is connected to the group of three vertical pieces in two non-overlapping ways; namely, through the hexes b4 and d3. The diagrammed connection pattern is a fairly common occurrence and the connection to the piece at c4 is just as strongly connected as the pieces in a two-chain.

=== Groups ===
''(See also the article [[Group]])''

A '''group''' is a collection of pieces that, considered in isolation from the rest of the position, have an unbreakable connection with each other. As you improve, it is important to learn to think in terms of safely connected groups of pieces. To illustrate why, consider the following two hex puzzles taken from [[Cameron Browne]]'s book "[[Hex Strategy]]."

<hex>R11 C11 Q1 Hj2 Hh3 Hc4 Vd4 Hf4 Vi4 Vj4 Vd5 Vg5 Hh5 Vi5 Vk5 Ve6 Hf6 Hg6 Hh6 Hi6 He7 Vg7 Hi7 Vj7 Vc8 Vi9</hex>

It is Blue's turn; how can he win?. The chain of pieces j2-h3-f4 is connected to the right edge and furthermore, Blue has no other way of connecting to the right edge. So to win, Blue has to extend this chain to the left edge. Looked at in isolation, there doesn't seem to be any way to do this, yet by thinking in terms of connected groups, the solution falls out easily.

Notice that the j2-h3-f4 chain threatens to connect to the i7-i6-h6-h5-g6-f6-e7 group in two non-overlapping ways, through locations h4 and f5. Hence, these two groups can be thought of as a single group of pieces already connected to the right edge (this is another example of "'''disjoint steps'''"). Now notice the key hex d6. This hex threatens to connect to Blue's big group in two distinct non-overlapping ways (through e5 and d7) hence a piece played at d6 would be part of the big group (disjoint steps again!). Furthermore, a blue piece at d6 could not be stopped from connecting to the left because the b4 piece acts as a ladder escape. Therefore, d6 wins.

<hex>R11 C11 Q1 Hj2 Vc3 Hd3 Vg3 Hj3 Hc4 He4 Vc5 Vd5 Hg5 Vi5 Vd6 He6 Vd7 Ve7 Vh7 Hb9</hex>

Again, it is Blue's turn and the task is to [[win]]. The c4 piece cannot be stopped from connecting to the left edge since after the block a5, Red can ladder down row B to the escape piece at b9. Hence, the group c4-d3-e4 is connected to the [[left edge]]. The group j2-j3 is connected to the [[right edge]]. Blue has a third group e6-g5. If Blue can play a single move that connects the e6-g5 group to both other groups, then this would be a winning move. Blue has a unique move which does this, namely play at g4. The g4-g5-e6 group is connected to the left group through f4 and e5. It threatens to connect to the j2-j3 group via h3 and i4. h3 is directly connected to g4 and two-chains to j2. None of the hexes involved, h3, i2, and i3, is involved in the connection threat i4 plus the two chain to g5. I.e. the threats don't overlap and hence the connection cannot be stopped. Therefore, g4 wins.

There is another way of coming up with this move. Red threatens to cut off the e6-g5 group to the left by two-chaining from g3 to f5. Red is also threatening to cut off the e6-g5 from the right by two-chaining from g3 to h4. However, these threats overlap and hence, Blue can stop them both by playing in the unique hex contained in the overlap, namely g4 again.

This illustrates that [[Offence equals defense]] in hex. Playing in regions of overlapping threats in order to stop all the threats is a defensive way of thinking. Trying to establish unbreakable connections between groups of your pieces is an offensive way of thinking. In this example, both offensive and defensive thinking techniques lead you to the unique best move. A lot of times defensive thinking is easier but sometimes offensive thinking is.

== Conclusion ==

The first two strategy guides cover what I consider to be the fundamentals of [[hex strategy]]. This information should be enough to move up into the 1800s or 1900s on [[PlaySite]]. To move up the ranks of the red guys (the topmost group) requires the following. First you need to improve your [[opening play]]. Playing any reasonable looking moves during the initial phase of the game is enough for an orange player, but to compete with the reds, you need to [[Consistency|consistently]] play one of the top two or maybe three moves. Unfortunately, I don't know a good way to describe how to do this; I'm not convinced the necessary information can be verbalized. After that, you need to know the [[Minimax]] principle (described in the [[Advanced (strategy guide)|Advanced strategy guide]]).

Also you need a certain mindset, call it [[willpower]] if you like, to move towards the top ranks. You have to try to hold onto every little [[Hex (board element)|hex]] the way a miser hoards gold pieces and you have use every optimization you can no matter how minor it may seem. The most useful optimizations, tricks, and special situations that I've learned so far are included in the Advanced strategy guide. But surely there are other things out there waiting to be discovered.

File:Hexposition02.jpg

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POV-Ray generated image, using modified source code for a Go board. The position is from Little Golem game 247486.

HexWiki:About

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HexWiki is a community initiative aimed at creating a central knowledge-base on the game [[Hex]]. The idea came about during discussions in the [http://www.littlegolem.net/jsp/forum/forum.jsp?forum=50 Hex forum] on [[Little Golem]].

HexWiki formerly ran on [[QwikiWiki]], but now uses the [[MediaWiki]] engine, known for serving, among other sites, [http://wikipedia.org Wikipedia].

Kurnik

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<div style="float:right;margin-left:1em">
[[Image:Kurnik.gif|200px|kurnik logo]]
</div>
'''kurnik''' is a Polish site featuring a number of online games, and is arguably the best real-time server on the net for [[Hex]].

Because most players on kurnik are from [http://en.wikipedia.org/wiki/Poland Poland], it is a good idea to know a few [[Polish phrases]].

For turn-based (non-real-time) hex games, [[Little Golem]] is the most popular site.

== Addresses ==

* http://www.kurnik.org — English version
* http://www.kurnik.pl — Polish version
* http://www.kurnik.org/intl/cs/ — Chech version
* http://www.kurnik.org/intl/et/ — Estonian version
* http://www.kurnik.org/intl/es/ — Spain version
* http://www.kurnik.org/intl/fr/ — French version
* http://www.kurnik.org/intl/it/ — Italian version
* http://www.kurnik.org/intl/hu/ — Hungarian version
* http://www.kurnik.org/intl/nl/ — Dutch version
* http://www.kurnik.org/intl/sk/ — Slovakian version
* http://www.kurnik.org/intl/de/ — Deutsch version

Win

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The game is won when there's a path between opposite sides of the board. The player owning those sides is the winner.

Back to the [[Rules_(Hex)|rules]]

Intermediate (strategy guide)

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File:Hexposition02.jpg

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POV-Ray generated image, using modified source code for a Go board. The position is from Little Golem game 247486.

HexWiki:About

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Piet Hein

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'''Piet Hein''' (1905-1996) was a Danish poet and mathematician, and the first inventor of Hex.

In Denmark, and in the rest of Scandinavia, he is most famous for his collections of short poems, which he called [http://en.wikipedia.org/wiki/Grook grooks]. Most of them are written in Danish, but some he himself translated into English. The following is an example of these poems, which ought to be taken to heart by all [[Hex]] players.

The road to wisdom?
Well, it's plain
and simple to express:
Err
and err
and err again
but less
and less
and less

==External links==

* [http://www.piethein.com Piet Hein Homepage]
* [http://www.ctaz.com/~dmn1/hein.htm Notes on Piet Hein]
* [http://chat.carleton.ca/~tcstewar/grooks/grooks.html Grooks by Piet Hein]

Hex theory

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Unlike many other games, it is possible to say certain things about [[Hex]], with absolute certainty. While, for example, nobody seriously believes that black has a winning strategy in [http://en.wikipedia.org/wiki/Chess chess], nobody has been able to prove that such a strategy doesn't exist. In Hex, on the other hand, a simple argument can show that the [[second player]] certainly does not have a winning strategy from the [[starting position]] (when the [[Swap rule|swap option]] is not used). Whether this makes Hex a better game is of course debatable, but many find this attribute charming.

The most important properties of Hex are the following:

* The game can not end in a [[draw]]. ([http://javhar1.googlepages.com/hexcannotendinadraw Proofs] on Javhar's page)
* The [[first player]] has a [[winning strategy]].
* When playing with the swap option, the second player has a winning strategy.

== See also ==

[[Open problems]]

Group

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A '''group''' is a set of [[piece]]s owned by the same [[player]], such that the pieces can only be disconnected from each other if the player allows it.

A group typically relies on certain cells being [[Empty hex|empty]]. When the opponent plays in one of those cells, it is called an [[intrusion]]. An intrusion means that the owner of the group must play another move if he wants to [[Restoring|restore]] the [[connection]] between his pieces.

A [[Hex (board element)|cell]] in which the opponent can intrude is called an [[intrusion point]].

== Examples of groups ==

* the [[bridge]]
* the [[box]]
* the [[mouth]]
* the [[wheel]]

Minimaxing

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The idea behind the term '''minimax''' is that you are playing a move that maintains a '''mini'''mal connectivity in one direction while building up (i.e. '''max'''imizing) your strength in the other direction.

