Newsgroups: rec.games.abstract
Subject: Re: Trax anyone?
From: Michael.Norrish@comp.vuw.ac.nz (Michael Norrish)
Date: Mon, 4 Jan 1993 22:12:55 GMT
Organization: Dept. of Computer Science, Victoria Uni. of Wellington, NZ.

Well, due to popular demand :-)

Here, without permission, are the rules to Trax, (as I remember them
in any case):

1. Two players, red and white.
2. Each plays in turn, placing one tile per turn.
   a. Every tile in the game is identical. On one face a tile has the
   following pattern:
                            +--------+ 	 Where the double lines are one
                            |   ||   | 	 colour, and the single lines
                            |   //   |	 another.
                            | ==   --|
                            |     /  |
                            |     |  |
			    +--------+
       On the other side, a tile has this pattern:
       	       	       	    +--------+
			    |   ||   |
			    |	||   |
			    |---||---|
			    |	||   |
			    |	||   |
			    +--------+

   b. When placing a tile, a player must place it so as to ensure that
   it connects up with at least one previously placed tile. (This
   connection must keep coloured lines appropriately linked). There
   are no restrictions otherwise, i.e. a tile may be placed with any
   orientation, either way up.

   3. As a result of placing a tile, it is possible that a player has
   created a situation that can not just be left as it is. The
   situation is if an empty space is touched by two incoming lines of
   the same colour.

   For example:
             +--------+--------+
	     |   ||   |   ||   |
	     |   //   |   \\   |
	     | ==   --|--   ===|
	     |     /  |  \     |
	     |     |  |   |    |
	     +--------+--------+
	     |     |  |
	     |	   \  |
	     |==    --|
	     |	\\    |
	     |	 ||   |
	     +--------+

   If either the rightmost or bottom tile has just been played, then
   the blank square in the lower right can not be left as it is
   because there are two lines of the 'single-line' colour pointing at
   it.

   When such a situation arises, it must be rectified by filling in
   the blank with a fresh tile that fits the hole. It is possible that
   in doing this new situations of this type will arise. These too
   must be rectified. These forced moves do not count against either
   player in any way, they just have to be made. Nor does it matter
   in which order these forced moves are made.

4. The first player to complete a loop of his or her colour wins. If
   two loops of opposing colours are created in the same turn, the
   person whose turn it was wins.


Notes on the above:

Rule 3 probably looks like a hideous kludge at first, second and maybe
even third glance. It is necessary however, as the placement of tiles
may otherwise create 'holes' that are unfillable. It is clear that
such a hole would exist if it was pointed at by more than two lines of
the same colour, (each tile has two exits of the same colour, no
more).

Rule 3 merely ensures that when a blank is surrounded by 2 same-colour
exits the potential problem is fixed. Note that 2 different coloured
exits, (as below), do not pose a problem:

        +--------+--------+
	|   ||   |   ||   |   There are still two ways in which the
	|   //   |   \\   |   hole can be filled, so there is no
	| ==   --|--   == |   forced move required.
	|     /  |  \     |
	|    |   |   |    |
	+--------+--------+
        |    |   |
	|    | 	 |
	|========|
	|    |   |
	|    |   |
	+--------+

The rules above are for what is called the advanced game. The
'simpler' game adds a rule:

It is also possible to win by having a line that stretches across the
playing area from one side to the other. (It must exit from each
side). This rule also requires that the game limit itself to an 8x8
grid in size. This is the 'playing area'. The 8x8 grid is not fixed
until the players discover its boundaries through play. In other
words, once there are 8 tiles in one dimension, (top to bottom / left
to right), whether all in a line or not, you can not play to extend
the board any further in this dimension.

This I do think is a bit of a kludge in that it makes draws possible
for a start. However, it does ensure that every game will finish
within a finite time, and means that you can't run out of tiles, (the
sets I've seen sold include just 64 tiles).

! Notice that this game can be played with pencil and (graph) paper. !

I hope I've explained this intelligibly. If I haven't, direct any
questions to me, and I'll attempt to clarify.

Have fun, anyway. Do people agree that this is quite an elegant game?
I certainly think it satisfies most of the criteria suggested earlier.
I don't know of any attempt to analyse it in terms of complexity or
first-move advantages and the like.

Michael.




Newsgroups: rec.games.abstract