The basic blocking technique is to identify reductions and consider the hexes where they overlap. Have a look at Diagram 68. How should White block the black stone from the bottom edge? First, note that from this position Black could jump directly towards the edge with a bridge and Template A-2 (Diagram 69a), or to the side with a bridge and Template A-3 (Diagram 69b). In each case I’ve highlighted all the hexes involved. Note how the points and are involved in both reductions. We say these reductions overlap at these points. If any block is to be successful, it must be at one of these two points: otherwise Black could simply play the other reduction and connect.
Diagram 68
White to play and block.
(a)
(b)
Diagram 69
Two reductions for Black.
Diagram 70 shows a successful block starting from . This is the classic bottleneck formation and the result is a second-row ladder.
Diagram 70
Successful block by White.
On the other hand, attempting to block at fails (Diagram 71), as Black takes advantage of the empty point in Template B-3 (Diagram 45). Identifying overlapping hexes is just the starting point when looking for a block. In order to find a successful block you must consider the possible follow-up moves. That said, finding the overlapping hexes is still extremely helpful: from potentially dozens of hexes in which to move we were able to identify just two that required further analysis. This simplifies matters greatly.
Diagram 71
Unsuccessful block by White.
Diagram 72 shows another example. Where should White play to split the two groups of black stones? Diagram 73 shows two reductions which would connect the two groups, each using a bridge. is common to both reductions, so White should play here. As can be seen in Diagram 74, this successfully blocks Black from connecting the two groups.
Diagram 72
White to play and block.
Diagram 73
Two reductions for Black.
Diagram 74
Successful block by White.
Diagram 75 shows two more examples, each with White to move, with the goal to block Black from connecting his stones. Both of these situations come up quite frequently. Can you identify the reductions involved and where they overlap? Given this, where should you block?
Diagram 76 shows Template A-4 and two reductions. These reductions overlap at the point . As we saw above, if White plays at the overlapping point she can intrude into both reductions with a single move, so Black needs another response for this situation. In this case, Black can use Template B-3 to save the connection, as shown in Diagram 77.
Because its reductions overlap, this template can’t be represented by a pivot diagram.
Template A-4 is a very important template to know. Study it carefully.
Diagram 76
Template A-4 and reductions.
Diagram 77
Response to White’s move at A.
The basic approach to analyzing templates is to first look for potential blocks where reductions overlap. If the reductions don’t overlap then there’s nothing else to do: we know how to respond to every intrusion. If the reductions do overlap, then every overlapping point requires a response that saves the connection (otherwise it wouldn’t be a template). Template A-4 was a somewhat simple example since we were able to simply use a third template to save the connection. A more complex one is Template C-4, shown in Diagram 78. We can reduce this template with bridges and Template A-2, which leaves the two overlapping hexes and .
Diagram 78
Template C-4 and reductions.
Responses to these intrusion points are shown in Diagram 79. For the response to we can see that is connected to the bottom via Template A-2, and is connected to the top group by a double threat. Try out the alternatives to White’s to see how Black should respond. For the response to we can see that Black has connected to the bottom by Template A-2 and a Trapezoid. Notice how was forced.
Note that these aren’t Black’s only replies: in both cases Black could have played his two moves in the opposite order, although White’s reply would be different.
Template C-4 is a strong template. Being compact, it can fit in small areas, and the pair of stones give it a large “surface” to which groups in the center of the board can connect to.
Response to A.
Response to B.
Diagram 79
Responses to the two intrusion points.
For another example we’ll look at Template E-4. Diagram 80 shows this template and its two reductions: on the left with Template A-2, and on the right with a bridge and Template A-3. These overlap at a single point, .
Diagram 80
Template E-4 and reductions.
The response to this intrusion point is shown in Diagram 81, beginning with a forcing move and then using the Crescent to connect.
Diagram 81
Response to intrusion at A.
Diagram 82 shows three more edge templates that are good to know. I’ll leave it up to you to figure out how to connect them.
Between equally matched opponents ladders tend to occur more frequently than direct connection via edge templates. So it’s important to know the various tactics available to both the attacker and defender, not just so that you’ll know what to do when a ladder forms, but so that you know under which circumstances a ladder will work to your favour.
At each step, the attacking player has three options (Diagram 83): pushing (), jumping (), or breaking (). Pushing continues to move the ladder forward as usual. Jumping with a bridge generally has the effect of moving the ladder back one row. This can be useful because sometimes ladder escapes require a ladder on a particular row. In Diagram 84, Black connects by jumping towards the fourth-row stone and then using Template A-3 (we will look at this situation in greater depth below).
Diagram 83
The attacking player’s options: push (), jump () or break ().
Diagram 84
Example of jumping to escape a ladder.
When the ladder is heading towards the acute corner, breaking generally results in the ladder “turning the corner,” reversing the roles of attacker and defender (see Diagram 85, note that is connected to the southeast with Template A-3). When performing this maneuver, be aware of any ladder escapes the other player may have available on their edge.
Diagram 85
Turning the corner.
When the ladder is heading towards the obtuse corner, breaking has a different effect (see Diagram 86). This scenario tends to be much better for the attacking player (Black in this case).
Diagram 86
Breaking in the obtuse corner.
When a ladder isn’t on the second row, the defensive player has the option of yielding, as in Diagram 87.
Diagram 87
Yielding by the defensive player.
Diagram 88 gives an example where yielding is crucial. It’s White’s turn and she must prevent Black from using the fourth-row stone as a ladder escape.
