HexWiki - User contributions [en]

Six

2008-02-22T10:14:59Z

Iain: /* Windows Port */

Six is a free [[Hex]] playing program running on Unix written by Gábor Melis. The currently offered version is 0.5.3. It has won [[ICGA]] Hex tournament in 2003, 2004 and 2006. Six is quite good against human beings too.

==Features==

*It allows playing form [[board size|size]] 4 to 15.
*It offers 4 different skill levels.
*Games as well as positions can be saved.

==Windows Port==
Six has been adapted to Windows by [http://www.littlegolem.net/jsp/info/player.jsp?plid=6603 ab]. The project came out [http://www.littlegolem.net/jsp/forum/topic2.jsp?forum=50&topic=301 a thread] in the [[Little Golem]] forum. "ab" separated the GUI from the Six engine, thus creating HexGui, inspired by GoGui.

To play the AI:
*Put HexGui.jar and six_gtp_engine.exe in one directory
*Double-click on HexGui.jar (or use "java -jar HexGui.jar")
*File menu / attach / "six_gtp_engine.exe --level=0"
*F5 to make a computer move, or
*Game menu / Computer plays / "Black" or "White" or "Both"

While the computer makes a move, which can take a while at expert level, you cannot access all the program functions.
The two zip files full of source code are unnecessary to play.

==See also==

[[Hexy]] is another Hex playing program. Hexy runs on Microsoft Windows.

[[Roland Illig vs. Six 0.5.3, 2007-09-28]].

==External links==

[http://six.retes.hu/ Six on Gábor Melis page].

[http://mgame99.mg.funpic.de/havannah.php Download Windows version].

[http://www.grappa.univ-lille3.fr/icga/round.php?tournament=100&round=1 8 games between Six and Mangoose] in the 8th Computer Olympiad in Graz (2003).

==References==

[http://www.littlegolem.net/jsp/forum/topic2.jsp?forum=50&topic=294 Six is pretty damn strong on a fast machine] a forum topic by David J Bush (top hex rating > 2150 on [[Little Golem]]).

[[category:Computer Hex]]

Six

2008-02-19T17:53:41Z

Iain: /* Windows Port */

Six is a free [[Hex]] playing program running on Unix written by Gábor Melis. The currently offered version is 0.5.3. It has won [[ICGA]] Hex tournament in 2003, 2004 and 2006. Six is quite good against human beings too.

==Features==

*It allows playing form [[board size|size]] 4 to 15.
*It offers 4 different skill levels.
*Games as well as positions can be saved.

==Windows Port==
Six has been adapted to Windows by [http://www.littlegolem.net/jsp/info/player.jsp?plid=6603 ab]. The project came out [http://www.littlegolem.net/jsp/forum/topic2.jsp?forum=50&topic=301 a thread] in the [[Little Golem]] forum. "ab" separated the GUI from the Six engine, thus creating HexGui, inspired by GoGui.

To play the AI:
*Put HexGui.jar and six_gtp_engine.exe in one directory
*Double-click on HexGui.jar (or use "java -jar HexGui.jar")
*File menu / attach / "six_gtp_engine.exe --level=0"
*F5 to make a computer move, or
*Game menu / Computer plays / "Black" or "White" or "Both"

While the computer makes a move, which can take a while at expert level, you cannot access all the program functions.
The two zip files full of source code are unnecessary to play.

The Windows port of Six is considerably slower than the original Linux version.

==See also==

[[Hexy]] is another Hex playing program. Hexy runs on Microsoft Windows.

[[Roland Illig vs. Six 0.5.3, 2007-09-28]].

==External links==

[http://six.retes.hu/ Six on Gábor Melis page].

[http://mgame99.mg.funpic.de/havannah.php Download Windows version].

[http://www.grappa.univ-lille3.fr/icga/round.php?tournament=100&round=1 8 games between Six and Mangoose] in the 8th Computer Olympiad in Graz (2003).

==References==

[http://www.littlegolem.net/jsp/forum/topic2.jsp?forum=50&topic=294 Six is pretty damn strong on a fast machine] a forum topic by David J Bush (top hex rating > 2150 on [[Little Golem]]).

[[category:Computer Hex]]

Six

2008-02-19T10:48:43Z

Iain: added Windows port section

Six is a free [[Hex]] playing program running on Unix written by Gábor Melis. The currently offered version is 0.5.3. It has won [[ICGA]] Hex tournament in 2003, 2004 and 2006. Six is quite good against human beings too.

==Features==

*It allows playing form [[board size|size]] 4 to 15.
*It offers 4 different skill levels.
*Games as well as positions can be saved.

