The New Zealand Trax Association Newsletter. Issue: 13
GoldToken Newsletter Article #2
First published in the GoldToken Monthly Newsletter, September 2005. Reproduced here with permission.
Article #1Hello again Trax players. This is the second article on how to play better Trax. In the first article we looked at "What should I be doing?" when playing Trax. To recap, we covered:
- forced plays, and how they arise
- the need to think of all the tiles played in a turn as a unit
- how making loop attacks can actually weaken your position
- introduced the concept of potential
- and measured potential by counting corners or the possible attacks you could make.
In this article, we will look in more detail at corners, and when is the right time to attack. The tips here are applicable to all 3 Trax variations found on GoldToken: 8x8Trax, Trax, and LoopTrax. As Trax is quite a visual game, rather than just describe some of the positions in this article, I give reference to positions taken from actual games.
A corner is defined as any section of track that may be made into a loop attack in one turn. The simplest corner is a single curve, which can easily be made into an attack by turning either end around to make a half loop. Corners do not have to consist only of a single tile. Consider game 2450599, at move 4 a wide attack is made using a multi-tile corner. See how the use of forced plays can enable the path to be extended further than if the path was simply turned. In a similar way, the forced tiles allow the attack to be closed off with move B0+ unless white defends.
A corner is therefore only 2 turns away from a win - the first turn extends one end of the track, and the second turn closes the loop (if the attack is not defended). Note that either of the 2 turns could be played first, giving 2 different ways that the attack could be made. In fact, any corner may be made into an attack in at least 2 ways, by bending either end. This is important, as we shall see shortly, as not all attacks are equal, and often attacking one way is better or stronger than attacking the other way.
In spite of their name, not all corners are necessarily found on the corner of the playing area. In the same game (2450599), at move 13, Black has what is known as a "flat corner". In the @ column (adjacent to the A column), the ends of the black path are too far apart to be closed off in a single turn. However they are close enough to link with 2 turns. Therefore the first turn is going to make an attack. This means that a flat corner fits our definition of a corner. In move 14, I turn one of the ends to make an attack. As before either end of the track could be turned to make the attack.
A third formation closely related to corners is the "connectable pair". A connectable pair consists of two paths that may be linked together at either end. In linking them, they too are made into an attack. Like corners, there are two ways to make the attack, by linking either end. Therefore, in terms of evaluating potential, connectable pairs can be considered as equivalent to corners.
So, why is all this important? Well, as we saw in the previous article, the ability to attack is strongly correlated with the strength of a position. Multiple stage threats make use of 1, 2, 3, or even more corners in particular configurations or patterns. To play Trax well, one needs to focus not on making attacks, which can usually be defended easily, but on setting up more complex threats. These are positions where you can make a sequence of attacks, ending up either with two independent attacks (only one can be defended), or a single undefendable attack. The more corners you have, the more likely your opponent is going to be restricted in what they can play without setting up a threat for you. Remember though, actually making attacks is generally weak because you lose attacking potential, and your opponent gains attacking potential.
You might ask, "If attacking is not good for my position, when should I attack?" The key is in the timing. At some stage, if you are going to win the game you must attack. If you go onto the attack too early, you can weaken your position and end up losing. If you leave it too late, your opponent gets in and wins before you. Recognising the right timing is the key to winning. In general, there are 4 situations when it is right to attack:
1) If your opponent has left you with a multistage threat. In this situation, you are able to make a sequence of attacks that will result in you winning. Much of Trax experience is in recognising the patterns that make up such multi-stage threats, and knowing how to capitalise on them to force a win. If you misjudge the position, and realise that the threat is not going to work, it is important to stop attacking as soon as possible. I have lost many games by trying to use a complex threat only to realise that my opponent has a key move that makes the whole threat faulty. After making several attacks my position had deteriorated to the extent where my opponent had built several threats while defending my attacks. By that stage, it is often too late, and the game is over. This brings us to the second situation:
2) If your opponent has multiple independent threats. In this situation, when your opponent gets their turn, they can use one of their threats to win. To do this they need the initiative. The only way you can prevent an immediate loss is to retain the initiative by making an attack. They are then forced to defend your attack rather than activate one of their threats. As long as you can keep the initiative by making attacks, you can avoid losing. Unfortunately, in an actual game, it is not as simple as this - attacking usually weakens your position and further strengthens your opponent. The key is to make the right attacks - those where the forced plays destroy one or more of your opponent’s threats, where your opponent cannot counter-attack, and where you limit the damage done to your position (in particular where your opponent cannot simply make another threat). I mentioned earlier that not all attacks are the same. Every corner can attack at least 2 ways, and one way is often better than another.
3) If your opponent is using a multistage threat, and you can counter-attack to regain the initiative. While your opponent is using a threat, there is often nothing you can do - you have to defend each attack that your opponent makes. If you can make a counter-attack (defend your opponent's attack with one of your own) you can regain the initiative and destroy the rest of the threat. This is another reason why corners are important. Corners in key positions can prevent your opponent from completing their threats. A corollary of this is that if you are using a multiple stage threat, and you have a choice of which attack to make to complete the threat, be careful not to let your opponent steal your win from you. On the other hand, if you are facing a threat, don’t give up or resign too early, especially if you have corners near those that your opponent is using in their threat. I have won many games that I should have lost where my opponent let me off the hook by allowing me to counter-attack.
4) If, by attacking, you manage to maintain your potential. Having said earlier that you should not attack, I’ll now moderate that by saying that not all attacks are bad. There are some situations where you can attack, and use forced plays to give yourself another corner, and when your opponent defends, you do not lose the corner you attacked with. Often wide attacks (for example game 2450599 after move 4) are stronger than narrow attacks (for example after move 10) because in defending, you are still left with a corner. Another situation is an attack with a hollow (the attack is in a 2 sided space, see move 14) because the defence possibilities are limited. In the example here, there are only 2 possible defences for 15: A4/ and A5/, and both of these leave the corner used to make the attack intact. Therefore, if you must attack, attacking into the hollow is usually stronger than attacking away from the hollow. These situations imply that some corners (and connectable pairs) are stronger than others.
Indeed, corners adjacent to a hollow are usually stronger than corners that are not, because you can attack into the hollow, where your opponent's defence options are more limited. Single tile deep hollows are stronger deeper hollows. Some corners adjacent to a hollow are not as strong. The most commonly occurring exception is where both players have a corner adjacent to a hollow. See game 2450599 after move 6. Black has a corner at A2 and white as one at B1. Neither of these corners is particularly strong because if one player attacks into the hollow, the other can counter-attack.
These factors mean that in counting corners, you should give a little more weight to corners and connectable pairs beside single deep hollows. Flat corners are also more valuable because when you make the attack, you create the hollow at the same time. Flat corners are also harder to destroy; doing so often leaves you with another corner.
To summarise, we have looked in more detail at corners and connectable pairs. With these, attacks can always be made at least two ways (although not always safely!). Do not actually make unnecessary attacks, because that will weaken your position. We looked at the situations when it is correct to attack, and the key element is timing. Finally, we saw that some attacks and corners are stronger than others, and have modified our simple corner counting evaluation introduced in the previous article. I hope that you are able to make use of these tips to improve your game. Remember that it is only with practise that you will master these techniques.
Until next time, happy Traxing!
Article #1