Edges

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Edges
Peter Aronson, with help from Jennifer Aronson
Edges is an abstract strategy game of placement for two, played on the 31 edges (not squares or points) of a three by four rectangular grid representing the canal network.
:Players Players:
:Time Length: unknown
:Complexity Complexity: Easy
Trios per color: 5
Number of colors: 2
Pyramid trios:
Monochr. stashes: 2
Five-color sets:
- - - - - - Other equipment - - - - - -
4x3 board, each space about 2"x2"
Setup time: 1 minute
Playing time:
Strategy depth: Medium
Random chance: None
Game mechanics:
Theme: Mars
BGG Link: 33280
Status: complete? (v1.0), Year released: 2987

Everyone on Mars is too busy playing Icehouse to pay attention to business! The government has essentially shut down because everyone working for it is too occupied moving around brightly-colored pyramids to do their jobs. But the Brigands of the Canals aren't playing, they're going to make a killing instead. They're seizing the canals, and making the farmers pay them for water. The farmers would fight back, but they're too busy playing Icehouse, so it's easier to pay...

Edges is an abstract strategy game of placement for two, played on the 31 edges (not squares or points) of a three by four rectangular grid representing the canal network.


Equipment

Edges requires a differently-colored stash of fifteen Icehouse pyramids per player (five large, five medium and five small each). The pyramids do not have to stack or nest, and they may be translucent or opaque. They should, however, be able to stand up. Edges also requires a board with a three by four grid on it. The cells should ideally be at least a little bit larger than two inches on a side, otherwise the large pyramids will bump into each other. The edges of the board should be a least an half of an inch or more from the edges of the grid. (We play on the squares of a tile-topped coffee table, but realize that option is not available for everyone.)


Goal

The goal of Edges is to surround squares with more points worth of pyramids than your opponent. Pyramids have the following strength.

Pyramid Size Strength
Large 3 points
Medium 2 points
Small 1 point

You score one point per square where you have more strength points worth of pyramids surrounding it than your opponent, and two points if you have the only pyramids surrounding it. Squares surrounded by equal strengths of pyramids are worth no points to either player.


Play

Randomly determine who moves first. The first player then plays any of their fifteen pyramids onto any edge on the board. The second player then has a choice: they may either play a pyramid onto any empty edge on the board, or they may remove the first player's pyramid (returning it to the first player), and place one of their own pyramids on the edge on which the first player's pyramid had been played. Thereafter, each player places a pyramid on an unoccupied edge in turn until all pyramids have been placed (there will be one unoccupied edge). Once the last pyramid has been placed, the game is over: add up the score and determine who has won.

The following image is of a completed game of Edges played using Zillions of Games.


The above game was a draw. Most of the squares are partially controlled by one player or the other. You can see a couple of exceptions on the top row, the leftmost square being completely surrounded by Red pieces, and so worth two points (and so marked), and the center square being surrounded by equal numbers of points of both player's pieces, and thus scoring no points for either player.


Variants

Edges can be played on other boards with other numbers of pyramids. Some that might be particularly interesting are:

Dimensions Large Pyramids Medium Pyramids Small Pyramids
3 x 3 4 4 4
4 x 4 7 7 6
5 x 5 10 10 10

Obviously, you'd have to use more than one color or more than one set for last two.

The 5 x 5 game can be played as a team game (Double Edges), where each player has a standard stash of 15 pyramids, and play rotates: Team A, 1st player; Team B, 1st player; Team A, 2nd player; Team B, 2nd player. No communication is allowed between teammates.

Notes and Comments

The modified pie rule (Schmittberger, 1992) used to start play of Edges (where the second player can take over the first player's position) may not be necessary, since it has to be demonstrated that it is an advantage to go first. However, if it were an advantage to go second, the first player could just play a small pyramid onto an outer edge, and then be in a position very close to going second. True, they don't get to make the last move then, but the last move is often irrelevant.

The bigger questions about Edges is that is it a forced win, loss or draw with perfect play, and how deep is the strategy tree? Is it shallow like Tic-Tac-Toe, or surprisingly deep like Dots and Boxes (Berlekamp, 2000)? I wrote the Zillions of Games implementation below in an effort to answer that question, but unfortunately, Zillions doesn't play this game very well.

The idea of playing on the edges of the board (as opposed to on the squares or intersections) comes from two games by Jared B. McComb, Danadazo and Border Wars. The theme was inspired by Glenn Overby's game Skurður, which involves canal travel on Mars. Glenn also suggested Double Edges.

Playtesting by Peter Aronson, Jennifer Aronson, Glenn Overby and Eric Clark.


Computer Play

An implementation of Edges for Zillions of Games (a general purpose boardgame engine) is available at Peter Aronson's Edges website. It plays both the 3x4 and the 4x4 versions. However you will need a copy of Zillions of Games (the full version that you pay for, not the free demo one) to play it.


References