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

Revision as of 02:44, 3 March 2020

Introduction

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

This document consider some basic advanced hex strategy. It does not consider the basics such as the rules, two-connections, 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 are 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, critics, questions, or find any bad spelling on this page please let me know.

Some terminology: Stones are what we places on empty hexes. The goal is to connect the two edges with each other. Group of stones or chains are stones that are solid 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:

• A solid connection is the strongest kind of connection there is. It can not be tampered with in any way. Stones that lies along each other forms solid connections. In some cases certain two-bridges or other constellation are in fact solid connections if invading these do not have any effect in the game. In these cases you can fill in the gaps with stones and still have an equivalent position.

• A strong connection cannot be broken if the opponent doesn't allow it. Every move you make he can counter 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.

Another example of a strong connection. Blue needs the area marked by stars to connect.

• 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.

• 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.

It is possible to define even stronger and weaker connections than these. For example a connection that 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 suffices. 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, and a weak block creates a weak connection from a potential. 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 all what Hex is about. Some would add also 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.

The weak block

In areas the opponent has a strong connection to an edge with a group you can only make weak blocks. These should be made very carefully. The goal of the weak block is not to break his connection (since it's 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 makes 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 gaining ground at 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 can reconnect so it may seem like there is no use of such a move. 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 could have made and most often leads to a direct loss. The line between a good weak block and a worthless move is usually very thin, and is one of the great challenges of Hex. Sometime you can make a chance with a weak block you think may be worthless and hope that the opponent reply on the block. This way you may gain some extra ground to win a game that otherwise would be lost. The psychology plays a great role here. Inexperienced players feel a need to be certain that they at least are connected to one side. If they are not 100% certain there is a chance they will reconnect a strong connection that already is 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 if your gain is worth it. Sometime you need to wait a few moves to see how certain things turned out before you know exactly where to make the weak block. Other times you better hurry up. This is typically the situation if the opponent has another strong connection to the very same edge but maybe more subtle. If he doesn't realize it and reconnect after you weak block you may have gained enough ground to turn the game to your favor.

The reply to a weak block can be either a strong block or a weak block. If your opponent made a weak block against one group of stones, you have the choice of either reconnect your stones making that weak connection a strong or making another weak connection from a parallel chain of stones. (or equivalent 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 exist you have no other choice but to reconnect to the edge by a strong block.

The strong block

A common situation when making a strong block is that only one hex will do the job, typically a hex in front of the opponents stones. At such times no greater thought need to be done if it is decided a strong block shall be done. 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 is 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.

When to use which?

Whether to use a strong or 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. The problem most of the time is not which to play but where to play. Often there are plenty of 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 critically 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 to be made depends on which helps most to the other direction.

If no immediate threat exists consider if there are area to be plundered with weak blocks without opponent getting any extra land. 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 land of his own. It may also be the case he already has another link to the edge that is strong, in this case it's very dangerous to make a weak block, he simply ignores it and strengthen that other chain instead.

If no good weak blocks can be made, try find any double blocks, that is a block that block two chains at the same time. It could be two strong blocks, two weak 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 parallel) the only way to have any use what so ever of that chain is to make a double block of some kind. Another usual situation is that you have two parallel chains that is 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 make a strong block. This should be made as discussed above, as far away from the thing you connect to as possible. It may help a little for the other end or maybe even block another place just enough even if this isn't obvious at first (disguised double block).

Summary

Every move one should consider which connections is 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, best way is to analyze if you got a weak connection at the same place. If you have, 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 at which area to play.

• First make any defense that is essential. Most often this means opponent has the initiative and force you to strong blocks.
• If no immediate threat exists you have the initiative. If possible plunder free area with weak blocks.
• If no free area search for double blocks.
• If no double blocks search for weak blocks that gives you more than the opponent.
• If all else fail, make a strong block. This move typically gives back the initiative to the opponent.

In both strong and weak blocks its important to remember to place the stones, if possible, at the edge of the connecting area to get as much ground as possible backwards and sideways. The only exception from this rule is if you have enough ground already and is sitting on a winning position. In that case care should instead be taken to minimize opponent's gain of land 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 threat 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.