Dots and Boxes variation: Lines and Boxes Dots and Boxes
6 replies. Last post: 2010-07-03
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6 replies. Last post: 2010-07-03
Reply to this topic Return to forumI 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?
(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!)
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”.
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
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.
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.