{{stub}}

Connection game

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Advanced (strategy guide)

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Turing: /* Template Va */ reply to Roland

== Advanced edge templates ==
=== Template IVc ===

<hex>R4 C4 Q1 Vc1 Vd1 Pc2 Sb3 Sc3 Pb4</hex>

This is a two-piece template and is useful for squeezing edge connections and ladder escapes into relatively small regions. Also, many players are unaware of it. If the opponent intrudes on the template with any move other than those marked by '+', Red two-chains to template II by playing at one of the hexes marked '*'.

==== Solution to intrusion at b4 ====

<hex>R4 C4 Q1 Vc1 Vd1 Hb4 Vd3 Hd2</hex>

<hex>R4 C4 Q1 Vc1 Vd1 Hb4 Vd3 Hd2 Vb3 Sc3 Sa4</hex>

If Blue (the horizontal player) intrudes at b4, then Red responds with d3 — d3 is connected to the edge via template II and threatens a direct connection via d2. So d2 by Blue is forced. Red then two-chains to b3 threatening to connect either via a4 or c3.

==== Solution to intrusion at c2 ====

<hex>R4 C4 Q1 Vc1 Vd1 Hc2 Vb3 Hb2</hex>

<hex>R4 C4 Q1 Vc1 Vd1 Hc2 Vb3 Hb2 Vd2 Hc4 Vc3</hex>

If Blue intrudes at c2, then Red responds with b3; b3 is connected to the edge via template II and threatens a direct connectione via b2. So b2 by Blue is forced. Then Red plays at d2. Red threatens to extend d2 to template II at c3 and d3, and threatens to two-chain from d2 to the edge at c4. The only hex that is in the overlap of all these threats is c4 thus, Blue is forced to play at c4. Then Red plays at c3 completing the connection.

=== Template Va ===

<hex>R6 C10 Q1 Vg2 Pf4 Pd6 Pf6 Sa1 Sb1 Sc1 Sd1 Se1 Sf1 Sg1 Sh1 Si1 Sj1 Sa2 Sb2 Sc2 Sd2 Se2 Si2 Sj2 Sa3 Sb3 Sc3 Sd3 Sj3 Sa4 Sb4 Sa5</hex>

: Does the hex at a1 really have to be empty? --[[User:Roland Illig|Roland Illig]] 14:02, 15 Jun 2007 (CEST)
::Not sure I understand your question, Roland. It says in the next paragraph that hexes marked '*' are not relevant to the template, i.e. it doesn't matter whether a1 is empty or not. I think I will move this discussion shortly to the Talk page, so that it doesn't disturb the flow of the tutorial. — [[User:Turing|turing]] 13:53, 14 Jul 2007 (CEST)

The hexes marked '*' are not relevant to the template.

If Blue intrudes in the template at any hex besides the three marked '+', Red makes a move that reduces the situation to a closer template.

==== Solution to the intrusion at f4 ====

The key move is the response d5. Yielding

<hex>R6 C10 Q1 Vg2 Pe3 Hf4 Vd5 Sa1 Sb1 Sc1 Sd1 Se1 Sf1 Sg1 Sh1 Si1 Sj1 Sa2 Sb2 Sc2 Sd2 Se2 Si2 Sj2 Sa3 Sb3 Sc3 Sd3 Sj3 Sa4 Sb4 Sa5</hex>

Red is threatening to play at the marked hex which would complete the connection of the g2 piece to the bottom. Blue must block by a playing at some hex between Red's two pieces. Red then plays h3 forcing Blue to block at h4 yielding

<hex>R6 C10 Q1 Vg2 He3 Hf4 Vd5 Vh3 Hh4 Sa1 Sb1 Sc1 Sd1 Se1 Sf1 Sg1 Sh1 Si1 Sj1 Sa2 Sb2 Sc2 Sd2 Se2 Si2 Sj2 Sa3 Sb3 Sc3 Sd3 Sj3 Sa4 Sb4 Sa5</hex>

Red has forced the most common pre-ladder formation. Red can get a second row ladder by squeezing through at g4 (Blue blocks at f6). Red's initial key d5 piece acts as a ladder escape which completes the connection. The final position is

<hex>R6 C10 Q1 Vg2 He3 Hf4 Vd5 Vh3 Hh4 Vg4 Hf6 Vf5 He6 Ve5 Sa1 Sb1 Sc1 Sd1 Se1 Sf1 Sg1 Sh1 Si1 Sj1 Sa2 Sb2 Sc2 Sd2 Se2 Si2 Sj2 Sa3 Sb3 Sc3 Sd3 Sj3 Sa4 Sb4 Sa5</hex>

==== Solution to the intrusion at d6 ====

Red's best response is to two-chain to h3. To stop the threatened immediate connection, Blue must block at h4 or play the forcing move g3 in the two-chain. The first play is defeated by the forcing sequence f5, g3, f3, f4, e4 yielding

<hex>R6 C10 Q1 Vg2 Hd6 Vh3 Hh4 Vf5 Hg3 Vf3 Hf4 Ve4 Sa1 Sb1 Sc1 Sd1 Se1 Sf1 Sg1 Sh1 Si1 Sj1 Sa2 Sb2 Sc2 Sd2 Se2 Si2 Sj2 Sa3 Sb3 Sc3 Sd3 Sj3 Sa4 Sb4 Sa5</hex>

Red is now threatening to connect to the bottom in two non-overlapping ways, by playing e5 or by two-chaining to c5. Blue cannot stop both threats with a single move. The other play, g3 (after Red's h3) is defeated by the forcing sequence h2, h4, f5, g4, f3, f4, e4 yielding

<hex>R6 C10 Q1 Vg2 Hd6 Vh3 Hg3 Vh2 Hh4 Vf5 Hg4 Vf3 Hf4 Ve4 Sa1 Sb1 Sc1 Sd1 Se1 Sf1 Sg1 Sh1 Si1 Sj1 Sa2 Sb2 Sc2 Sd2 Se2 Si2 Sj2 Sa3 Sb3 Sc3 Sd3 Sj3 Sa4 Sb4 Sa5</hex>

Red is again threatening to connect to the bottom in the same two non-overlapping ways: by playing at e5 or two-chaining to c5. Blue cannot stop both threats with a single move.

==== Solution to the intrusion at f6 ====

Red's best response is play e5 which is connected to the bottom and forms a loose connection with the g2 piece. To stop the immediate connection, Blue must play in the middle of the loose connection at one of the hexes marked "+" in the following diagram.

<hex>R6 C10 Q1 Vg2 Pf3 Pf4 Ve5 Hf6 Sa1 Sb1 Sc1 Sd1 Se1 Sf1 Sg1 Sh1 Si1 Sj1 Sa2 Sb2 Sc2 Sd2 Se2 Si2 Sj2 Sa3 Sb3 Sc3 Sd3 Sj3 Sa4 Sb4 Sa5</hex>

The move f3 is defeated by the forcing sequence g3, f4, g4 yielding

<hex>R6 C10 Q1 Vg2 Hf3 Ve5 Hf6 Vg3 Hf4 Vg4 Sa1 Sb1 Sc1 Sd1 Se1 Sf1 Sg1 Sh1 Si1 Sj1 Sa2 Sb2 Sc2 Sd2 Se2 Si2 Sj2 Sa3 Sb3 Sc3 Sd3 Sj3 Sa4 Sb4 Sa5</hex>

Red is threatening to connect to the bottom in two non-overlapping ways: by playing at f5 or two-chaining to h5. The alternative response, f4, is defeated by the forcing sequence e3, d6, e6, e4, d4 yielding

<hex>R6 C10 Q1 Vg2 Hf4 Ve5 Hf6 Ve3 Hd6 Ve6 He4 Vd4 Sa1 Sb1 Sc1 Sd1 Se1 Sf1 Sg1 Sh1 Si1 Sj1 Sa2 Sb2 Sc2 Sd2 Se2 Si2 Sj2 Sa3 Sb3 Sc3 Sd3 Sj3 Sa4 Sb4 Sa5</hex>

Red is threatening to connect to the bottom in two non-overlapping ways, by playing at d5 or c5.

Note that template Va occurs in a mirror-image form (in the mirror image form, the three hexes on the 5th row (from the bottom) are shifted over 1 hex to the G, H, and I columns). It may seem that this template is very strong because it reaches 5 rows into the board but it rarely occurs because of the huge size of the template; the template requires 31 empty hexes and 10 hexes along an edge — the entire edge on the 10x10 board!

Furthermore, the large perimeter makes it more vulnerable to encroaching adjacent plays and forcing moves. Additionally, template area surrounds the 5th row piece on both "shoulders" so that non-overlapping plays from the 5th row piece can occur in only two directions.

