Dots and Boxes variation: Lines and Boxes Dots and Boxes

6 replies. Last post: 2010-07-03

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Dots and Boxes variation: Lines and Boxes
  • juane at 2010-07-01

    I was reading about Dots and Boxes on the “internets” and found a variation that is new to me:

    “Although the goal of capturing boxes by making the final surrounding move remains the same, LINES and BOXES differs from Dots and Boxes in three ways:

    # Players alternate turns regardless of whether they capture a box or not;

    # Your move may connect any two dots on a horizontal or vertical line provided that your move does not overlap an already “taken” segment;

    # You play on a square or rectangular board that may not be empty when the game begins.”

    source: http://dinsights.com/POTM/LINESANDBOXES/details.php

    The third difference was there for the computer tournament that the site was organizing.

    What do the d+b experts think of this variation? would it be more challenging or less than the current game?

  • Aganju at 2010-07-01

    (even though you didn't ask me:) sounds definitely interesting to me!

    When I read it first, I missed the 'horizontal or vertical' part. Without that, I imagined a variant where you could make any diagonal or angled move - just connect ANY two dots; you may never cross an existing line. That would be wild (and probably bot-save!)

  • Macbi at 2010-07-02

    What does “overlap” mean? Is a horizontal line allowed to cross a vertical line? Are two lines allowed to share endpoints?

    The first thing to consider when analysing a dots variant is that the endgame (just before the first sacrifice) will always consist of a board filled with loops and chains (since the players are averse to giving away boxes, no boxes in the endgame will have 3 edges filled in, but since there are no free moves, almost all will have 2).

    In this game it looks like the boxes then have to be taken one at a time (depending on what “overlap” means)(and apart from loops (unlikelym I feel), where one player will get two boxes) so the game becomes “last move wins”.

  • Aganju at 2010-07-02

    If you check the example, you'll see that the point is that one line can close multiple boxes. Not sure if you can force this, but it would make a bit more sense

  • juane at 2010-07-02

    Yes a horizontal line can cross a vertical line. Two lines can not share both endpoints (it would be the same line…) but they can share one endpoint.

    Overlap means that a line can't share a segment (between two adjacent points) already used by another line.

  • FatPhil at 2010-07-03

    Not playing again means that the particular game theory associated with the long-chain battle disappears. A different parity battle emerges instead though, where basically even-length chains become neutral in score, but flip who's in control, and odd-length chains score 1 to the person who's in control, and keep him in control. So it looks like the game's decided by who has control as the endgame is entered, much like large*large normal dots and boxes. I can't see any reason to sacrifice, which would be a clear indication that this is a far more robotic game, and less tactical.

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