Difference between revisions of "Climbing"

Latest revision as of 12:53, 27 April 2024

Climbing means playing a series of forcing moves by which a player gains significant distance across the board and potentially connects to the opposite edge, by repeatedly threatening to connect to the player's nearby pieces.

Here is an idealized example. Red to move.

Red wins by climbing from e8.

Note that every single one of Blue's moves is forced. Although Blue could intrude into some of Red's bridges or other templates, this does not help.

Note that climbing was possible even though Blue seemed to have more strength on the right side of the board than Red. What makes climbing work is the exposed flank of unprotected Red pieces that Red can repeatedly threaten to connect to. The potential for climbing is often difficult for beginners to spot, and can lead to swift and unexpected defeat. It is therefore a good idea to try to deny the opponent opportunities to climb.

Example

Climbing does not always have to proceed by bridges. A combination of bridges and adjacent moves is common. Here is an example from an actual game. Red to move.

Red starts a 3rd row ladder, then immediately breaks and climbs.

At this point, Red is connected by an interior ziggurat, shaded in the above diagram, to edge template IV2d. Blue resigns.

Zipper

Zippering is a special case of climbing where the player's threatened connections are all on one side, and the attacker mostly proceeds by bridges. This is called a "zipper" because it vaguely looks like an actual zipper (see the illustration on the right). For example, consider the following position, with Red to move:

Red pushes the ladder, breaks, and zippers all the way to the opposite edge.

Move 1 was actually unnecessary; we have shown it to make it more obvious why 3 was forcing. Red could have immediately started with 3.

Climbing from a ladder

Climbing often starts from a ladder. The attacker pushes the ladder to a certain point, then pivots, often by playing one hex ahead of the ladder. The defender must close the gap between the ladder and the pivot piece, which gives the attacker an opportunity to climb. To find good climbing opportunities, it is useful to consider how far the attacker can climb "unassisted", starting from various ladders. After that, the attacker can potentially climb even further if there are additional forcing moves available.

2nd row ladder

Scenario 1: In this scenario, Red's space is limited. Red can climb to the 4th row, potentially bridging to a stone on the 6th row. The shaded cells are not needed for this and can be occupied by Blue.

Scenario 2: If Red has slightly more space, Red can climb to the 5th row, potentially bridging to a stone on the 7th row.

Scenario 3: In this scenario, Red's 2nd row ladder comes with a switchback threat, i.e., a 2nd-to-4th row switchback would allow Red to connect. In this case, Red can climb to the 6th row, potentially bridging to a stone on the 8th row. This kind of play is also called a switchback fork.

Scenario 4: Finally, if Red has a switchback threat and slightly more space on the right, Red can climb all the way to the 7th row, potentially bridging to a stone on the 9th row. This is highly threatening; note that on an 11×11 board, the 9th row is almost on the opposite side of he board.

Of course, there are many variations of these basic scenarios, depending on what other pieces Red and Blue have on the board. But the four scenarios shown above are common, and are good starting points for planning more complex ladder escape forks.

Scenario 5: If Red has enough space, Red can also yield to the 3rd row and then climb to the 6th row, even without a switchback threat. This is basically the same as Scenario 2 for 3rd row ladders below.

Scenario 6: Given a different amount of space and no switchback threat, Red can still climb to the 6th row as follows:

Note that 5 is connected to the edge by double threats marked "*", and 11 is connected to 9 and 5 by an interior ziggurat.

Scenario 7: Given an enormous amount of space, Red can climb to the 7th row without a switchback threat:

Note that 19 is connected to the edge by edge template V2-f. Also, move 9 is similar to a cornering move, but requires more space in the situation shown here.

3rd row ladder

The situation for 3rd row ladders is largely similar to that of 2nd row ladders. Scenarios 1—3 work without much modification.

Scenario 1: In the most constrained scenario, Red can climb to the 5th row, potentially bridging to a stone on the 7th row.

Scenario 2: If Red has slightly more space, Red can climb to the 6th row, potentially bridging to a stone on the 8th row.

However, if the ladder starts further away and Blue yields at just the right moment, Red needs more space to climb to the 6th row.

After the optional 1-2 exchange, 3 and 9 can be played in either order; they are the only two winning moves for Red within this space.

Scenario 3: If Red's 3rd row ladder comes with a switchback threat, Red can play a switchback fork and climb to the 7th row, potentially bridging to a stone on the 9th row.

Scenario 4: If Red has a switchback threat and significantly more space on the right, Red can climb all the way to the 8th row, potentially bridging to a stone on the 10th row. The shaded cells are not required to be empty.

Yielding: Yielding to the 2nd row does not help Blue in any of these scenarios. If Blue yields at the last possible moment in scenarios 1–4, Red can use a few extra moves to achieve the same outcome as without yielding, and actually requires slightly less space. For example, this is how scenario 1 plays out if Blue yields:

If Blue tries to yield earlier in scenarios 1–3, Red can play, respectively, scenarios 2–4 for 2nd row ladders to achieve the same outcome, and does not even require the 3rd-to-5th row switchback threat. For example, this is how scenario 3 plays out if Blue yields early:

In scenario 4, if Blue yields any earlier than the second-to-last opportunity, Red can simply jump back to the 3rd row. The final and most interesting case is when Blue yields exactly at the second-to-last opportunity. In that case, after optionally invading Blue's bridge, the unique winning move is 3:

After this, there are several possibilities, depending on how Blue responds. The main line is as follows:

Climbing from a 3rd row ladder in an obtuse corner: Another special case to consider is when the 3rd row ladder is approaching an obtuse corner and there is very little space. Consider the following example, with Red's ladder approaching from the right:

There's not enough room for Red to push one more time, as this will give Blue a 2nd row ladder:

The obvious solution is for Red to pivot immediately and hold Blue to a 5th row ladder:

However, this is not optimal, because Blue has a forcing move at x, giving Blue 2nd and 3rd row ladder escapes: A slightly better solution is the following:

Note that Red has formed edge template IV2d, still holding Blue to a 5th row ladder. Blue still has a forcing move at x, but because Red can respond at y, this only gives Blue a 2nd row ladder escape, rather than a 3rd row escape.

However, even this solution is not optimal for Red. It turns out that playing a different move 3 is even better for Red:

Move 3 is named Eric's move after Eric Demer, who discovered it. If Red plays there, Blue in theory no longer gets a 5th row ladder, nor any kind of ladder. If Blue plays at a or c, Red responds at b; if Blue plays at b, Red responds at a; if Blue plays at d, Red responds at e; if Blue plays at f, Red responds at d. This works in essentially the same way as blocking a 5th row ladder when there's not enough space under the ladder stone; see theory of ladder escapes.

4th row and higher ladders

The situation for 4th row and higher ladders is essentially similar, provided that the attacker can guarantee that the pivot piece connects to the edge. For example, in the following situation, the pivot piece "1" is not connected to the edge, and Blue could foil by playing at "a":

However, if Red had, for example, one more piece at either of the locations marked "*" (or pretty much anywhere else near the bottom edge), then the pivot piece would be sufficiently connected for the pivot to work in the same way as for 2nd or 3rd row ladders.