Difference between revisions of "Jonathan Rydh's strategy guide"

Latest revision as of 20:29, 11 September 2021

Introduction

(Used with permission, recovered from https://web.archive.org/web/20070214095946/http://www.nada.kth.se/~rydh/Hex/strategy.html)

This document considers some advanced Hex strategy. It does not consider the basics such as the rules, bridges, templates, ladders, ladder escapes, walls etc. If you want to learn more about those topics I suggest you check out some of my links. I also have a page with useful templates. I do not claim that the strategy discussed below is the only way to play or that it even is a good strategy, but merely one way of thinking of Hex. If you have any suggestions, criticism, questions, or find any typos on this page please let me know.

Some terminology: Stones are what we place on empty hexes. The goal is to connect the two edges with each other. Groups of stones or chains are stones that are solidly connected (see below). Groups, stones and edges are all various kinds of nodes. Two nodes are connected with some kind of connection if there exists a path from one to another.

The four basic connections

Hex is a game of connections. From here on I will, when discussing blocks and connections, mostly speak about connections between a group of stones and one edge but everything can easily be adapted to any kind of nodes.

Connections can be categorized in four categories:

Solid connection

A solid connection or chain is the strongest kind of connection there is. It can not be tampered with in any way. Stones that are adjacent to each other form solid connections. In some cases certain bridges or other constellations are in fact solid connections if invading these does not have any effect in the game. In these cases you can fill in the gaps with stones and still have an equivalent position.

Here, the stones 1 and 2 are solidly connected:

Strong connection

A strong connection or virtual connection cannot be broken if the opponent doesn't allow it. He can counter every move you make so that he maintains his strong connection. A strong connection is almost solid but in some cases it is better to let the opponent break it than to defend it as described in later sections.

Here, 1 and 2 are strongly connected:

Another example of a strong connection. Blue needs the shaded area to connect groups 1 and 2:

Weak connection

A weak connection is such that it can be made strong by placing one stone. This goes for both players so the first player to place a stone in this area gets a strong connection. It's not difficult to grasp (but it is important that you do!) that two parallel weak connections between two nodes are together a strong connection and two weak connections after each other are a strong connection for the opponent.

An example of a weak connection:

Potential connection

A potential connection is the connection across a strong connection of the opponent. It is a connection that will be weak if you place a stone in it. To make it strong you need to place two stones in this area.

An example of a potential connection for Blue:

It is possible to define even stronger and weaker connections than these. For example a connection for which it takes three stones to create a strong connection for the opponent is a strong connection of magnitude 2 and so on. But in most cases, these four suffice. It is never a good idea to make a strong connection even stronger just for the sake of it. However, if you get it as a bonus in a double block (see below), it may actually be a good idea.

The two basic moves

There are two basic moves in Hex, the strong block and the weak block. Yes that's right, every move can be considered a block. The strong one blocks the opponent so that he cannot connect at all to one edge with a group of stones. After a strong block, the opponent has to use another group to connect to that edge, or break the strong connection twice to get through. The weak block blocks the opponent so that he has to place another stone in that area to reconnect that group to that edge. In terms of connections, a strong block creates a strong connection from a weak one, and a weak block creates a weak connection from a potential one. An alternative term for strong and weak blocks could therefore be strong and weak linking, depending on which way you see it.

Strong and weak blocks are very different in nature. A weak block usually maintain your initiative, and is therefore better to play, despite its name. If you have the option, play a weak block; but it can be very difficult to find a good weak block, and at other times you are forced to play a strong one. Which to play, and how to play it, is what Hex is all about. Some would also add "when", and it's true that timing is an essential factor. But it is important to realize that it is better to make a good move at the wrong time than making a bad move at the right time.

A more modern term for a weak block is intrusion.

The weak block

In areas where the opponent has a strong connection, you can only play weak blocks. These should be played very carefully. The goal of the weak block is not to break the opponent's connection (since that is impossible), but to steal ground by forcing him to reconnect. Typically you first estimate which hexes he needs to connect the group, and then place a stone at the perimeter of this so-called connecting area. Templates make this process a lot faster for smaller areas. It is almost always a mistake to place a stone in the middle of a connecting area. The opponent will create a new strong connection and will at the same time gain ground in the other direction.

Here is an example. Red is strongly connected between 1 and the top edge. If Blue were to make a weak block in this area, Red could reconnect. So it may seem like such a move is of no use. However, only a weak block in the perimeter of this area will win. Can you see it?

Placing a stone outside the connecting area, thinking it is a weak block, is usually catastrophic. It's often the worst move you can make and most often leads to a direct loss. There is usually a very fine line between a good weak block and a worthless move, and this is one of the great challenges of Hex. Sometime you can take a chance with a weak block that you think may be worthless, and hope that the opponent replies to the block. This way, you may gain some extra ground to win a game that otherwise would be lost. Psychology plays a great role here. Inexperienced players feel a need to be certain that they are at least connected to one side. If they are not 100% certain, there is a chance they will reconnect a strong connection that is already strong. This is as bad as placing a stone outside the connecting area.

