Go on a Board Without Lines

Table of contents Introduction Why no name? History Rules The future Interesting notes General discussion

Index of sub-pages Go on a Board Without Lines Bildstein's Implementation Discussion

Introduction

This is an intentionally nameless variant of Go, on a board without any lines. Pieces can be placed anywhere on the board, but otherwise the rules are as close to the rules of Go as I could manage (which I think is fairly close).^[1] Sebastian has now written quite a good page on a somewhat revolutionary implementation of this idea, called Euclidean Go, which has some very interesting qualities. His page has lots of informative and descriptive pictures, and is well worth a look once you understand the basic ideas of playing Go in continuous space.

Why no name?

Because I don't want anyone to think there are any hard and fast rules. It's not like we're going to have a tournament in this variant. It's more of an experiment. Perhaps one day enough people will start playing it that it warrants a name of its own, but until then it can just be "Go on a board with no lines."

History

My Honours thesis involved using artificial neural networks to play Go. While writing it, I realised that my approach was taking advantage of the fact that a position on a Go board could be reduced to a certain number of discrete inputs, but when people play Go, they don't take advantage of this nearly as much. We simply don't see the big space in the middle of the board after 31 moves as 110 individual empty intersections, we just see it as an empty region about so big.

So I started thinking, "How could we make the game of Go harder for computers to play?", which is really masochistic, I know, because it's already way too hard. But this variation of Go was the answer to that question (in my opinion). I haven't played it yet (it will have to wait until I write a client for it), but I think that people will find it easy to play, that being strong in Go will translate to being strong in this variant, and that being strong in this (if you were to learn this variant before learning Go) would translate to being strong at Go. And I think if this turns out to be true, that it might mean that we are going about writing Go playing software the wrong way.

Rules

• Connection - Two friendly stones are connected if they touch or are connected to a third one.
• Capture - A stone is captured if there is not enough room to place another stone touching it or one it is connected to. A move includes identification of all captured opposing stones and - after that - their removal.
• Suicide - It is illegal to play a move that will result in friendly stones being captured. (This includes a stone that is surrounded by friendly stones that are not touching but are close enough not to leave space for another stone to be placed.)
• Ko - It is illegal to immediately capture the last stone played if it is connected to no other stones and was used to capture exactly one stone. ^[2]
• Scoring - Captured stones count like normal, as does any komi, but the value of each player's territory is defined by the number of additional stones that can be placed within it. This can only be achieved by experimentation, and it is up to the players to find the optimum arrangement of stones inside their territory to establish their score.

The future

Playing this game in reality would be nigh on impossible, due to the accuracy required to implement the rules (Is there space for an another stone in between these four?), so I plan to write a computer program to be the ultimate adjudicator. Here's a few features I hope to implement, in the order in which I think I'll add them:

1. A simple board. The user can place stones of either colour and it is up to them to alternate. Captured stones are identified and removed by the user. The program will tell you whether or not a move is valid when you try to make it. Scoring is done by manually adding extra stones of a third colour and counting how many you ended up with.
2. Two people running the software can connect to each other across the Internet and play, either one being able to place or remove stones.
3. The rules are enforced.
4. The software will do simple calculations for the user, for example to allow him to place a stone touching two other stones, or with enough room left between it and another stone for an eye.

I've now started work on this software. For more details, go to FreeGo. (Update by Sebastian:) Latest version available at http://www.helm.org/s/go/continuous/.

Interesting notes

I think I've figured out what the smallest groups with two eyes are under this set of rules:

• The smallest living group you can make in the corner is 4 stones, instead of 6 in regular Go.
• The smallest living group you can make on the edge is 5 stones, instead of 8 in regular Go.
• The smallest living group you can make in the center is 8 stones, instead of 10 in regular Go.

See this page, which contains some pictures I created to demonstrate these minimal groups.

- Bildstein

General discussion

(moved to GoOnABoardWithoutLines/Discussion) Anyone who feels like doing a WikiMasterEdit of the discussion page would be appreciated. I'll try to get around to it some time.

[1] See the page DougRidgway suggests for similar variations: http://www.di.fc.ul.pt/~jpn/gv/boards.htm

[2] Thanks Rubyflame.