=== Template Vb ===

<hex>R6 C10 Q1 Vf2 Vg2 Pf3 Pe5 Sa1 Sb1 Sc1 Sd1 Se1 Sf1 Sg1 Sh1 Si1 Sj1 Sa2 Sb2 Sc2 Sd2 Se2 Sh2 Si2 Sj2 Sa3 Sb3 Sc3 Sd3 Sh3 Si3 Sj3 Sa4 Sb4 Sc4 Si4 Sj4 Sa5 Sb5 Si5 Sj5 Sa6 Si6 Sj6</hex>

The hexes marked '*' are not relevant to the template.

If the horizontal player Blue intrudes in the template at any hex besides the three marked '+', Red makes a move that reduces the situation to a closer template.

==== Solution to the intrusion at f3 ====

There are several solutions but the simplest is to respond with g3. Blue's only play to stop the immediate connection is f5. Then Red plays e4 yielding

<hex>R6 C10 Q1 Vf2 Vg2 Hf3 Vg3 Hf5 Ve4 Sa1 Sb1 Sc1 Sd1 Se1 Sf1 Sg1 Sh1 Si1 Sj1 Sa2 Sb2 Sc2 Sd2 Se2 Sh2 Si2 Sj2 Sa3 Sb3 Sc3 Sd3 Sh3 Si3 Sj3 Sa4 Sb4 Sc4 Si4 Sj4 Sa5 Sb5 Si5 Sj5 Sa6 Si6 Sj6</hex>

The e4 piece is connected to the bottom via a 3rd row template and e4 is connected to the other group of red pieces through e3 and f4. Thus, the connection is complete.

==== Solution to the intrusion at e5 ====

Red's best response is g4. This piece is connected to the bottom via a 3rd row template and hence Blue must block at g3. Red then plays e4 yielding

<hex>R6 C10 Q1 Vf2 Vg2 He5 Vg4 Hg3 Ve4 Sa1 Sb1 Sc1 Sd1 Se1 Sf1 Sg1 Sh1 Si1 Sj1 Sa2 Sb2 Sc2 Sd2 Se2 Sh2 Si2 Sj2 Sa3 Sb3 Sc3 Sd3 Sh3 Si3 Sj3 Sa4 Sb4 Sc4 Si4 Sj4 Sa5 Sb5 Si5 Sj5 Sa6 Si6 Sj6</hex>

The e4 piece threatens to connect to the bottom in two non-overlapping ways, to d5 and to g4 (through f4). Hence the connection is unstoppable.

Unlike template Va, this template is not a rare occurrence and many hex players are not familiar with it.

== Advanced templates as ladder escapes ==

Templates IVc and Vb are valid escapes for row 2, row 3, and row 4 ladders. Template Va is not a valid ladder escape.

Exception: Template Vb is not valid for 3rd and 4th row ladders coming from the right side in the above diagram if the Horizontal player has a piece at h3. For the horizontal player to defeat the 3rd row ladder in this case, connecting to h3 must provide a strong threat that the vertical player needs to respond to.

Note: The unique way to win with template Vb and a 2nd row ladder is as follows. As soon as your head ladder piece intrudes on the template, your very next move must be to two-chain up to the 3rd row (this is true no matter which side of the template you are entering from). Then you break off the ladder (this piece will be connected to the edge via a smaller edge template).

== The minimax principle ==
(See also the page [[Minimax]])

Suppose you have multiple ways of establishing/maintaining a connection to an edge. A move that maintains as strong a connection as possible is not preferable to other connection moves because you only need to get some connection; you don't win extra points by connecting more strongly.

In fact it is generally better to play a move that maintains as ''weak'' a connection as possible; the reason being that such a piece may help you extend the connection towards the opposite edge. This principle is sometimes called "mini-maxing."

The idea behind the term is that you are playing a move that maintains a minimal connectivity in one direction while building up (i.e. maximizing) your strength in the other direction. I'll illustrate this with a couple of positions from my games. (Note that this principle applies equally well when establishing/maintaining a connection to ''a group of pieces''.)

<hex>R10 C10 Q1 Va3 Vc6 Hf5</hex>

My opponent, Blue played the minimax move f4. This move maintains a minimal strength connection to the left while building up strength to the right; in fact the f4-f5 group is almost connected to the right edge via template Vb. I responded with my own minimax move d5 (d6 is the other minimax option) yielding the following position.

<hex>R10 C10 Q1 Va3 Vc6 Hf5 Hf4 Vd5</hex>

d5 maintains a minimal strength connection to the bottom while maximizing my strength to the top. (d6 would have maintained a minimal strength connection to the top while maximizing my strength to the bottom.) A move that is even stronger towards the top, such as d4, would be a mistake. My opponent could then block at the bottom with c7, which is connected to the left edge via a 3rd row template and which threatens to link up with the central group. If I try to stop the connection to the central group with e6, my opponent responds with d5 yielding the following position.

<hex>R10 C10 Q1 Va3 Vc6 Hf5 Hf4 Vd4 Hc7 Ve6 Hd5</hex>

d5 is connected to the central group via a 2-chain and the combined threats c5 and d6 guarantee a connection to the left edge (a7 is defeated by c5, b5, b6, a6, b7, a8, b9). I would be in dire straits as the central pair f4-f5 is almost connected to the right edge.

Now back to the game; after my minimax move d5, I can safely meet c7 with e6. Yielding

<hex>R10 C10 Q1 Va3 Vc6 Hf5 Hf4 Vd5 Hc7 Ve6</hex>

In fact, the c7, e6 sequence occurred in the actual game. I eventually won after a close hard fought battle.

<hex>R10 C10 Q1 Va3 Vc6 Vb8 Vc8 Vd8 Ve8 Vg6 Vg7 Vg8 Hf5 Hf7 Hf8 He9 Hd9 Hc9 Hb9 Hd7</hex>

In this position, I was the vertical player and was expecting f6 to which h4 would give me an excellent position (with best play, this position would in fact be winning though this is not obvious). Instead my opponent played the excellent minimax move f4. This move fights in both directions and is in fact a killer move. I can't block the f4-f5 pair from the right due to the forking ladder escape at h9. Thus, I must meekly submit to the forcing sequence f6, e7, e6, d5 yielding

<hex>R10 C10 Q1 Va3 Vc6 Vb8 Vc8 Vd8 Ve8 Vg6 Vg7 Vg8 Hf5 Hf7 Hf8 He9 Hd9 Hc9 Hb9 Hd7 Hf4 Vf6 He7 Ve6 Hd5</hex>

The game is over. The f4-f5 pair is connected to d5 which in turn threatens to connect to left in two non-overlapping ways, c5 (a 3rd row template) and d6, hence the pair is connected to the left. If I try to block at the right, the best I can do is yield a ladder (e.g. h4, h3, j2, i3 and H has a second row ladder) and then the forking ladder escape at h9 wins the game.

In the next example, I am the horizontal player and it is my move.

<hex>C10 R10 Q1 Va3 Vb5 Vb8 Vc7 Vd6 Vd5 Vf4 Hc6 Hc5 Hd4 He4 He5 Hf5</hex>

Most hex players would probably connect to the left side with a7 (or b6 or b7). Despite its apparent necessity, this move actually loses (against best play). Instead I played the winning minimax move d3! By adding a second non-overlapping connection threat to the left, my group of pieces maintains a connection to the left. And despite its modest appearance, d3 also helps out on the right and in fact guarantees a winning connection from f5 to the right by defeating one of the main potential blocking plays.

<hex>C10 R10 Q1 Va3 Vb5 Vb8 Vc7 Vd6 Vd5 Vf4 Hc6 Hc5 Hd4 He4 He5 Hf5 Hd3</hex>

E.g. suppose V tries to block the f5 piece from the right as follows. g5, g4, i3 (or h4), i2 and now I have a forced winning ladder down row 2 — h3, h2, g3, g2, f3, f2, e3, e2 completing the win.

<hex>C10 R10 Q1 Va3 Vb5 Vb8 Vc7 Vd6 Vd5 Vf4 Hc6 Hc5 Hd4 He4 He5 Hf5 Hd3 Vg5 Hg4 Vi3 Hi2 Vh3 Hh2 Vg3 Hg2 Vf3 Hf2 Ve3 He2</hex>

This line clearly shows the usefullness of d3. If I hadn't played d3 (playing a7 instead, for instance), the vertical player could continue d3, d2, a4! and eventually winning with best play (considerable deep analysis is needed to show this).

<hex>C10 R10 Q1 Va3 Vb5 Vb8 Vc7 Vd6 Vd5 Vf4 Hc6 Hc5 Hd4 He4 He5 Hf5 Ha7 Vg5 Hg4 Vi3 Hi2 Vh3 Hh2 Vg3 Hg2 Vf3 Hf2 Ve3 He2 Vd3 Hd2 Va4</hex>

Minimax moves are not always "parallel" moves. The principle of maintaining a minimal amount of connectivity in one direction while maximizing your strength in the opposite direction is more general than that. The final example from a game of mine illustrates non-parallel mini-max moves. I was the vertical player and opened with 1. a3 and my opponent responded with 1... e4 yielding the following position.