Diagram 88
White to move.
If White blindly pushes the ladder forward, Black connects with Template A-3 (Diagram 89).
Diagram 89
White pushes.
If she yields, however, Black has no means of forcing the connection (Diagram 90).
Diagram 90
White yields.
But timing is critical: had White yielded even one turn earlier Black could have forced the connection by intruding into the bridge and then jumping, using Template E-4 (Diagram 91).
Diagram 91
White yields too early.
In other situations, a player can’t yield the ladder because it would allow the opponent to use a ladder escape. In Diagram 92, White cannot yield the ladder to the second row or else will escape it. As long as she keeps this ladder on the third row, Black can’t escape it.
Knowing that a player can’t yield a ladder can simplify the analysis of some board positions.
It’s important to know what stones can serve as valid ladder escapes. For example, if you know that you have a second-row ladder escape on one edge of the board, then getting a second-row ladder on that edge is as good as connecting to it. Not only is this much easier to do (as compared to connecting directly), but when mentally calculating possible lines you can now stop at any line that yields such a ladder. With good tactical knowledge you free your mind to focus more on the unique position of the game.
Diagram 93 shows the simplest escapes for a second-row ladder. Try to work out the solution to each. If you’re wondering why the last two count as distinct ladder escapes, remember that the unshaded hexes are not part of the template and could be occupied by white stones. This means that in some circumstances only one of these two connections might be possible.
(a)
(b)
(c)
(d)
Diagram 93
Second-row escapes.
Diagram 94 shows the simplest escapes for third-row ladders. You should work out the solutions to these as well.
(a)
(b)
Diagram 94
Third-row escapes.
Less trivial is using a single stone on the fourth row as a second-row ladder escape, as in Diagram 95.
Diagram 95
Ladder escape with a stone on the fourth row.
In order to use this stone as a ladder escape, Black pushes the ladder and then jumps, connecting to the stone with two bridges. If White jumps as well then Black connects with Template A-3 (Diagram 96a). If White tries to intrude into the bridge, as with moves and in Diagram 96b, then Black responds with the forcing move followed by , which connects with a Trapezoid.
Diagram 97 shows an alternate second-row escape with the fourth-row stone. Note how it’s essentially like approaching the previous template from the other side. Black’s approach is very similar.
Diagram 97
Alternate ladder escape with a stone on the fourth row.
You might have noticed that many of these ladder escapes look like edge templates. Template B-3 and Template B-4 can also be used this way for second-row ladders. While many edge templates can be used as ladder escapes this isn’t the case in general. For example, Template A-3 serves as valid third-row ladder escape from one direction only (as we saw in Diagram 94b). An important consequence of this is that a third-row stone on the edge of the board (such as a black stone on a3) can’t be used as a ladder escape. Diagram 98 shows why. In Diagram 98a we see that simply laddering across allows White to block by bridging to her edge. In Diagram 98b Black attempts an alternative approach by double bridging to the stone, but White intrudes into the bridges and uses a Crescent to block. The inability of a3 to serve as a third-row ladder escape is significant because it’s a common opening move.
(a)
(b)
Diagram 98
a3 can’t escape a third-row ladder.
Template A-4 isn’t a valid third-row ladder escape from either direction. We already saw in Diagram 90 how to block the third-row ladder approaching Template A-4 from one side, a similar approach may be used to block it from the other side. In order for a stone on the fourth row to serve as a third-row ladder escape, slightly more space is required (Diagram 99, note that the hexes on either side of the fourth-row stone are required).
In Diagram 100 it’s Black’s turn to move. He can start a second-row ladder from , but there is no ladder escape available. Noting the ladder escape in Diagram 93c, Black intrudes into White’s bridge with g11 (Diagram 101). In addition to being a second-row ladder escape, this also threatens to connect through with Template A-3. Therefore, this move constitutes a ladder-escape fork, correct?
Diagram 100
Diagram 101
No it doesn’t! White can block both the ladder escape and the edge template by responding with f12 (Diagram 102). When creating ladder-escape forks be sure that your opponent cannot meet both threats.
Have a look at Diagram 103. What will happen when the third-row ladder reaches ? White cannot yield the ladder to the second row, or else will escape it. And the presence of the surrounding white stones means the black stone can’t escape the third-row ladder.
Diagram 103
What happens when the ladder reaches the black stone?
We can see what happens in Diagram 104: the ladder drops down to the second row. We call this a cascading ladder. Situations such as these can often occur when a player intrudes into a bridge (notice how could result from a bridge intrusion).
Diagram 104
A cascading ladder.
Sometimes multiple cascades can occur one after another. In Diagram 105, Black’s fourth-row ladder drops to the third and then second row before eventually reaching the ladder escape.
Sometimes breaking can be used to force a connection that would have not otherwise been possible. Diagram 106 shows one such situation. Black breaks with , forcing the White response . After , Black has a double threat through either or .
Black to move.
Black connects with a double threat.
Diagram 106
Using a break to connect.
In Diagram 107 Black has a more difficult situation. However he can connect by combining a jump and a break. Black jumps with , and then breaks with , which is connected to the southeast with Template A-3. White is forced to block the connection with . But then makes for a double threat: connecting directly or with two bridges. The situation looks very similar to the ladder-escape fork (Diagram 31), but there is a major difference here: whereas in that situation the fork could be played right away, here Black must first ladder right up to the intended ladder escape and then break, forcing White to respond with . Only then can serve as a double threat.