==Windows Port==
Six has been adapted to Windows by "ab". The project came out this thread [http://www.littlegolem.net/jsp/forum/topic2.jsp?forum=50&topic=301] in the [[Little Golem]] forum. "ab" separated the GUI from the Six engine, thus creating HexGui, inspired by GoGui.

To play the AI:
*Put HexGui.jar and six_gtp_engine.exe in one directory
*Double-click on HexGui.jar (or use "java -jar HexGui.jar")
*File menu / attach / "six_gtp_engine.exe --level=0"
*F5 to make a computer move, or
*Game menu / Computer plays / "Black" or "White" or "Both"

While the computer makes a move, which can take a while at expert level, you cannot access all the program functions.
The two zip files full of source code are unnecessary to play.

The Windows port of Six is considerably slower than the original Linux version.

==See also==

[[Hexy]] is another Hex playing program. Hexy runs on Microsoft Windows.

[[Roland Illig vs. Six 0.5.3, 2007-09-28]].

==External links==

[http://six.retes.hu/ Six on Gábor Melis page].

[http://mgame99.mg.funpic.de/havannah.php Download Windows version].

[http://www.grappa.univ-lille3.fr/icga/round.php?tournament=100&round=1 8 games between Six and Mangoose] in the 8th Computer Olympiad in Graz (2003).

==References==

[http://www.littlegolem.net/jsp/forum/topic2.jsp?forum=50&topic=294 Six is pretty damn strong on a fast machine] a forum topic by David J Bush (top hex rating > 2150 on [[Little Golem]]).

[[category:Computer Hex]]

Edge templates with one stone

2008-02-19T00:07:25Z

Iain: /* Sixth row edge template */

Here you can see all known [[Edge template|edge templates]] with one stone to be connected to the bottom row. Not all of them are useful to know. The [[Fifth row|fifth-row]] [[template]] occurs very seldom in real play.

There is some overlap with the article [[Edge templates everybody should know]].

== First row edge template ==
<hex>R1 C1 Va1</hex>

== Second row edge template ==
<hex>R2 C2 Vb1 Sa1</hex>

== Third row edge templates ==
=== [[defending against intrusions in template 1-IIIa|edge template III1a]] ===
[[Image:Ziggurat.png]]

=== [[defending against intrusions in template 1-IIIb|edge template III1b]] ===
[[Image:Template-1-3b.png]]



== Fourth row edge templates ==
=== [[defending against intrusions in template 1-IVa|edge template IV1a]] ===
[[Image:Template-1-4a.png]]

=== [[edge template IV1b]] ===
[[Image:Template-1-4b.png]]

=== [[edge template IV1c]] ===
<hex> R5 C11
Sa1 Sb1 Sc1 Sd1 Se1 Sf1 Sj1 Sk1
Sa2 Sb2 Sc2 Sd2 Vf2 Sk2
Sa3 Sb3
Sa4
Sc5 </hex>

== [[edge template V1|Fifth row edge template]] ==
<hex>R5 C10 Vg1 Sa1 Sa2 Sa3 Sa4 Sb1 Sb2 Sb3 Sc1 Sc2 Sd1 Sd2 Se1 Si1 Sj1 Sj2</hex>
== Sixth row edge template ==
There are almost certainly no edge templates with one stone on the [[Sixth row|sixth row]], but this is unproven.

[[Category: Edge templates]]

Intermediate (strategy guide)

2008-02-17T21:05:52Z

Iain: /* Groups */ correction

''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 [[overlapping connections|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 ==

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]]).

In the templates, all points that are irrelevant for the connection are marked with a star. Important points are marked with a plus, and everything else is left empty.

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

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

<hex>R2 C3 Q1 1:BRB 2:BRB</hex>

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

<hex>R3 C4 Q1 1:BBRB 2:BBRB 3:B__B</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 C6 Q1
1:BBBRBB
2:BBBR_B
3:BB+_+B
4:B____B
</hex>

If the opponent intrudes on the template, then Red plays at one of the two marked points achieving [[template II]]. Since the c3 template and the two-chain/e3 template combination don't overlap, the opponent cannot stop both. (This template exists in a mirror image form with the red piece at e2).

=== See also ===

Continue with the page [[Edge templates everybody should know]].

== 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.