<hex>C10 R10 Q1 Va3 He4</hex>

I played the minimax move 2. f5 yielding

<hex>C10 R10 Q1 Va3 He4 Vf5</hex>

By connecting as far away as possible from the top, I increase my strength towards the bottom. (i.e. I am maintaining a minimal strength connection to the top while maximizing my strength towards the bottom). Before playing such a move, I have to verify that my opponent can't stop me from reaching the top. I could meet the attempted block with 2...g4 or 2...h2 by getting a third row ladder (2...g4 3.f4 g2 4.f3, etc. or 2...h2 3.g3 g2 4.f3, etc.), laddering down to e3, and then playing b4 (how to play a third row to a3 is described in a later section). I would be happy with such a line. My opponent however played the excellent e3. This move takes away the ladder, hence forcing me to reconnect to the top, while at the same time increasing his strength to the left.

<hex>C10 R10 Q1 Va3 He4 Vf5 He3</hex>

Here I played the minimax move g4. g4 has the potential to help block my opponent from going across the bottom of the board (e.g. Blue e7, Red f7, Blue f6, Red h5 and now g4 is helping out) or equivalently helps me to connect downwards on the right. I.e. g4 maintains a minimal strength connection towards the top while maximizing my strength towards the bottom. Note that a stronger move towards the top such as g3 does not have the same potential to help out towards the bottom. This potential may seem remote but in fact I would not have won the game without it! The rest of the game does not illustrate minimaxing but it is instructive nevertheless. The most important variation is as follows (there were two mistakes in the actual game which took the game out of the path it should have followed into a shorter less instructive branch).

{| cellspacing="0" style="width: 500px"
| 3. || g4 || h3 || Again forcing me to reconnect to the top and hence, getting a free hex that could potentially help him connect to the right (h3 provides an escape for ladders up row I).
|-
| 4. || g3 || f8 || As good of a block towards the bottom that there is.
|-
| 5. || e8 ||   || Necessary.
|-
| 5. || ... || e9 || Essential. Note that this move stops any ladders on row 9 coming from the right and using e8 as an escape.
|-
| 6. || g7! ||   || Excellent. Reconnecting e8 to the bottom with the d8 or d9 is defeated by e7. I can't stop e7 from connecting to the left because e4-e3 provides enough help (e.g. 6.d8 e7 7.c7 d6 8.b6 c6 9.c7 b5 10.c5 c4) nor could I stop e7 from connecting to the right — e7 is aided by f8, e9, and h3 (e.g. 6.d8 e7 7.f7 f6 8.h5 g6 9.h6 g7 10.h7 h8 11.g8 f10 12.g9 g10 13.i9 h9 14.j7 i7 and the h3 piece provides the ladder escape). 6.g7! may look strange and unconventional but it maintains a very slim advantage.
|}

<hex>C10 R10 Q1 Va3 He4 Vf5 He3 Vg4 Hh3 Vg3 Hf8 Ve8 He9 Vg7</hex>

{| cellspacing="0" style="width: 500px"
|-
| 6. || ... || f7 || The toughest move to meet. Note that 6.... g8 loses quickly to 7.d8 e7 8.f7 f6 9.h5
|-
| 7. || e7 ||   || I can't stop f7-f8-e9 from connecting to the right, so I block to the left in the only satisfactory way. I can't allow my opponent to connect from his f7 towards e3-e4.
|-
| 7. || ... || d9 || An essential block.
|-
| 8. || c8 ||   || c9 is no good. I can't allow my opponent to come up row D towards e3-e4. I need to force him as far away from e3-e4 as possible.
|-
| 8. || ... || b10 ||  
|-
| 9. || a10 || b9 || I've forced my opponent into a second row ladder which is not sufficient because my a3 piece is just barely inside the Vb template.
|-
| 10. || a9 || b8 ||  
|-
| 11. || a8 || f2! || A nice idea. e4-e3-f2 is just strong enough for the second row ladder to work and at the same time, it threatens to cut off my main group of pieces from the top. This looks like it wins but there is a way out!
|}

<hex>C10 R10 Q1 Va3 He4 Vf5 He3 Vg4 Hh3 Vg3 Hf8 Ve8 He9 Vg7 Hf7 Ve7 Hd9 Vc8 Hb10 Va10 Hb9 Va9 Hb8 Va8 Hf2</hex>

{| cellspacing="0" style="width: 500px"
|-
| 12. || i2! ||   || A subtle improvement over simply reconnecting with g2 or h2 (both of which are losing). This maintains the connection and i2 interferes with the usefulness of h3. This may seem insignificant but it makes the difference between winning and losing! (In hex, the difference between winning and losing is often very slight)
|-
| 13. || ... || c6 || Continuing with his plan to connect to the left which now works due to f2.
|-
| 14. || h8! ||   || The unique move that stops my opponent from connecting on the right. Note that 14.g8 is not satisfactory. 14.g8 g6 15.i5 h9. h9 is a forking ladder escape that guarantees a connection to the right.
|-
| 14. || ... || g6 ||  
|-
| 15. || i5 || h7 || Note that h7 is threatens to connect to the horizontal player's main group in two distinct ways, through g8 and through h6, and thus is connected to his main group.
|-
| 16. || g8 ||   || Not necessary but it doesn't hurt as the reply is forced.
|-
| 16. || ... || h6 ||  
|-
| 17. || j6 || i9 ||  
|-
| 18. || i8 || g10 ||  
|-
| 19. || f10 || h4 ||  
|-
| 20. || j3 ||   || I now have an unbreakable chain on the right side.
|}

<hex>C10 R10 Q1 Va3 He4 Vf5 He3 Vg4 Hh3 Vg3 Hf8 Ve8 He9 Vg7 Hf7 Ve7 Hd9 Vc8 Hb10 Va10 Hb9 Va9 Hb8 Va8 Hf2 Vi2 Hc6 Vh8 Hg6 Vi5 Hh7 Vg8 Hh6 Vj6 Hi9 Vi8 Hg10 Vf10 Hh4 Vj3</hex>

== Special situations, tricks, etc. ==

=== Reconnecting edge template IIIa after an intrusion ===

<hex>R4 C10 Q1 Ve2 Hd3 Pf2 Se3</hex>

In this diagram, suppose you are Red and Blue has just played d3 intruding upon the third row template connecting your e2 to the bottom. Most hex players would reconnect with e3 without giving it much if any thought, yet there three distinct ways to reconnect and there is often a reason for preferring one over the other.

A second way for Red to reconnect is to play f2 — the hex f2 and the empty hexes g2,e3,f3,g3,d4,e4,f4, and g4 form edge template IIIa; hence f2 has an unbreakable connection to the bottom and f2 is connected to e2.

The potential advantage of reconnecting with f2 over e3 is that it is easier to connect other pieces to the the group e2-f2 than to the group e2-e3 (e.g. h1 is a two-chain away from f2 but is not a two-chain away from either e2 nor e3). The extra connection possibilities can make a critical difference. For example, consider the following position with Red to move.

<hex>R9 C9 Q1 Vg2 Vf3 Ve4 Vd5 Vd6 Vh3 Vh4 Vf7 Hi4 Hc6 Hb8 Hc8 He6 Hf6 Hg6</hex>

Red can win by laddering 1. d7 d8 2. e7. Suppose instead Red plays 1.h5 intruding on the g6 edge template. If Blue reconnects with h6, then Red would have nothing else to do except play the winning line. So Blue reconnects with g7 making the win tougher. (Red could still win by d7, d8, e7, e9, f8, f9, h8! — a forking ladder escape which decides the issue).

Now suppose that Red again intrudes on the edge template with 2. h6. Now the game continues 2...g8 (again reconnecting by playing parallel to the edge) 3. h7 (persistent) h8, 4. d7 d8, 5. e7 e9! and now Blue has an unbreakable winning chain at the bottom. By reconnecting with the parallel moves instead of the direct reconnection, Blue's group had a new way to connect to the left and this extra possibility turned a defeat into a win.

So is it always better to reconnect with the parallel move? No!! Sometimes the parallel reconnection can lose the game while the simple direct connection wins! The potential weakness of the parallel reconnection is that your opponent might then be able to use a double threat to defeat the edge connection. For example, consider the following position with Red to move.

<hex>R9 C9 Q1 Vh3 Vg2 Vf3 Ve4 Vd5 Vd6 Hc6 Hb8 Hc8 He6 Hg5 Hi3</hex>

With best play Blue wins, so Red tries 1. h4. If Blue responds with the direct reconnection h5, then the win is assured and Red may as well resign. Suppose instead that Blue reconnects with 1... g6. Then Red can respond with 2.h7! — this forking ladder escape is a killer. Red now has two disjoint winning threats, laddering from d7 to h7 and play i5 (This double two-chain cutoff threat occurs in situations besides cutting off third row edge templates. It is well worth being familiar with this idea.). Blue cannot stop them both so Red wins.

But this doesn't exhaust the reconnection possibilities. There is a third way to reconnect; a way that most players don't seem to discover.