Remember that what you gain by making a weak block can often be countered by the opponents reply. Therefore, it is important to consider whether your gain is worth it. Sometimes you need to wait a few moves to see how certain things turn out before you know exactly where to make the weak block. At other times, you better hurry up. This is typically the situation if the opponent has another strong connection to the very same edge, but may be more subtle. If he doesn't realize it and reconnects after your weak block, you may have gained enough ground to turn the game to your favor.

The reply to a weak block can either be a strong block or a weak block. If your opponent played a weak block against a group of your stones, you have the choice to either reconnect your stones, making that weak connection strong, or to create another weak connection from a parallel chain of stones (or equivalently, trespassing on your opponent's strong connection). The latter, if possible, is usually a stronger move, but can be much more difficult to find. If no such move exists, you have no other choice but to reconnect to the edge by a strong block.

The strong block

A common situation when playing a strong block is that only one hex will do the job, typically a hex in front of the opponent's stones. At such times, no greater thought needs to be put into it, once you decide to play a strong block. However, at other times you have more of a choice. Great care should be taken when making such a strong block. It's a beginner's mistake to make the strong block "too strong". Your goal is to connect, but it is essential that you connect in such a way that after your move your stones are connected just barely. Why? Because every bit of help is needed to connect towards the other direction. When making a strong block think: "Can I place it here, am I connected?" If the answer is yes place the stone a little bit farther from the edge and repeat the question until you know which positions exactly connects. Now place the stone at the most suitable location that helps the other direction as much as possible. See also minimaxing.

When to use which?

Whether to use a strong block or a weak block in a particular area depends on whether the opponent has a strong or weak connection there. Basically, a weak connection should be blocked with a strong block and strong connection with a weak block. Most of the time, the problem is not which to play but where to play. Often, there are many chains and connections, weak and strong. Which of them should be blocked?

First and foremost, if you are weakly connected to one side with one and only one connection, it is critical that you place a strong block here unless you can make another weak connection from a potential connection (but then you didn't really have one connection did you?). Which strong block to play depends on what helps most in the other direction.

If no immediate threat exists, consider whether there are area to be plundered with weak blocks without the opponent getting any extra territory. If he has to reconnect, there is no question about it; you should play a weak block here. If however he has other means of connecting he may create another weak connection gaining some territory of his own. It may also be the case that he already has another strong link to the edge. In this case, it is very dangerous to play a weak block, as the opponent can simply ignore it and strengthen that other link instead.

If no good weak blocks can be made, try finding a double block, that is, a block that blocks two connections at the same time. It could be two strong blocks, two weak blocks, or one of each kind. These kinds of moves are often killer moves. For example, the so-called ladder escape is a double weak block. If you have two or more weak connections totally in one potential chain (after each other, not in parallel), the only way to make any use whatsoever of that chain is to play a double block of some kind. Another common situation is that you have two parallel chains that are both weakly connected to both edges (4 weak connections). You then either have to connect these two chains with each other or find a double strong block to connect two of these loose ends.

If no double block or satisfactory weak block can be found, play a strong block. This should be played as discussed above, as far away from the thing you connect to as possible. It may help a little towards the other direction, or maybe even block elsewhere just enough, even if this isn't obvious at first (disguised double block).

Summary

Before every move, one should consider which connections are strong, weak and potential. You can either analyze your stones or the opponent's. Often one is easier than the other. If the opponent has a strong connection, yours is potential and vice versa. If you find that the opponent has at least a weak connection but isn't sure if it is weak or actually strong, the best way is to analyze if you have a weak connection in the same place. If you do, the connection is weak, otherwise it's strong (remember a weak connection is is per definition always weak for both players at the same time).

After the first phase of analyzing you should determine in which area to play.

• First play any defensive move that is essential. Most often, this means the opponent has the initiative and forces you to play strong blocks.
• If no immediate threat exists, you have the initiative. If possible, steal free territory with weak blocks.
• If no free territory can be stolen, search for double blocks.
• If no double blocks exist, search for weak blocks that give you more than the opponent.
• If all else fails, play a strong block. This move typically gives back the initiative to the opponent.

With both strong and weak blocks, it is important to remember to place the stones, if possible, at the edge of the connecting area to gain as much ground as possible backwards and sideways. The only exception from this rule is if you have enough ground already and are sitting on a winning position. In that case, care should instead be taken to minimize the opponent's gain of territory from your moves, so that he doesn't trick you into a trap like a double block. Also beware of the false weak block that doesn't really threaten your strong connection but which fools you to place another stone there in vain. If you are playing in a game you are losing you could of course play such a false weak block yourself and hope for the best.