<hex>R9 C9 Q1 Ve3 Vd4 Vd5 Vc6 Vc7 Hb8 Hb9 Hd7 He6 Hf6
Mc8 Mc9 Md8 Md9 Me8 Me9 Mf8 Mf9</hex>

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 Mc8 Mc9 Md8 Md9 Me8 Me9 Mf8 Mf9 Mg8</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 template]])

* [[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 Hc6 Hd6 He7 Hf7 Hg7 Hi7 Hg9 +c7 +b8 +c8 +d8 +a9 +b9 +c9 +d9 Md7</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 Hc6 Hd6 Hd8 He6 He7 Hf7 Hg7 Hi7 Hg9 Md7 Md8 Mc8 Me6</hex>

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

<hex>R9 C9 Q1 Vg3 Vf4 Vf5 Vg5 Vh6 Vh7 Hc6 Hd6 Hf7 Hg7 Hi7 Hg9 +c7 +b8 +c8 +d8 +a9 +b9 +c9 +d9 Md7</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 Hc6 Hd6 Hf7 Hg7 Hi7 Hg9 Md7 Md8 Mc8 Me6</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 Hc6 Hd6 Hf7 Hg7 Hi7 Hg9 Md7 Md8 Mc8 Me6 Mg8 Mf9 Mf8 Me9 Me8</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 [[red|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 Me8 Me7 Mg7 Mf9 Mf8</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 Mh2 Mg2 Mi3</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 Mb3 Mc3</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 Q1 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 [[overlapping connections|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 Making the Right Connections|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 c4 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 [[offense equals defense|offence equals defence]] 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 [[strategy|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.

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

[[category:strategy]]

Basic (strategy guide)

2008-02-17T17:41:29Z

Iain: /* Offense equals defense */

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

== Rules of Hex ==
''(See also the article [[Rules]])''

[[Hex]] is a two player [[Wikipedia:Board_game|board game]] played on an ''n × n'' grid of [[hexagon]]s.

A [[Move|turn]] in Hex consists of placing a [[piece]] of your [[color]] on a [[Hex (board element)|hexagon]]. The [[first player]]'s goal is to form an unbroken [[chain]] of hexes of his color that [[connection|connects]] the [[top edge|top]] to the [[bottom edge|bottom]] while the [[second player]] tries to form an unbroken chain connecting the [[left edge|left]] and [[right edge|right]] sides.

[[Swap rule]]: After the initial play only, the second player has the option of either responding with his turn or swapping sides taking the initial play as his first turn.

Without the swap rule, the first player has a strong [[advantage]]. The swap rule equalizes this advantage by forcing the first player to make a move that leads to a roughly equal game. If the first player makes a very strong opening move, the second player will swap sides and start with an advantage. If the first player makes a very weak opening move, the second player won't swap and again will start with an advantage.

== Basic strategy ==

Notation: the [[row]]s of the board are [[coordinates|indexed]] by numbers and the [[column]]s are indexed by letters. Individual hexes are referred to by listing the column index followed by the row index; e.g. hex c2 is the one in column c row 2. Here at [[HexWiki:About|HexWiki]], red pieces belong to the [[vertical (player)|"vertical" player]], and blue pieces belong to the [[horizontal (player)|"horizontal" player]]. An empty 4 × 4 board looks like follows.

<hex>R4 C4 Q1</hex>

=== The two-bridge ===
''(See also the article [[Bridge]])''

The [[pattern|formation]] consisting of two pieces that are [[non-adjacent]] but have two empty [[adjacent|neighboring]] hexes in common is referred to as a [[bridge|two-bridge]]; e.g. the pieces on b2 and c3, and the [[empty hex]]es b3 and c2 in the following diagram form a two-bridge.

<hex>R4 C4 Q1 Vb2 Vc3</hex>

The two pieces are almost as strongly connected as a solid chain from b2 to c3. The opponent can attempt to break this connection only by playing a piece at either b3 or c2, and no matter which one the opponent plays, you can play the other and restore the link. For most purposes you can think of the two-bridge pieces as already being connected. By connecting pieces via two-bridges, you can spread across the board twice as fast as by playing adjacent hexes.

{| border="0" cellpadding="2"
| <hex>R7 C7 Q1 Ve1 Ve2 Vd3</hex> || <hex>R7 C7 Q1 Ve2 Vd4 Vc6</hex>
|-
| <center>''Expanding by adjacent moves''</center> || <center>''Expanding by two-chains''</center>
|}

Considered in isolation the pieces in a two-chain are [[strong connection|connected]] but sometimes a two-chain can be broken by playing a piece in the middle of a two-chain that contains some other [[threat]] that must be immediately answered. After the opponent answers the threat, you can then play in the other hex in the two-chain breaking the connection.

