HexWiki - User contributions [en]

Small boards

2009-02-05T21:50:11Z

Javerberg: /* Winner depending on the first move */

Playing [[Hex]] on [[board]]s of size smaller than 10 × 10 is not very interesting, since many players will be able to play almost perfectly. However it may still be intersting for theoretical studies, and for making [[Puzzles|problems]].

The boards of size up to five can be solved by hand. Hex on 6 × 6 has been solved by [[Queenbee]].

Here are the winning first moves on the small boards. [[Red (player)|Red]] is vertical and plays first. The [[Hex (board element)|cells]] containing a red [[Piece|stone]] are winning moves for red, while those containing a blue stone are losing. For more details, visit Queenbee's own [http://www.cs.ualberta.ca/~queenbee/openings.html opening page].

''Update:'' The 7 × 7 board has been solved by [[Ryan Hayward|R. Hayward]], et.al. For more details, visit http://www.cs.ualberta.ca/~hayward/hex7trees/

== Winner depending on the first move ==
The following boards can help you decide where you should [[swap]] when playing on small boards, and it might give you ideas of patterns for bigger boards.
<hex>R2 C2 Q1 Vb1 Va2 Ha1 Hb2</hex>

<hex>R3 C3 Q1 Va2 Va3 Hb1 Vb2 Hb3 Vc1 Vc2 Ha1 Hc3</hex>

<hex>R4 C4 Q1 Va4 Vb3 Vc2 Vd1 Ha1 Ha2 Ha3 Hb1 Hb2 Hb4 Hc1 Hc3 Hc4 Hd2 Hd3 Hd4</hex>

<hex>R5 C5 Q1 Ve1 Vb2 Vc2 Vd2 Ve2 Vb3 Vc3 Vd3 Va4 Vb4 Vc4 Vd4 Va5 Ha1 Ha2 Ha3 Hb1 Hc1 Hd1 Hb5 Hc5 Hd5 He5 He4 He3</hex>

<hex>R6 C6 Q1 Ve1 Vb2 Vc2 Vd2 Ve2 Vb3 Vc3 Vd3 Va4 Vb4 Vc4 Vd4 Va5 Ha1 Ha2 Va3 Hb1 Hc1 Hd1 He1 Vb5 Vc5 Vd5 Ve5 Ve4 Ve3 Vf1 Vf2 Vf3 Vf4 Hf5 Hf6 He6 Hd6 Hc6 Hb6 Va6</hex>

=== Size 7 ===

Size 7 was first solved by [[Ryan Hayward]] using [[domination]].

<hex>R7 C7 Q1 Ha1 Hb1 Hc1 Hd1 He1 Hf1 Vg1 Ha2 Hb2 Vc2 Hd2 Ve2 Vf2 Vg2 Ha3 Vb3 Vc3 Vd3 Ve3 Vf3 Hg3 Va4 Vb4 Vc4 Vd4 Ve4 Vf4 Vg4 Ha5 Vb5 Vc5 Vd5 Ve5 Vf5 Hg5 Va6 Vb6 Vc6 Hd6 Ve6 Hf6 Hg6 Va7 Hb7 Hc7 Hd7 He7 Hf7 Hg7</hex>

=== Size 8 ===

The outcomes for size 8 were computer generated by [[Javerberg]].

<hex>
R8 C8 Q1
Ha1 Hb1 Hc1 Hd1 He1 Hf1 Hg1 Vh1
Ha2 Hb2 Hc2 Hd2 He2 Hf2 Vg2 Vh2
Ha3 Vb3 Vc3 Vd3 Ve3 Vf3 Vg3 Hh3
Ha4 Vb4 Vc4 Vd4 Ve4 Vf4 Vg4 Vh4
Va5 Vb5 Vc5 Vd5 Ve5 Vf5 Vg5 Hh5
Ha6 Vb6 Vc6 Vd6 Ve6 Vf6 Vg6 Hh6
Va7 Vb7 Hc7 Hd7 He7 Hf7 Hg7 Hh7
Va8 Hb8 Hc8 Hd8 He8 Hf8 Hg8 Hh8
</hex>

== Reference ==
* [[Queenbee]]'s opening [http://www.cs.ualberta.ca/~queenbee/openings.html page] is a reference for sizes under 6x6.
* This [http://www.ru.is/faculty/yngvi/pdf/HaywardBJKPR05.pdf article] by Ryan Hayward ''et al.'' is a reference for 7x7.
* This [[Little Golem]]'s forum [http://www.littlegolem.net/jsp/forum/topic2.jsp?forum=50&topic=338 thread] is a reference for size 8x8.

== See also ==

* [[Board size]]
* [[Jing Yang]] designed a [[decomposition method]] to find winning strategy in Hex. [http://www.ee.umanitoba.ca/~jingyang/index.html Home Page].

