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Mind Ninja» Forums » Variants

Subject: Pattern Idea (and more): Equicolored Neighbors rss

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I don't know if it has been done before. This variant uses two colors and can be played on any board, which should be full at the end. A point has equicolored neighbors if it has the same number of red and blue neighbors. The goal is to have more blue than red points with equicolored neighbors.

The other idea: instead of alternate turns, the builder could place for example two stones, the blocker one, and so on during the whole game. It could be used when the pattern is really difficoult. More precisely, the pattern-chooser could decide the order of the steps, like builder, builder, blocker, blocker, builder, blocker and so on (in general a sequence with length equal to the size of the board is needed, but it could be narrowed down to the following: the builder puts x stones, then the blocker y stones and so on).
Adding this additional rule a difficoult pattern can be played without filling almost the whole board as initial position.
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Nick Bentley
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Note: this pattern is the winner of the first Mind Ninja pattern design contest:

http://www.boardgamegeek.com/thread/328769

I assumed that the pattern was to be played on a hexhex board. In the pattern as proposed, it doesn't say whether the edge cells can be counted as equicolored (i.e. when surrounded with two red and two blue). For the purpose of the contest, I assumed that edge cells count. I also assumed that corner cells do not count, because they don't have an even number of neighbors.
 
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Yes, that is the game on a hexhex board, but it can be played (theoretically) on any other board too. Cells with an odd number of neighbors cannot have equicolored neighbors, hence they don't count, all the other cells do. On a simple grid the corners count, and the edge cells don't. Or if a strange board contains some cells without neighbors, they will always have equicolored neighbors.
 
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Nick Bentley
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Thanks to Arty Sandler, this pattern is now playable at the iggamecenter. It has a different name there, however: Equilibrium. Also, the builder is trying for more red cells with equicolored neighbors, as is the convention on iggamecenter.

Here's a link to a completed game that you can review step by step from the beginning to the end:

http://www.iggamecenter.com/gm.php?gid=17&sid=32063

This particular match was a close, draining struggle (33 to 30 was final score). This pattern requires great concentration, and I'm both mystified and delighted by its strange dynamics. Truly, a pattern from another planet.

Here's what the game looked like after the last move (click to see bigger version of image):





 
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Nick Bentley
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I've been thinking about this pattern, and I would like to point out a strategical starting point for anyone who wants to try it. The first time you play the pattern, you'll be tempted into thinking in a math-y way, and you'll find yourself counting cells alot, and the whole exercise may drain you without helping you much.

To avoid all that, consider this: there are only four fundamental geometrical shapes that matter for this pattern. Here they are:



To win at this pattern, you need to ensure there are more instances of these shapes in the color that matters to you than in the other color (note: the shapes can partly overlap, and share certain pieces). No need for counting. Think in terms of these pictures and the pattern will start to open up for you.

[EDIT: note that three more shapes, each consisting of three colored cells a piece are needed in order to think about scoring along the edges of the board. They're real simple, so I'll let you figure them out for yourself.]

Nick



 
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Nick Bentley
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More thinking: one way to discover good strategies for this pattern might be to look for regular tilings of the board that maximize the difference between scores for the two colors. If you could find such tilings, you could use them to guide your moves in play. I haven't tried to look for such tilings yet, but it's an idea anyway.
 
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