Also, playing in the middle of a two-chain can be a good play even when the opponent should and does respond by saving the link. The reason being that the piece played may be useful later.

=== Blocking moves ===

When you have no pieces in the area, it is usually best to start blocking at a distance. If you block too close, then the opponent can simply flow around the attempted block. For example, suppose you are trying to stop the vertical player from connecting to the bottom in the following diagram.

<hex>R11 C11 Q1 Vh1 Vh2 Vh3 Vg4 Vg5 Vg6</hex>

If you try to block by playing adjacent to the [[leading piece]], say by playing at g7, then the vertical player can simply step around it at f7 (see diagram below). Then the attempted block at say e8, could similarly be met by playing at f8. Obviously, you are not making any progress here.

<hex>R11 C11 Q1 Vh1 Vh2 Vh3 Vg4 Vg5 Vg6 MH Mg7 Mf7 Me8 Mf8</hex>

Another try from the original position would be to block at a two-chain distance away at f8 (see diagram below). This is better than the [[adjacent block]] but sometimes the opponent can flow around this too by two-chaining at an angle — e.g. by playing h7 in response to f8. (h7 should be met by either h8 or g9.)

<hex>R11 C11 Q1 Vh1 Vh2 Vh3 Vg4 Vg5 Vg6 MH Mf8 Mh7</hex>

Another possibility is to combine the above two ideas by first doing an adjacent block at g7 and then if the vertical player responds with f7, you block at a two-chain distance away at e9. Then your opponent cannot two-chain towards the right because of the initial g7 piece.

<hex>R11 C11 Q1 Vh1 Vh2 Vh3 Vg4 Vg5 Vg6 MH Mg7 Mf7 Me9</hex>

A good block in the original position is to block at one hex farther back than the two-chain block at either e9 or f9 (sometimes this is referred to as the [[classic block]]). For example suppose H blocks at f9 (see diagram below). Two-chaining to f8 is met by e9. Two-chaining to the lower right (h7) is met by h8 and two-chaining towards the lower-left (e7) is met by d8. By blocking at a distance, you have a move or two before the advancing head reaches the blocking pieces. Note that when the board size is smaller than 11 × 11, then the classic block is much less useful due to the lack of space.

<hex>R11 C11 Q1 Vh1 Vh2 Vh3 Vg4 Vg5 Vg6 MH Mf9 Mf8 Me9 Mh7 Mh8 Me7 Md8</hex>

== General principles ==

=== A position is only as good as the weakest link ===
''(See also the page [[Weakest link]])''

Thus, with each move you should attempt to either improve your weakest link or make your opponent's weakest link even weaker. A move which does both is a strong move. For example, in the position below the hex f6 is the weakest point in the Red's best connection across the board. It is also the weakest link in the Blue's best connection across the board. Thus, the player whose turn it is to move would be wise to play at f6. In fact, whoever plays next has a forced win after playing f6.

<hex>R11 C11 Q1 Vh2 Vg4 Hb5 Hh5 Hc6 Sf6 Hi6 Ve8 Vd10</hex>

=== Offense equals defense ===
''(See also the page [[Offense equals defense]])''

In Hex, good [[offense]] and good [[defense]] are entirely equivalent. If you complete a connection between your sides, then your opponent is prevented from completing theirs. Conversely, if your opponent is prevented from completing a connection, then you must have completed yours (draws cannot occur in Hex). Furthermore, the only way to complete a connection is to prevent your opponent from making a connection and the only way to prevent your opponent from connecting is to complete your connection. In a very real sense, you don't have to worry about whether you should play offensively or defensively since they are the same. The critical point to remember is that unless you are making a sequence of [[forcing move|forcing plays]], it is generally easier to think in terms of good defense than good offense regardless of whether you are currently winning or losing. This point about thinking defensively should frequently be used with point 3.1 above. Often it is best to look for the connection that your opponent is going to have the toughest time making (point 3.1 above). For example, suppose that my opponent's most difficult connection to complete looks like the connection to the right edge of the board. Then I'll look for good defensive moves that make it even more difficult for my opponent to connect up to the right edge.

=== Momentum ===
''(See also the page [[Momentum]])''

The player who is dictating the play is said to have the '''momentum'''. Alternatively, the momentum is against the player who is being forced to respond to the opponent. The player with the momentum usually has the advantage and this advantage is often decisive. You should generally not hand over the momentum to the opponent unless you have a very good reason for doing so. In well played close matches, the momentum often swings between the two players with each move.

