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On Trax
The New Zealand Trax Association Newsletter. Issue: 4

Trax Tips - Forced Tiles


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Trax Tips

The key strategic significance of the forced tile rule is that it allows you to do more than one thing in a turn. This is achieved by having the primary tile do one thing, and one or more of the forced tiles do other things. If you can do this consistently, and your opponent does not, you can gain a considerable advantage quite quickly.

Counter-attackExtend lineI will illustrate this idea of doing several things at once by two examples. The first is counterattacking. In the left position, Black can make an attack with the primary tile, and use the forced tile to actually defend White's attack. In the second example, White straightens a line with the primary tile, while forming an attack with the forced tiles.

Notice that in both cases there was a change in colour along the edge for each forced tile. (The third forced tile in the second example was in a hollow, which will always be forced regardless of the colour.) It is this change in colour that results in the forced play. If there was a further change in colour, in other words an alternating sequence, there would be further forced tiles as shown below. This is called the ripple effect.
Ripple effect

Forced tiles will continue along the edge until one of two conditions is met:
  1. An outside corner is reached - tiles can never be forced around outside corners.
  2. There is no change in colour, unless this is right inside a hollow.
What does this mean in terms of strategy? Whenever you want to play a particular tile (for example as an attack or defence), check for alternating colours. You may be able to play at quite some distance from where you want to, and have the forced tiles ripple along. Here are a couple of examples to give some practise:

How many different moves successfully defend this white attack?
Defence puzzle

How many different ways can white make an attack in this next position?
Attack puzzle

L threatThe L threat is just a special case of using the ripple effect to make two attacks at once. Making the attack at the top of the L forces the attack at the base because of the ripple effect.

Another common example of using the ripple effect is capping off an edge to form your own edge. When the paths in the middle are linked, the forced tiles give the corners on the ends, giving a new edge.

Edge threat gives Capped edge
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Bits for Beginners

ForceThe forced tile rule is the key to the playability of Trax. It also forms the basis of most Trax strategy. So just what is this rule and why is it so important for Trax?

The forced tile rule requires that whenever two paths of the same colour enter an empty space, a forced tile must be played which links those paths. In such a position, there is only one possible way that a tile can be played there anyway, so all this rule says is that you must play that tile as part of your turn. That tile may in turn force other tiles to be played, and so on. The net result is that a turn consists of playing not just of a single tile but of a group of tiles.

No forceWhile the application of the forced tile rule is purely mechanical, the consequences of all the forced tiles on the overall position can often be a little difficult to visualise. Many games have been won or lost purely as a result of not anticipating a particular forced tile. Most beginners think only in terms of the primary tile, and let any forced tiles take care of themselves. This is very dangerous since all the tiles affect the position. Try to think of all the tiles played as a single turn rather than as a primary tile followed by any forced tiles.

The other key is playing the right tile first. Tiles don't always force both ways. In the example above, playing the second tile first doesn't force the other!
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Extras for Experts

Non-filling hollowFilling hollowAlthough the ripple effect cannot force around outside corners, it can force around inside corners (hollows). Consider the following two positions. The move on the left results in only four tiles being played - the forced plays stop at the hollow. With the move on the right, 12 tiles are played, completely filling in the hollow.

What is the difference between these two, or more importantly, is there a simple rule for determining if the ripple effect carries past the hollow?

Ripples in hollowsFortunately there is. If the ends marked with the arrows (one out on each side of the hollow) are the same colour then the ripple effect will continue past the hollow. When the ripple effect goes past a hollow like this, it will always result in a block being filled. If the colours of the marked ends are different, the ripple effect will stop in the hollow.

Another way of looking at this is to consider the empty spaces rather than the edges of the tiles. The spaces with the arrows have white paths going into them, and the hollow has a black path going in. Since there is an alternating sequence of spaces going around the hollow: WBW the ripple effect will continue past the hollow.
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Solutions

10 defences, 8 attacks.
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