<hex>R4 C10 Q1 Ve2 Hd3</hex>

Again starting at the initial position in this section, Red's e2 piece is connected to the bottom via edge template IIIa and Blue intrudes upon it with d3. In addition to e3 and f2, Red can reconnect with the surprising f1!

<hex>R4 C10 Q1 Ve2 Hd3 Vf1</hex>

Red is threatening to connect e2-f1 to the bottom with e3. If Blue tries to block this with e3, then Red can reconnect by playing g2. g2 is connected to the bottom via template IIIa (Blue's e9 piece is just outside of this template) and h3 connects to f1 via a two-chain.

But what if Blue blocks with e4 instead of e3? (note the e4 is within the g2 piece's edge template). Then Red can still reconnect by playing as follows. 1. e3 d4 (forced) 2. g3 f3 (forced again) 3.g2 ending up with the following position.

<hex>R4 C10 Q1 Ve2 Hd3 Vf1 He4 Ve3 Hd4 Vg3 Hf3 Vg2</hex>

How does this method compare to the previous two? Compared to the parallel reconnection, it is quite a bit more susceptible to forking plays and plays that encroach upon the increased area that is needed to reconnect, but by playing away from the edge, you have even more potential to connect the edge group towards the opposite edge. Sometimes the extra connection possibilities generated by playing away from the edge is exactly what is needed.

For example consider the beautiful solution to the following position (I wish I could take the credit for its discovery but the original over the board play was found by Tom239 on _Playsite_ (he was at the orange level at the time!). The position below is a slight modification of one constructed by Kevin O'Gorman, the maintainer of the Ohex data base).

<hex>R10 C10 Q1 Va2 Va3 Va4 Va5 Va6 Va7 Va8 Va9 Ha10 Hb2 Hb3 Hb4 Hb5 Hb6 Hb7 Hb8 Vc6 Hc7 Vd5 Hd6 Vd7 Ve4 He5 Vf3 Hf4 Vg2 Hg3 Vh1 Hh2 Hi2</hex>

It is Red's move. To win, Red must connect his a9 piece to bottom. To do this, Red must make some ladder escape that additionally must somehow use the d7 piece to threaten another way to connect to the ladder. This looks impossible but yet there is a way. Red can win by starting with 1.b9 b10 2.c9 c10 3.f8!!

<hex>R10 C10 Q1 Va2 Va3 Va4 Va5 Va6 Va7 Va8 Va9 Ha10 Hb2 Hb3 Hb4 Hb5 Hb6 Hb7 Hb8 Vc6 Hc7 Vd5 Hd6 Vd7 Ve4 He5 Vf3 Hf4 Vg2 Hg3 Vh1 Hh2 Hi2 Vb9 Hb10 Vc9 Hc10 Vf8</hex>

This brilliant move is the only way to win. 3.g7 is defeated only by 3...d9 and 3.d9 d10 4.g7 is defeated only by 4...f8 (it takes a ''lot'' of analysis to demonstrate these claims). Blue's only good attempt is to intrude on the edge template with 3... e9. But Red can defeat this by reconnecting with 4.g7! (this is what Red had in mind when playing 3.f8!!)

<hex>R10 C10 Q1 Va2 Va3 Va4 Va5 Va6 Va7 Va8 Va9 Ha10 Hb2 Hb3 Hb4 Hb5 Hb6 Hb7 Hb8 Vc6 Hc7 Vd5 Hd6 Vd7 Ve4 He5 Vf3 Hf4 Vg2 Hg3 Vh1 Hh2 Hi2 Vb9 Hb10 Vc9 Hc10 Vf8 He9 Vg7</hex>

Now f8-g7 has an unbreakable connection to the bottom and Red threatens two distinct ways of connecting this group back to the group containing c9; Red threatens f6, double two-chaining between d7 and g7, and Red threatens e8 two-chaining to c9. Blue's only possible defense is the forcing move 4...d8. This interferes with the immediate connection threat between c9 and f8, and it prepares to meet the f6 threat with c8 cutting off d7 from c9. But this move is still not sufficient because after 4...d8, Red can win with 5.d9 d10 (forced) 6.e8.

In practice, you can think of the parallel reconnection as your "standard" response (more often than not, it is the correct choice). But if the potential threat to cut off the parallel play from the edge is serious, then go with the direct reconnection. The "away" reconnection entails a substantially increased risk of being cut off from the edge but if you can see that it will be safe or if you need the stronger connection possibilities towards the opposite edge, then go with the "away" connection.

=== Third row ladder to a3 and its symmetric analogues ===
(See also the page [[a3 escape trick]])

The following position is from one of my games.

<hex>R10 C10 Q1 Hg2 Vi2 He3 Hg3 Hb4 Hc4 He4 Vf4 Vg4 Vb5 Vc5 Ve6 Vf6 Hh10</hex>

I am Blue and it is my move. Red's e6-f6(-f4-g4) group is connected to bottom via template Vb. Red's i2 piece is connected to the top via edge template II. In order to stop these two groups from connecting to each and completing a win, I must start laddering down column H. So I ladder down to h6 forcing Red to follow down column I to i6 yielding the following position.

<hex>R10 C10 Q1 Hg2 Vi2 He3 Hg3 Hb4 Hc4 He4 Vf4 Vg4 Vb5 Vc5 Ve6 Vf6 Hh10 Hh3 Vi3 Hh4 Vi4 Hh5 Vi5 Hh6 Vi6</hex>

My h10 piece is ''not'' a valid ladder escape. If I ladder all the way down to h10, then Red follows down to i8 and his response to h9 is not i9 but j9!

<hex>R10 C10 Q1 Hg2 Vi2 He3 Hg3 Hb4 Hc4 He4 Vf4 Vg4 Vb5 Vc5 Ve6 Vf6 Hh10 Hh3 Vi3 Hh4 Vi4 Hh5 Vi5 Hh6 Vi6 Hh7 Vi7 Hh8 Vi8 Hh9 Vj9</hex>

Red has a winning chain on the right side. You might think I could win by instead laddering down one more hex, and then double two-chain to the h10 piece yielding the following position.

<hex>R10 C10 Q1 Hg2 Vi2 He3 Hg3 Hb4 Hc4 He4 Vf4 Vg4 Vb5 Vc5 Ve6 Vf6 Hh10 Hh3 Vi3 Hh4 Vi4 Hh5 Vi5 Hh6 Vi6 Hh7 Vi7 Hg9</hex>

This may appear to settle the matter in my favor but in actuality, Red has a winning position! Red can win by 1. h8 (h9 also works but h8 is slightly more deceptive). If I respond by saving the link, i.e. by 1...g8, then Red wins by playing 2.h9 g10 (forced) 3. j9.

<hex>R10 C10 Q1 Hg2 Vi2 He3 Hg3 Hb4 Hc4 He4 Vf4 Vg4 Vb5 Vc5 Ve6 Vf6 Hh10 Hh3 Vi3 Hh4 Vi4 Hh5 Vi5 Hh6 Vi6 Hh7 Vi7 Hg9 Vh8 Hg8 Vh9 Hg10 Vj9</hex>

Red has an unbreakable winning chain down the right. Instead it is better for me to respond to Red's 1.h8 with 1...h9. My g9-h9-h10 group is now solidly connected to the right but Red can continue 2.g8 and I cannot stop g8 from connecting to the bottom because of the help provided by Red's e6-f6 pieces (work it out!)

In the initial position I cannot afford to ladder down any farther than g6. If I ladder down one more hex, I lose against best play no matter what. If there are no other pieces in the area, as is the case here, then the strongest way to play it is to ladder down one hex short of the hex that could double two-chain to the "almost-escape" piece, and then two chain up from the almost-escape piece which in our present case yields the following position.

<hex>R10 C10 Q1 Hg2 Vi2 He3 Hg3 Hb4 Hc4 He4 Vf4 Vg4 Vb5 Vc5 Ve6 Vf6 Hh10 Hh3 Vi3 Hh4 Vi4 Hh5 Vi5 Hh6 Vi6 Hg9</hex>

Red has three tries to stop the connection between the h6 and g9 pieces.

* g8 is defeated by continuing the ladder down (try it!).
* h7 and h8 are best met by f8 (double two-chaining in the same direction).
* Meeting the play h8 with g8 (connecting up to h6) doesn't work for the same reason that laddering down to h7 and double two-chaining to h10 doesn't work (work it out and you should see what I mean).

Also, note that Red's attempt h9 is of no consequence. Against h9 you should save the link with g10 and then again meet either h7 or h8 with f8.

In the actual game my opponent played h7 and I responded with f8. f8 threatens to connect with with h6 through g7. So my opponent played g7 to which I responded with f7. Again this threatens a winning connection from f7 to h6 through g6. So my opponent played g6 and I responded with c9 with a winning position.

