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Early Pieces and Rubik Distance

25/11/2011

Okay, so you know that you need to move toward the middle of the board at the start of the game, and you know that you should be doing it with your biggest pieces.  But which pieces?  And which orientation should they be in?

As for which pieces, some are just better than others.  It is convenient to think about the “maximum distance from one corner to another corner within one piece”.  This is called the “Rubik Distance” of a piece, named for Rubik87 who was one of the first to use this idea.  For example, the i5 has a Rubik distance of 6 – if you start at one corner, count corners as you move along the piece as far as you can go.  In the image below, see the Rubik distance of a few pieces.

The I5 and W have Rubik distance 6, the T5 has Rubik distance 5, and the O4 has Rubik distance 4.

The best pieces to use at the start are the ones with the biggest Rubik distance – they get you to the center as fast as possible.  You should check the Rubik distance of each piece as practice, and figure out which ones have the maximum (6).

Hint: there are 6 pieces with Rubik distance 6.  You should also check the Rubik distance of the other pieces.  If you are blue, and want to connect blue and red at the start of the game, you need 4 blue pieces, and 3 red pieces, and of these 7 pieces, 6 of the must have Rubik distance 6, and the other must have Rubik distance at least 5 – if you use pieces with smaller Rubik distance (total less than 41) you won’t be able to make a complete connection in the middle of the board.

This still leaves the question of which specific pieces, and which orientations you should use.  The specifics of this deserve their own post, but I will make a brief comment about the general idea:

The idea that should guide your decisions is this: you would like to place pieces that give you the ability to set up good blocks later in the game.  In general, you would like to avoid having long edges in the middle of the board, and definitely long L-shaped regions in the middle of the board.  For more on this, see the post: Shaping Your Zone

2 Comments
  1. kuuk permalink

    Hi,

    First, there is an error in the definition of Rubik distance : replace maximum by minimum, and it is ok (as you could choose to go clockwise with the T5). Giving this minor change, this is a good definition of the length of a piece.

    Still, I prefer using this definition :
    the length of a piece is the minimum number of squares of the board needed to go from the starting square of a piece to its farthest square.
    Notice you don’t have to stay within the piece to count its length, although, U5 aside, the count can be done “inside” the piece. Don’t forget to count the starting square.

    Therefore, in my definition, I5 has got a length of … 5, which is pretty nice for a piece of 5-piece.
    Every piece has got a length of 5 or less. Square has got a length of 3.

    Every piece has got a length of Rubik distance -1, and lengthes are going from 1 (i1) to 5 (I5, L5, N5, V5, Z, W). U5 has got a length of 4 (or 3), depending on which is the ending square you want to consider (same thing in Rubik distance : 5 or 4).

    Feel free to call it : kuuk distance , and say that rubik distance = kuuk genuine distance + 1

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