HexWiki - User contributions [en]

Parallel ladder

2012-11-09T15:27:20Z

Hex player1: +category

A [[parallel ladder]] is a situation in which the attacker can make two [[ladder]]s on top of each other.

== 2nd and 4th rows ==

=== In game ===

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 [[connection|connected]] to the [[Top edge|top]]. At the bottom, Red has a [[second row]] ladder with no possible [[ladder 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 N:on Vf9 Hf10 Vh9 Hg9 Vh8 Hg8 Vh7</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 (player)|Blue]] stop Red from connecting to the bottom? d9 lets Red [[bridge|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 move|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 [[Multiple threats|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 [[blocking|blocks]] this, say with 11...g5, then Red continues 12.i3 i2 13.h3 h2 and 14.g3 completes the [[win]].

=== Conceptualisation ===

Here are presented the essential features of the '''parallel lader trick''' on 2nd and 4th row.

The star marked fields must be connected to the top edge.

<hex>R7 C6
Ha1 Hb1 Vc1 Hd1 He1 Sf1
Ha2 Hb2 Vc2 Sd2
Ha3 Vb3 Hc3
Ha4 Vb4 Sc4
Va5 Hb5
Sa6 </hex>

Note that every blue move is [[forcing move|forced]]. In the following diagram, the threat is connecting to bottom edge with a [[ziggurat]].
<hex>R7 C6
Ha1 Hb1 Vc1 Hd1 He1
Ha2 Hb2 Vc2
Ha3 Vb3 Hc3
Ha4 Vb4 V1c4 V3d4
Va5 Hb5 H2c5 H4d5
</hex>

<hex>R7 C6
Ha1 Hb1 Vc1 Hd1 He1
Ha2 Hb2 Vc2
Ha3 Vb3 Hc3
Ha4 Vb4 Vc4 Vd4
Va5 Hb5 Hc5 Hd5
V1a6 V3b6 V5c6 V7d6 V9f6
H2a7 H4b7 H6c7 H8d7
</hex>

<hex>R7 C6
Ha1 Hb1 Vc1 Hd1 He1
Ha2 Hb2 Vc2
Ha3 Vb3 Hc3
Ha4 Vb4 Vc4 Vd4 H6e4 V5f4
Va5 Hb5 Hc5 Hd5 H4e5 V3f5
Va6 Vb6 Vc6 Vd6 H2e6 Vf6
Ha7 Hb7 Hc7 Hd7
</hex>

Finally Red is assured to connect to top edge.

<hex>R7 C6
Ha1 Hb1 Vc1 Hd1 He1
Ha2 Hb2 Vc2 Se2 V3f2
Ha3 Vb3 Hc3 H2e3 V1f3
Ha4 Vb4 Vc4 Vd4 He4 Vf4
Va5 Hb5 Hc5 Hd5 He5 Vf5
Va6 Vb6 Vc6 Vd6 He6 Vf6
Ha7 Hb7 Hc7 Hd7
</hex>
== 3rd and 5th rows ==

It is possible to use this trick off from one row farther back; i.e. with ladders on the [[third row|third]] and [[fifth row]] but this occurs far less frequently and one has 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 the [[second row]], 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 edge|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 presence 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!

== A parallel ladder trick puzzle==

Consider the following position with Red to play.
<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>

The solution is 1.f8 (this is, essentially, [[Tom's move]]). Let's see what are Blue's options.

=== Blue plays 2.d9===
2.d9 3.e7 makes easy connection with [[edge template IIIa]]

<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
N:on Vf8 Hd9 Ve7</hex>

=== Blue plays 2.e8===
2.e8 is not better :
3.c9 4.c10 5.d9 6.d10 7.e9 8.e10 9.g9 connects through [[edge template III2b]] linking to bottom.

<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 Vf8

Hb10
MB M2e8
N:on Vc9 Hc10 Vd9 Hd10 Ve9</hex>

=== Blue plays 2.e9 ===
2.e9 is the best move in almost all situations like this, but it does not work here: 3.c9 4.c10 5.d9 6.d10 7.g7.