<hex>R10 C10 Q1 Hg2 Vi2 He3 Hg3 Hb4 Hc4 He4 Vf4 Vg4 Vb5 Vc5 Ve6 Vf6 Hh10 Hh3 Vi3 Hh4 Vi4 Hh5 Vi5 Hh6 Vi6 Hg9 Vh7 Hf8 Vg7 Hf7 Vg6 Hc9</hex>

Further play no longer concerns the topic under discussion but the remaining moves were d9, e7, d7, d8, b9, c8, a8, b8, a9, b7, a7, d6, resigns. My opponent doesn't need to see g8, f9, h9, g10, j9, i8

The key play of two-chaining up from the escape piece is also useful in another common type of third row ladder position. For example, consider the following position with the vertical player to move.

<hex>R10 C10 Q1 He2 Vi2 Va3 Hf3 Hc4 Vd4 He4 Hf4 Vh4 Vi4 Vc5 Hd5 Hf5 Hh5 Vi5 Vc6 Hf6 Hg6 Hi6 Vc7 Hd7 He7 Vf7 Hg7 Vh7 Vc8 Vd8 Ve8 Hg8 Hh8 Hb9 Vc9</hex>

Red has a chain running from the bottom at c9 up to d4. The only way Red can win is to connect this group to the top. Red can ladder d3, c3, b3 but as we saw earlier, the a3 piece is not a valid ladder escape. But Red can still win by two-chaining from a3 to b4.

<hex>R10 C10 Q1 He2 Vi2 Va3 Hf3 Hc4 Vd4 He4 Hf4 Vh4 Vi4 Vc5 Hd5 Hf5 Hh5 Vi5 Vc6 Hf6 Hg6 Hi6 Vc7 Hd7 He7 Vf7 Hg7 Vh7 Vc8 Vd8 Ve8 Hg8 Hh8 Hb9 Vc9 Vb4</hex>

This threatens a winning connection to c5 through b5. If Blue blocks this with b5, then Red plays the ladder because now the pair a3-b4 are a valid ladder escape. If instead Blue blocks off the ladder with say c3, then Red wins with the line b5, b3, a4 (forced), b1, d2!

<hex>R10 C10 Q1 He2 Vi2 Va3 Hf3 Hc4 Vd4 He4 Hf4 Vh4 Vi4 Vc5 Hd5 Hf5 Hh5 Vi5 Vc6 Hf6 Hg6 Hi6 Vc7 Hd7 He7 Vf7 Hg7 Vh7 Vc8 Vd8 Ve8 Hg8 Hh8 Hb9 Vc9 Vb4 Hc3 Vb5 Hb3 Va4 Hb1 Vd2</hex>

d2 is a forking ladder escape; it threatens d3 and it provides an escape to the 2nd row ladder starting with b2. Blue cannot stop both winning threats with a single move, thus Red wins.

a3/j8 is a common opening move. If you frequently play it or play against somebody who does, then you will run into these 3rd row ladder situations and hence, it will be beneficial to learn how to play them.

=== The parallel ladder trick ===
(See also the page [[Parallel ladder]])

Consider the following position with Red to play.

<hex>R10 C10 Q1 Hc1 Vd2 Vd3 He3 Vf3 Vd4 Ve4 Hf4 Hg4 Ve5 Vc6 Vd6 He6 Hi6 Hc7 Vd7 Ha8 Hb8 Vc8 Hd8 Hb10</hex>

All of Red's pieces form a connected group. This group is connected to the top. At the bottom, Red has a second row ladder with no possible escape on the left. The potential escapes on the right are inadequate. For example, suppose Red ladders to f9. Then tries to escape with 5.h9 g9 6.h8 g8 7.h7 f7.

<hex>R10 C10 Q1 Hc1 Vd2 Vd3 He3 Vf3 Vd4 Ve4 Hf4 Hg4 Ve5 Vc6 Vd6 He6 Hi6 Hc7 Vd7 Ha8 Hb8 Vc8 Hd8 Hb10 Vc9 Hc10 Vd9 Hd10 Ve9 He10 Vf9 Hf10 Vh9 Hg9 Vh8 Hg8 Vh7 Hf7</hex>

Now Red's only reasonable try is 8.g7 f8. Now 9.g6 loses to 9...f5 and 9.h5 loses to the forcing sequence 9...g6 10.h6 h4 11.g5 f5. All the other escape attempts likewise fail. Is Red done for?

No! Red can create a sufficient escape by making use of a parallel ladder. In the original position Red plays 1.e7. How can Blue stop Red from connecting to the bottom? d9 lets Red two-chain from e7 to f8 connecting to the bottom; e9 and e10 allow d9 which is connected to the bottom and threatens to connect to Red's big group through c9 and e8; d10 loses to e8, f9 (forced), c10; hence, Blue is forced to play the parallel ladder move 1...e8. It is simplest for Red to repeat this and ladder to f7 forcing the 2...f8 response.

<hex>R10 C10 Q1 Hc1 Vd2 Vd3 He3 Vf3 Vd4 Ve4 Hf4 Hg4 Ve5 Vc6 Vd6 He6 Hi6 Hc7 Vd7 Ha8 Hb8 Vc8 Hd8 Hb10 Ve7 He8 Vf7 Hf8</hex>

Now Red now goes back to the second row ladder and tries to escape. What have we gained by preceding this with the parallel ladder moves? When trying to escape, the threat to connect to d7-e7-f7 is stronger than the previous weak threat to connect to d7. This extra threat will let us push our escape chain farther up the board and in this case, just far enough to win the game.

Red's winning sequence is long but rather simple because every one of Blue's replies is forced. As before, Red ladders to f9 and escapes with 7. h9. Play continues 7...g9 8.h8 g8 9.h7 g7 10.h6 g6 11.h5. Red is threatening to play g5 with the double winning threats f5 and f6. But if Blue blocks this, say with 11...g5, then Red continues 12.i3 i2 13.h3 and 14.g3 completes the win.

I have managed to pull this trick off from one row farther back; i.e. with ladders on row 3 and 5 but this occurs far less frequently and you have to examine some additional defensive possibilities. Consider the following position.

<hex>R10 C10 Q1 Vd5 He5 Vd6 Ve6 Hb7 Vc7 Hd7 Hb9</hex>

Red has just played e6 trying the parallel ladder trick. With the closer ladder on row 2, we saw that Blue was forced to respond with the parallel ladder play e7. But here Blue has two additional possibilities e8 and c9 (the only other possibility where Red doesn't have a way to force his group to connect to the bottom is c10. But Red can respond with f8 and now Blue has nothing better than e7, g6).

e8 yields a second row ladder after d8, e7, c8, c10, d9. The play c9 also leads to a second row ladder after the likely f7, f8, e8 (d9 is met by e7) d10. In the latter case, Red could again try the parallel ladder trick by playing g7. Of course, the existence of other pieces in the area can change the possibilities.

Minimaxing

2007-07-14T11:46:03Z

Turing: reverted conent spam

HexWiki:Community Portal

2007-07-14T11:42:33Z

Turing: moved Roland Illig's question here, replied

Does anyone know how to contact the sysop for this wiki? I and a few others are interested in contributing new content with hex diagrams, and note that the markup that used to work no longer does. Perhaps we can fix that.

-- kogorman

:Yes, here I am. Mail (through hexwiki@yahoogroups.com) is a good way, just as you did. I've replied to you now. Sorry for the delay. — [[User:Turing|turing]] 12:38, 14 Jul 2007 (CEST)

Question: Where is the Hex plugin for this wiki documented? Is it possible to mark moves with numbers like this:? <nowiki><hex>R11 C11 Va4[1] Ha5:2</hex></nowiki> I want to be able to draw diagrams like these: [http://senseis.xmp.net/?MonkeyJump]. --[[User:Roland Illig|Roland Illig]] 16:17, 13 Jun 2007 (CEST)

:Not possible in current plugin, sadly. Many of us would like it to, I think. Expertise is needed in how to improve the plugin, which right now is in a sad state. See recent mail on hexwiki@yahoogroups.com — [[User:Turing|turing]] 13:42, 14 Jul 2007 (CEST)

Help:Contents

2007-07-14T11:40:56Z

Turing: moved question to community portal

[[HexWiki]] is a [http://en.wikipedia.org/wiki/Wiki wiki] for the game of [[Hex]], i.e., it is a website written collaboratively by people from around the world.

The [http://en.wikipedia.org/wiki/Help:Contents help page for Wikipedia] contains guidance and information about participating which is mostly applicable to HexWiki as well (since both the Wikipedia and HexWiki are based on the MediaWiki software).

Win

2007-07-14T11:39:04Z

Turing: reverted conent spam

The game is won when there's a path between opposite sides of the board. The player owning those sides is the winner.

Back to the [[Rules_(Hex)|rules]]

Connection game

2007-07-14T11:38:09Z

Turing: /* Timeline */ found page about quax

HexWiki:About

2007-07-14T11:33:04Z

Turing: reverted conent spam

Edge template

2007-07-14T11:32:48Z

Turing: reverted conent spam

An '''edge template''' is a [[pattern]] which guarantees a [[connection]] the [[edge]].