=== Multiple threats per move ===
''(See also the page [[Multiple threats]])''

Whenever possible, a player should make each move achieve at least two different goals or threats. Moves that contain only a single threat are generally not hard to meet. If a move contains multiple threats, the opponent may not be able to stop all the threats with a single move.

=== The center ===

The central region of the board is strategically the most important area. From the center, connections can spread out in many directions giving you more flexibility and options than starting from an edge. Furthermore, centrally played pieces are more nearly equidistant from both of your edges — this is related to point 3.1 about improving your weakest link. The greater distance apart two pieces are, the harder they are to connect up, i.e. their potential link is weaker.

== The opening ==

Without the [[swap rule]], the initial move would be easy. Playing in the [[center hex]] is the strongest opening move. The weakest opening move is to play in one of the acute corners (a1 and the opposite corner) and is one of only two opening moves that are a proven loss (without the swap option). The other is right next to it at b1. Suppose the [[red|vertical player]] moves first. Which opening moves should you swap and which should you not swap? The following is my personal rules for the 10 × 10 board.

=== 10 × 10 swap rules ===

# Don't swap any of Vertical's border row moves except for the obtuse corner.
# Don't swap a2, or b2 (nor the symmetrically equivalents i9 and j9).
# Swap all other initial moves.

Note: the possible theoretical exceptions to these rules are the opening moves a2, b2, c2 and a3 (and their symmetric equivalents). The winning/losing margin with these moves is so razor thin that nobody has been able to determine with any confidence whether these moves should theoretically be swapped or not.

=== Good opening moves on the 10 × 10 ===

The best opening moves against an experienced player are the [[border hex]]es (except don't open a1!) and b2 and c2. b2—d2 are probably the only good non-border moves against an experienced player (b2 is essentially equivalent to the move a2 which is a popular opening choice and there is almost no difference between b2 and c2). Against lesser experienced players you can play something stronger such as one out from the obtuse corner (b9/i2) because they might not realize its strength and even if they do swap, they may not be capable of taking advantage of it anyway.

a2/b2 and a3 both lead to a balanced game and seem to be the most popular choices. Except for games between expert players, you can safely play either side of a2/b2 or a3 and have an equal chance of winning (and similarly for other opening plays). Also some variation in opening play is generally good. Varying your opening is the first thing to try against an opponent that seems to have your number. Sometimes you can find a weakness in a player's personal swap rules by trying out different openings.

=== The second and third moves ===

A very common but not the only good response to a border opening is to play in one of the two central hexes e6 or f5. The third move in response to a central reply should be a blocking move on the side of e6/f5 that is farthest from the edge. e6 is one hex closer to the left edge and f5 is one hex closer to the right edge. In accordance with the principle of exploiting your opponent's weakest link, you should therefore block f5 on the left and e6 on the right. Thus, a typical opening sequence would be a2, ''swap'', f5, c6. In my opinion, the strength of the central response is overrated; practically any move that is not in one of the 3 rows closest to your border rows and that is also not too close to the opponent's border, is a near equally good response. If there is any difference in strength, it is for all practical purposes non-existent.

== Board size ==

Hex can be played on any size [[board]]. If the board is [[Small boards|too small]], the game becomes trivial and uninteresting. The "standard" size at the online site [[PlaySite]] is 10 × 10 but in my opinion, this is just a little too small and the "standard" size should really be 11 × 11 (11 × 11 is the standard size at [[pbmserv|the PBM play by email site]]). Some experienced players prefer a larger board such as 14 × 14 or 17 × 17. As the board size gets larger and larger, the game becomes more subtle and strategic. Hex is actually of comparable complexity and depth to the oriental board game [[Go]] played on the same size board (many Go players consider Go to be the deepest and most complex perfect information strategy game ever invented).

A typical hex game fills about one-third of the board. We can use this to get a good estimate of the average number of moves for any board size.

* 10 × 10: 16 moves per side
* 11 × 11: 20 moves per side
* 14 × 14: 28 moves per side
* 17 × 17: 48 moves per side
* 19 × 19: 60 moves per side (this is the standard size in Go)

One of the pleasant aspects of Hex is that games generally do not last as long as in other strategy games of comparable complexity (e.g. Go typically lasts around 100 moves per side). The 11 × 11 game is very good and takes only about 20 moves per side. For those wanting a more complex game, the 14 × 14 game provides it without having the length of the game blow up to marathon proportions.

== Reference bibliography ==

''Hex Strategy: Making the Right Connections'', by Cameron Browne, A.K. Peters Ltd., 2001. — The strategy part of this book is generally very sound. The primary exception is that the suggested opening swap rules are not correct at all.

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

[[category:strategy]]