[[Category: Theory]]

Opening

2009-02-04T18:31:07Z

Javerberg:

The '''opening''' is the first few moves of a [[Hex]] game. Exactly how many moves are considered part of the opening varies depending on the type of opening, and also on whom you ask. Typically, however, the two first moves are always considered part of the opening.

== Opening Theory ==

The two most basic questions in the opening theory of Hex are:

* Where should I play my first move?
* Should I [[swap]]?

The two questions are closely related. The situation is probably most difficult for the [[first player]] — his move should not be too strong, since the [[second player]] then will [[swap]], but it should not be too weak either, as the second player then will decline the swap and have [[Advantage|a better situation]]. So the first player has to find a move which gives about equal chances to both players.

=== The first move ===

Fortunately strong players have thought thoroughly through this, and there are certain moves that are considered to be about equal, which one can safely play. For example are a2, a3 and b2 quite common opening moves.

But these moves are only suggestions, and there are many other moves that may be tried such as a4, a8, a6 or a10 (on a 10 × 10 board).

=== Swapping ===

When to swap? One commonly used rule of thumb is to swap any opening, except if the first move was played on the [[first row]], adjacent to a [[friendly edge]], and not in the [[obtuse corner]]. You may also check out [[winning opening moves for small boards]].

[[Swap|Detailled article : Swap]]

== External link==

[http://www.f.kth.se/~rydh/Hex/openings.html Jonatan Rydh's page on openings]

== Openings deserving their own articles ==

* [[A2 opening]]
* [[A3 opening]]
* [[B2 opening]]
* [[Center opening]]
* [[A1 opening]]
* [[Obtuse corner opening]]
* [[The Hungarian (opening)]]

[[category:opening]]

Opening

2009-02-04T18:30:36Z

Javerberg:

The '''opening''' is the first few moves of a [[Hex]] game. Exactly how many moves are considered part of the opening varies depending on the type of opening, and also on whom you ask. Typically, however, the two first moves are always considered part of the opening.

== Opening Theory ==

The two most basic questions in the opening theory of Hex are:

* Where should I play my first move?
* Should I [[swap]]?

The two questions are closely related. The situation is probably most difficult for the [[first player]] — his move should not be too strong, since the [[second player]] then will [[swap]], but it should not be too weak either, as the second player then will decline the swap and have [[Advantage|a better situation]]. So the first player has to find a move which gives about equal chances to both players.

=== The first move ===

Fortunately strong players have thought thoroughly through this, and there are certain moves that are considered to be about equal, which one can safely play. For example are a2, a3 and b2 quite common opening moves.

But these moves are only suggestions, and there are many other moves that may be tried such as a4, a8, a6 or a10 (on a 10 × 10 board).

=== Swapping ===

When to swap? One commonly used rule of thumb is to swap any opening, except if the first move was played on the [[first row]], adjacent to a [[friendly edge]], and not in the [[obtuse corner]]. You may also check out [winning opening moves for small boards]].

[[Swap|Detailled article : Swap]]

== External link==

[http://www.f.kth.se/~rydh/Hex/openings.html Jonatan Rydh's page on openings]

== Openings deserving their own articles ==

* [[A2 opening]]
* [[A3 opening]]
* [[B2 opening]]
* [[Center opening]]
* [[A1 opening]]
* [[Obtuse corner opening]]
* [[The Hungarian (opening)]]

[[category:opening]]

Opening

2009-02-04T18:29:02Z

Javerberg:

The '''opening''' is the first few moves of a [[Hex]] game. Exactly how many moves are considered part of the opening varies depending on the type of opening, and also on whom you ask. Typically, however, the two first moves are always considered part of the opening.

== Opening Theory ==

The two most basic questions in the opening theory of Hex are:

* Where should I play my first move?
* Should I [[swap]]?

The two questions are closely related. The situation is probably most difficult for the [[first player]] — his move should not be too strong, since the [[second player]] then will [[swap]], but it should not be too weak either, as the second player then will decline the swap and have [[Advantage|a better situation]]. So the first player has to find a move which gives about equal chances to both players.

=== The first move ===

Fortunately strong players have thought thoroughly through this, and there are certain moves that are considered to be about equal, which one can safely play. For example are a2, a3 and b2 quite common opening moves.

But these moves are only suggestions, and there are many other moves that may be tried such as a4, a8, a6 or a10 (on a 10 × 10 board).

=== Swapping ===

When to swap? One commonly used rule of thumb is to swap any opening, except if the first move was played on the [[first row]], adjacent to a [[friendly edge]], and not in the [[obtuse corner]]. You may also check out winning opening moves for [[smaller boards]].

[[Swap|Detailled article : Swap]]

== External link==

[http://www.f.kth.se/~rydh/Hex/openings.html Jonatan Rydh's page on openings]

== Openings deserving their own articles ==

* [[A2 opening]]
* [[A3 opening]]
* [[B2 opening]]
* [[Center opening]]
* [[A1 opening]]
* [[Obtuse corner opening]]
* [[The Hungarian (opening)]]

[[category:opening]]