Here is an example of a [[Third row|third-row]] edge template ([[template IIIa]], also known as the ''Ziggurat''):

[[Image:Ziggurat.png]]



The red stone has a certain connection to the bottom, using only the shaded hexagons, even if blue moves first.



Countless edge templates can be constructed, all of them of varying degrees of usefulness and frequency of occurance.

* [[Edge templates everybody should know]]
* [[Edge templates with one stone]]
* [[Edge templates with two adjacent stones]]
* [[Edge templates with a bridge]]

Piet Hein

2007-07-14T11:32:17Z

Turing: reverted conent spam

Kurnik

2007-07-14T11:09:51Z

Turing: reverted vandalism

HexWiki:Community Portal

2007-07-14T10:38:08Z

Turing: reply, and reverted vandalism

Connection game

2007-07-14T10:36:18Z

Turing: added quax, don't know when it was created, though

A '''connection game''' is a [[game]] where the goal is to use the [[Piece (general)|piece]]s to create a connection between some parts of the [[Board (general)|board]]. The first connection game was [[Hex]], which was invented in [http://en.wikipedia.org/wiki/1942 1942], after which several other connection games have been created.

== Timeline ==

;[[Hex]] ([[Piet Hein]] [http://en.wikipedia.org/wiki/1942 1942] and [[John Nash]] [http://en.wikipedia.org/wiki/1948 1948])
:The original connection game. Played on a [[rhombic hex grid]].
;[[Y]] ([[Craige Schenstead]] and [[Charles Titus]], [http://en.wikipedia.org/wiki/1950s 1950s])
:Played on a [[triangluar grid of hexagons]]
;[[Twixt]] ([[Alex Randolph]], [http://en.wikipedia.org/wiki/1960s 1960s])
:Played on a [[square grid]] of holes into which the players place [[peg]]s. The pegs can be connected via [[Bridge (general)|bridges]].
;[[Havannah]] ([[Christian Freeling]], [http://en.wikipedia.org/wiki/1980 1980])
;[[Onyx]] ([[Larry Back]], [http://en.wikipedia.org/wiki/2000 2000])
:Played on an original grid consisting of both triangles and squares. It is the first connection game with a [[capturing rule]].
;[[Gonnect]] ([[João Pedro Neto]], [http://en.wikipedia.org/wiki/2000 2000])
:This game is simply [[Go]], but with a different goal, namely to create a connection between any two opposite sides.
;[[Unlur]] ([[Jorge Gómez Arrausi]], [http://en.wikipedia.org/wiki/2001 2001])
:Played on a [[hexagonal hex grid]]. Unique in the way that the players have [[different objectives]].
;Quax

== References ==

;[[Cameron Browne]], [http://www.amazon.com/Connection-Games-Variations-Cameron-Browne/dp/1568812248/ref=pd_bbs_sr_1/104-1532904-9846317?ie=UTF8&s=books&qid=1177663469&sr=8-1 "Connection Games: Variations on a Theme"]

Connection game

2007-07-14T10:35:05Z

Turing: reverted conent spam

A '''connection game''' is a [[game]] where the goal is to use the [[Piece (general)|piece]]s to create a connection between some parts of the [[Board (general)|board]]. The first connection game was [[Hex]], which was invented in [http://en.wikipedia.org/wiki/1942 1942], after which several other connection games have been created.

== Timeline ==

;[[Hex]] ([[Piet Hein]] [http://en.wikipedia.org/wiki/1942 1942] and [[John Nash]] [http://en.wikipedia.org/wiki/1948 1948])
:The original connection game. Played on a [[rhombic hex grid]].
;[[Y]] ([[Craige Schenstead]] and [[Charles Titus]], [http://en.wikipedia.org/wiki/1950s 1950s])
:Played on a [[triangluar grid of hexagons]]
;[[Twixt]] ([[Alex Randolph]], [http://en.wikipedia.org/wiki/1960s 1960s])
:Played on a [[square grid]] of holes into which the players place [[peg]]s. The pegs can be connected via [[Bridge (general)|bridges]].
;[[Havannah]] ([[Christian Freeling]], [http://en.wikipedia.org/wiki/1980 1980])
;[[Onyx]] ([[Larry Back]], [http://en.wikipedia.org/wiki/2000 2000])
:Played on an original grid consisting of both triangles and squares. It is the first connection game with a [[capturing rule]].
;[[Gonnect]] ([[João Pedro Neto]], [http://en.wikipedia.org/wiki/2000 2000])
:This game is simply [[Go]], but with a different goal, namely to create a connection between any two opposite sides.
;[[Unlur]] ([[Jorge Gómez Arrausi]], [http://en.wikipedia.org/wiki/2001 2001])
:Played on a [[hexagonal hex grid]]. Unique in the way that the players have [[different objectives]].

== References ==

;[[Cameron Browne]], [http://www.amazon.com/Connection-Games-Variations-Cameron-Browne/dp/1568812248/ref=pd_bbs_sr_1/104-1532904-9846317?ie=UTF8&s=books&qid=1177663469&sr=8-1 "Connection Games: Variations on a Theme"]

Intermediate (strategy guide)

2007-07-14T10:34:38Z

Turing: reverted conent spam

File:Hexposition02.jpg

2007-07-14T10:33:36Z

Turing: reverted conent spam

POV-Ray generated image, using modified source code for a Go board. The position is from Little Golem game 247486.

Hex theory

2007-07-14T10:32:57Z

Turing: reverted conent spam

Group

2007-07-14T10:32:49Z

Turing: reverted conent spam

Go

2007-01-26T13:31:31Z

Turing: replaced external wp links with internal namespaced ones

'''Go''' is a 3000 years old game, originally from [[wikipedia:China|China]]. It is played on a rectangular grid of size 19 × 19, and the players play by alternatingly placing pieces of their colour on the intersections on the board. The object of the game is to get the largest territory.

There are many similarities between Go and [[Hex]], and people who like Go often find Hex interesting, and vice versa.

Some basic information on Go can be found in the [[wikipedia:Go_(board_game)|Wikipedia article on Go]].
Complete rules are available at [http://senseis.xmp.net Sensei's Library], which is a [[wikipedia:Wiki|wiki]] for Go.

Cooper's Hex

2006-09-27T04:45:56Z

Turing: description

A variant of [[Hex]] or of [[Y]], where move order is changed from the ordinary alteration of Black and White (BWBWBWBW...) to a system where each player sometimes gets two moves (BWWBWBBWWBBWBWWBW...). The sequence is given by the odd-even parity of the sum of the binary digits of the natural numbers:

{|border="1"
! Natural number !! Sum of Digits !! Parity !! Player
|-
| 0 || 0 || E || B
|-
| 1 || 1 || O || W
|-
| 10 || 1 || O || W
|-
| 11 || 2 || E || B
|-
| 100 || 1 || O || W
|-
| 101 || 2 || E || B
|-
| 110 || 2 || E || B
|-
| 111 || 3 || O || W
|-
| 1000 || 1 || O || W
|}

Early reports indicate that in strategy, the game is somewhat similar to [[Halsør's Hex]], where each player has two moves after Black's first move.

Talk:Programming the bent Y board

2006-09-03T10:38:27Z

Turing: comment

This is a useful page; thank you. Even more useful would perhaps be the algorithm used for generating the coordinates. — [[User:Turing|turing]] 12:38, 3 Sep 2006 (CEST)

User talk:Oriol

2006-08-15T15:34:57Z

Turing: /* Nombres a les peces */ reply

i wold like to make a page with hex problems

:Sounds good. May I suggest posting them on the [[Puzzles]] page? — [[User:Turing|turing]] 11:41, 25 Jun 2006 (CEST)

But I'm new in hexwiki and I'm not shure how it works. Can I create a new page? I wold like to make a "basic" hex problems for new players.

