Advanced (strategy guide)

Template IVc
R4 C4 Q1 Vc1 Vd1 Pc2 Sb3 Sc3 Pb4

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
R4 C4 Q1 Vc1 Vd1  Hb4 Vd3 Hd2

R4 C4 Q1 Vc1 Vd1  Hb4 Vd3 Hd2   Vb3 Sc3 Sa4

If Blue (the horizontal player) intrudes at b4, then Red responds with d3 &mdash; 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
R4 C4 Q1 Vc1 Vd1  Hc2 Vb3 Hb2

R4 C4 Q1 Vc1 Vd1  Hc2 Vb3 Hb2   Vd2 Hc4 Vc3

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
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

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

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

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

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

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

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

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

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

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

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

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.

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

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

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

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

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

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 &mdash; 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
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

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

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

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

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

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.)

R10 C10 Q1 Va3 Vc6 Hf5

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.

R10 C10 Q1 Va3 Vc6 Hf5  Hf4 Vd5

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.

R10 C10 Q1 Va3 Vc6 Hf5 Hf4 Vd4 Hc7 Ve6 Hd5

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

R10 C10 Q1 Va3 Vc6 Hf5  Hf4 Vd5   Hc7 Ve6

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

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

In this position, I was the vertical player and was expecting f6 to which h5 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

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

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.

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

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.

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

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 &mdash; h3, h2, g3, g2, f3, f2, e3, e2 completing the win.

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

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).

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

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.

C10 R10 Q1 Va3 He4

I played the minimax move 2. f5 yielding

C10 R10 Q1 Va3 He4    Vf5

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.

C10 R10 Q1 Va3 He4    Vf5   He3

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).

C10 R10 Q1 Va3 He4    Vf5   He3    Vg4 Hh3 Vg3 Hf8 Ve8 He9 Vg7

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

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

Reconnecting edge template IIIa after an intrusion
R4 C10 Q1 Ve2 Hd3 Pf2 Se3

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 &mdash; 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.

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

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! &mdash; 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.

R9 C9 Q1 Vh3 Vg2 Vf3 Ve4 Vd5 Vd6 Hc6 Hb8 Hc8 He6 Hg5 Hi3

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! &mdash; 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.

R4 C10 Q1 Ve2 Hd3

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!

R4 C10 Q1 Ve2 Hd3  Vf1

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.

R4 C10 Q1 Ve2 Hd3  Vf1   He4 Ve3 Hd4 Vg3 Hf3 Vg2

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).

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

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!!

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

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!!)

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

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.

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

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.

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

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!

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

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.

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

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.

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

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.

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

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.

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

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.

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

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.

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

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!

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

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.

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

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.

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

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.

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

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.

R10 C10 Q1 Vd5 He5 Vd6 Ve6 Hb7 Vc7 Hd7 Hb9

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.