Group g7,f8 is connected to bottom thanks to [[edge template IV2b]]. And it is connected to the big group with either f6 or e8

<hex>R10 C10 Q1
Hc1
Vd2
Vd3 He3 Vf3
Vd4 Ve4 Hf4 Hg4
Ve5 Hh5
Vc6 Vd6 He6 Sf6 Hi6
Hc7 Vd7
Ha8 Hb8 Vc8 Hd8 Se8 Vf8

Hb10
MB M2e9
N:on Vc9 Hc10 Vd9 Hd10 Vg7</hex>

Red 3.c9 could not be e7 nor d9 ... try to think why.

[[category:ladder]]
[[category:Advanced Strategy]]

Basic (strategy guide)

2012-11-09T12:38:30Z

Hex player1: +category

''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 hexagon. The [[first player]]'s goal is to form an unbroken [[chain]] of hexes of his color that [[connection|connects]] the top to the bottom while the [[second player]] tries to form an unbroken chain connecting the left and 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 formation consisting of two pieces that are non-adjacent but have two empty neighboring hexes in common is referred to as a [[bridge|two-bridge]]; e.g. the pieces on b2 and c3, and the empty hexes 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 broadly close to at least one of your edges and not too close to the opponent's piece.

If your blocking move has too little influence on both your edges, then the opponent has at least two good zones of the board that are worth trying, one for each side. For example, compare the situation for blue in these two cases.

<hex>R11 C11 Q1 MV Mf6 Me9 Mg8 Mf7 Mh6 Mh9 Mc9</hex>

In this case, the blue initial pieces (E9 and F7) have very little influence on both blue's edges and thus don't provide any immediate threat on bottom. Blue has no choice but to play D8, which however is still far from being connected to any blue's edge.

<hex>R11 C11 Q1 MV Mf6 Mf8 Me8 Mf7 Me7 Md3</hex>

This position on the other hand is quite more tricky for red to play correctly than the first. Blue is still too much focused (unavoidably, given the weak position) on bottom but, after having obtained a reasonable influence on the right side, he can now concentrate his efforts on the left side of the board.

If you block too close to the opponent, then he 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>

Suppose Red opens with G4 and Blue plays E6 yielding the following.

<hex>R10 C10 Q1 Vg4 He6</hex>

Blue's play is what I call an indirect block; it does not directly block the Red G4 from the bottom rather it threatens to block it on the next move. Red
cannot afford to ignore this threat. If for example Red plays G3, Blue responds
with G5 completely cutting off Red's pieces from the bottom.

<hex>R10 C10 Q1 Vg4 Vg3 He6 MH Mg5</hex>

Instead Red can play towards the bottom with F6 and blue can complete his block
by playing E8 for example.

<hex>R10 C10 Q1 Vg4 He6 MV Mf6 Me8</hex>

Blocking Summation 
The most important thing for a beginner to do is to avoid the mistake of repeatedly trying to block by playing adjacent to the head of the chain as shown in the first example. Playing ahead of the chain as in the classic block gives you a move or two to place your pieces before the advancing chain meets your pieces.

== 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.

Update: The top players now show a definite preference for non-central responses. On the 13 by 13 game at littlegolem, most of the top players prefer to respond to a border opening with something on the 5'th row from one of their edges over the central response G7. I.e. the consensus is that responding to a border opening by playing in the center is NOT the best reply!

== 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 140 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:opening]]
[[category:Basic Strategy]]

Talk:Kurnik

2008-08-12T18:08:12Z

Hex player1:

I think it is better to link directly to hex in different languages, as (for example in Spanish) hex doesn't appear in the start page. --[[User:RBerenguel|RBerenguel]] 18:57, 13 November 2007 (CET)

You are right. Change whatever you want [[User:Halladba|Halladba]] 21:59, 13 November 2007 (CET)

Can anyone who speaks polish or knows more about Kurnik please give more info, or a link, to more info about the decision to close? Ididn't use it myself, but there were always people playing when I logged on to look. [[User:Vintermann|Vintermann]] 17:22, 7 August 2008 (CEST)

yes, really bad that they removed it, it was the best place to play hex ... [[User:Hex player1|Hex player1]] 20:08, 12 August 2008 (CEST)