:Yes, creating a new page is perfectly ok too if you want. Just create a link somewhere, [[This page does not exist|like this]], so that you can go to the page and add content to it. Good luck! And [[Wikipedia:Wikipedia:Be bold in updating pages|be bold]]. — [[User:Turing|turing]] 15:05, 3 Jul 2006 (CEST)

I just making some test to know how wiki works

Problem X
Vertical to play and win
<hex>R9 C9 Q1 Vg3 Vf4 Vf5 Vg5 Vh6 Vh7 Ve7 Hd9 Hd7 Hc6 Hd6 Hf7 Hg7 Hi7 Hg9</hex>

Wrong
Playing in the lader don't seems good
<hex>R9 C9 Q1 Vg3 Vf4 Vf5 Vg5 Vh6 Vh7 Ve7 Hd9 Hd7 Hc6 Hd6 Hf7 Hg7 Hi7 Hg9 Vg8 Vf8 Ve8 Hf9 He9 Hd8</hex>

Correct
<hex>R9 C9 Q1 Vg3 Vf4 Vf5 Vg5 Vh6 Vh7 Ve7 Hd9 Hd7 Hc6 Hd6 Hf7 Hg7 Hi7 Hg9 Vf8</hex>

its a test

== Puzzle X2 ==
(from templates seccion)

Blue seems connected. How can Red block it?
<hex>R7 C7 Vd5 Ve6 Hd4 He4</hex>

==Solution Puzzle X2 ==

Blue is connected to the right due to A3 template.
Blue is not connected to the left. Can connect if play in b5. Then Red must to play in one of the following *

<hex>R7 C7 Vd5 Ve6 Hd4 He4 Sa5 Sa6 Sb5 Sc4 Sc5</hex>

a6, b5 and c5 can be responded by c3 connecting with A3 template

<hex>R7 C7 Vd5 Ve6 Hd4 He4 Va6 Vb5 Vc5 Hc3</hex>

a5 can be responded by c4 connecting with B3 template

<hex>R7 C7 Vd5 Ve6 Hd4 He4 Va5 Hc4</hex>

correct solution: c4
althougt it's not sure who win

<hex>R7 C7 Vd5 Ve6 Hd4 He4 Vc4</hex>

'''Note: it's only a test, not the final hex problems page. I'm testing the edit in wiki. Can somebody help me? How I can delete or modify my talk page? I only know add comments but no modify the existing ones. Thanks'''

:To edit the page, simply click the ''edit'' button at the top of this page. Until now you have presumably clicked the +, which is next to the ''edit'' and allows you to add extra comments, but not modify the earlier ones. Note that in the diagram above, blue has an easy win if he plays b3. [[User:Taral|Taral]] 19:24, 18 Jul 2006 (CEST)

==Nombres a les peces==

Ei, pel que he vist de la manera de fer-ho, ha de ser fàcil de numerar les jugades.

La cosa seria fer:

<nowiki>
<hex ordered=yes>
R7
C7
Vd5
Hd4
Ve3
Hd6
</hex>
</nowiki>

Comenta'ls als que porten el wiki si ho podrien programar. Si et diuen que no, que no en tenen ganes o no tenen temps, digue'ls que si et passen el codi font de com es fa ara hi ha algú (jo) que ho podria fer. --[[User:Viktor|Viktor]] 22:46, 13 Aug 2006 (CEST)

:Could somebody who masters the above romance language step in and serve as an interpreter? I think I understand Viktor's question, but I'm not sure if I understand all of his additional comments... Anyway, the board rendering engine is at a dead end (because it uses a non-viable combination of PHP and HTML tables), and I would love to see a different solution where we could actually make additions like this. Kindly contact me if you would like to collaborate on such an effort. — [[User:Turing|turing]] 17:34, 15 Aug 2006 (CEST)

Tournaments

2006-08-15T15:32:57Z

Turing: after the oslo event

==International Tournament 2006 in Oslo==

Took place on August 11th - 13th 2006. Photos and results can be found on [http://www.littlegolem.net/jsp/forum/topic2.jsp?forum=50&topic=244 littlegolem].

==International Tournament 2005 in Wrocław==

The first international Hex tournament was held in May 2005 in Wrocław, Poland.

Here is some information:
* a [http://masak.org/carl/wroclaw/ blog with results]
* a page with [http://www.photos-wroclaw.prv.pl/ photos from the event]

Wroclaw game 09

2006-07-08T07:06:33Z

Turing: history, boards

'''Red player:''' passenger 
'''Blue player:''' David Rydh 
'''Date:''' 2005-05-07

{|
| 1. b2 || d8
|-
| 2. f8 || i10
|-
| 3. k10 ||
|}

<hex>
R13 C13 Q1 Vb2 Hd8 Vf8 Hi10 Vk10
</hex>

{|
| 3. ... || j6
|-
| 4. i8 || f7
|-
| 5. g7 || h5
|-
| 6. i5 ||
|}

<hex>
R13 C13 Q1 Vb2 Hd8 Vf8 Hi10 Vk10 Hj6 Vi8 Hf7 Vg7 Hh5 Vi5
</hex>

{|
| 6. ... || h6
|-
| 7. i6 || h7
|-
| 8. i7 || j3
|}

<hex>
R13 C13 Q1 Vb2 Hd8 Vf8 Hi10 Vk10 Hj6 Vi8 Hf7 Vg7 Hh5 Vi5 Hh6 Vi6 Hh7 Vi7 Hj3
</hex>

{|
| 9. e7 || f6
|-
| 10. g5 || h4
|-
| 11. g6 || g4
|}

<hex>
R13 C13 Q1 Vb2 Hd8 Vf8 Hi10 Vk10 Hj6 Vi8 Hf7 Vg7 Hh5 Vi5 Hh6 Vi6 Hh7 Vi7 Hj3 Ve7 Hf6 Vg5 Hh4 Vg6 Hg4
</hex>

{|
| 12. ''resign''
|}

[[Category:Wroclaw_games]]

Wroclaw game 08

2006-07-06T17:59:12Z

Turing: boards, history

'''Red player:''' na_wspak 
'''Blue player:''' David Rydh 
'''Date:''' 2005-05-07

{|
| 1. m7 || g7
|-
| 2. e7 || e8
|-
| 3. c9 || d9
|}

<hex>
R13 C13 Q1 Vm7 Hg7 Ve7 He8 Vc9 Hd9
</hex>

{|
| 4. f7 || f9
|-
| 5. c10 || c7
|-
| 6. f8 || e9
|-
| 7. d7 || c11
|}

<hex>
R13 C13 Q1 Vm7 Hg7 Ve7 He8 Vc9 Hd9 Vf7 Hf9 Vc10 Hc7 Vf8 He9 Vd7 Hc11
</hex>

{|
| 8. d10 || c10
|-
| 9. e10 || e11
|-
| 10. g10 || h10
|}

<hex>
R13 C13 Q1 Vm7 Hg7 Ve7 He8 Vc9 Hd9 Vf7 Hf9 Vc10 Hc7 Vf8 He9 Vd7 Hc11 Vd10 Hc10 Ve10 He11 Vg10 Hh10
</hex>

{|
| 11. g11 || f10
|-
| 12. h8 || g8
|-
| 13. i6 || i5
|-
| 14. h6 || h4
|-
| 15. g6 || g3
|}

<hex>
R13 C13 Q1 Vm7 Hg7 Ve7 He8 Vc9 Hd9 Vf7 Hf9 Vc10 Hc7 Vf8 He9 Vd7 Hc11 Vd10 Hc10 Ve10 He11 Vg10 Hh10 Vg11 Hf10 Vh8 Hg8 Vi6 Hi5 Vh6 Hh4 Vg6 Hg3
</hex>

{|
| 16. d4 || e5
|-
| 17. c5 || d5
|-
| 18. g4 || h2
|-
| 19. f4 || ''resigns''
|}

<hex>
R13 C13 Q1 Vm7 Hg7 Ve7 He8 Vc9 Hd9 Vf7 Hf9 Vc10 Hc7 Vf8 He9 Vd7 Hc11 Vd10 Hc10 Ve10 He11 Vg10 Hh10 Vg11 Hf10 Vh8 Hg8 Vi6 Hi5 Vh6 Hh4 Vg6 Hg3 Vd4 He5 Vc5 Hd5 Vg4 Hh2 Vf4
</hex>

[[Category:Wroclaw_games]]

Wroclaw game 07

2006-07-03T14:57:32Z

Turing: boards, histories

'''Red player:''' Piszczyk 
'''Blue player:''' David Rydh 
'''Date:''' 2005-05-07

{|
| 1. b2 || e6
|-
| 2. h6 || i10
|}

<hex>
R13 C13 Q1 Vb2 He6 Vh6 Hi10
</hex>

{|
| 3. e8 || e9
|-
| 4. h9 || h5
|-
| 5. i5 ||
|}

<hex>
R13 C13 Q1 Vb2 He6 Vh6 Hi10 Ve8 He9 Vh9 Hh5 Vi5
</hex>

{|
| 5. ... || j3
|-
| 6. i4 || i3
|-
| 7. g4 || h4
|-
| 8. f6 || g6
|-
| 9. f8 || f9
|-
| 10. h8 || g8
|}

<hex>
R13 C13 Q1 Vb2 He6 Vh6 Hi10 Ve8 He9 Vh9 Hh5 Vi5 Hj3 Vi4 Hi3 Vg4 Hh4 Vf6 Hg6 Vf8 Hf9 Vh8 Hg8
</hex>

{|
| 11. g7 || h7
|-
| 12. j7 || i7
|-
| 13. j7 || i8
|-
| 14. j8 || g10
|-
| 15. ''resigns''
|}

<hex>
R13 C13 Q1 Vb2 He6 Vh6 Hi10 Ve8 He9 Vh9 Hh5 Vi5 Hj3 Vi4 Hi3 Vg4 Hh4 Vf6 Hg6 Vf8 Hf9 Vh8 Hg8 Vg7 Hh7 Vj7 Hi7 Vj7 Hi8 Vj8 Hg10
</hex>

[[Category:Wroclaw_games]]