The game is played on a grid, usually 19x19, with black and white pebbles. Each turn, a player places one of his pebbles on one of the grid's intersections. Each intersection has four adjoining intersections, except for those on the edge of the board, which have three, and the corners, which have two. These are known as "liberties." If one of your pebbles or group of pebbles is surrounded by your opponent's pebbles, so that there are no more available liberties, they are "captured" and removed from the game. Ultimately, the game ends when both players agree that it is finished, and a player's total score is computed by subtracting the spaces he does control by the number of his pebbles that were captured. Highest score wins.
After first being introduced to the game, I began creating variations. One of the first was a three person variation. Pebbles were red, black, and white, and your pieces were captured whenever they were completely surrounded. I managed to coerce a few of my friends into playing a few games with me. What would usually happen is that two of the players would gang up on whichever player was in the strongest position. Then, since the strongest player would be quickly reduced, the next strongest player would be the strongest, and the two weaker ones would gang up on him.
The end result was one of the most frustrating games ever played. Each player was at any time either losing or fighting against superior odds. It did not last long among my group of friends.
Other variations I would experiment with usually involved variations on the board. By lopping off corners, or by removing the a few parts of the center of the grid, or even by removing all edges by having the board be a globe, I could radically change the strategies and tactics needed to win. The obvious problem was that such boards were irritating to construct. Most had to be drawn on pieces of papers, and some, like the globe, could not be made at all but a system of coordinates, like longitude and latitude, had to be used. At this point I realized that using only coordinates, two people could play a game by just shouting positions to each other, like blind chess.
All of this brings us to the day before yesterday, when while thinking about something completely unrelated, I realized how irritating it was to try to envision four spatial dimensions. I felt that if I had some way to practice it, I could think in higher dimensions more easily. What I came up with was 4d Go.
The rules for 4d Go and regular Go are exactly the same, except 4d Go has more liberties per intersection. 2d Go has four, 3d Go has six (the original four plus one above and one below), and 4d Go has 8 (the six of 3d Go plus the two above and below 4 dimensionally).
The trouble is, with each additional dimension, the playing space becomes absurdly large. A typical 19 x 19 board has 361 intersections. A 3d 19 x 19 x 19 board would have 6859 intersections and a 4d 19 x 19 x 19 x 19 board has 130,321 intersections. Obviously, the size of the space makes it impossible to play mentally, or even realistically.
To simplify this, I shrunk the board considerably to 4 x 4 x 4 x4. With 256 intersections, the board is still very large, but comprehensible. Still, it is difficult to hold the board in mind, so to practice, I began playing Go mentally on just a 4 x 4 board. The game is too small to end in anything but a draw, but it is good practice. Then, I moved on to a 4 x 4 x 4 board which has 64 intersections. It's a challenge to keep in mind, and I haven't yet fully played it out. I have, though, found that it can be easily played on chess board by dividing the board into four quadrants and imagining the quadrants stacked atop one another.
The result is a version of Go which is surprisingly easy to play and which I plan on subjecting my friends to.
No comments:
Post a Comment