I do not currently have an office suite installed, and Google Docs doesn't seem to understand the code.

Either way, I think I understand what you're doing. Basically, you're playing 2D games of go on a 4D field, with a 3D interface. I don't mean to put your game down with any of this (although I am hoping that this discussion won't confuse anyone who may want to download the game I made), but I do consider it much further from go (my version sticks to the three rules that I feel define the game; I'll paste them here later on). My version may be a good deal less playable, though, as everything tends to end up being one giant capturing race.

No time to write more now, will expand on this later on.

[sgf-full]http://www.yawnguy.com/go/4x4x4_versionA_commented_game_1.sgf[/sgf-full]

I'm currently editing an sgf record of an ongoing game on CGoban3. It has been playing using the usual sgf reading software at this site, so you should be able to read it OK. It's not quite the same as the linked spreadsheet I have uploaded and linked to. Apart from it only being a record (duh), it automatically removes stones that have been captured. While this might seem correct, it depends on the ruleset.

I'm tweaking the rules right now to see what seems to work best. Some things have to change, and it is a question of deciding on workable changes. Otherwise the game ends up being silly and no-one will want to play it — a bit like the tale of the surgeon saying the operation was a success but the patient died.

So this isn't a done deal and I am editing it right now and uploading new versions every half an hour or so with moves added but maybe earlier changes too.

I'll post further when I have more to say!

Paul

What is the reasoning behind the stones in column 3 not being removed?

Remember the moves in the right-hand three columns are generated three at a time by playing on the grid on the left, and are not made independently. So a move on the left can cause a capture on one of the boards on the right, but not the other two. If a player later sees the "empty" intersection in one of the right-hand columns, he might feel it's OK to play in it, like in a ko, or a snapback. However, it's impossible to play a move in the left-hand playing grid, the only place where one is allowed to play a stone, to place a stone at the "right" point because there is already a stone sitting there!

Leaving captured stones on the board, but marking them as captured, prevents this happening. The intersection is read as not having a stone on it for liberty purposes, but cannot be played on by either player.

Now, in the first game I played out yesterday, this meant that it is impossible to capture a group which has such a point next to it. It's as good as having two eyes.

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Another questionable point is that of committing suicide. Let's say one wants to play a perfectly legal-looking move on the grid at the left, and in two of the right-hand columns it looks fine, but in the third maybe the play would be illegal, like playing the 1-1 point when the two adjacent 1-2 points have enemy stones on them and no capture of the enemy stones would take place. In yesterday's game I decided that meant the move was illegal and couldn't be played. At the end of the game there were four points that could be played by White but couldn't be played by Black, and a few points that couldn't be played by either player. Which again allows groups to live without two eyes as such.

As I said I'm tweaking the ruleset to see how else it can be done.

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Also note that there is much more attention on capturing going on in this game than in the previous game I played, which was more obviously aimed at gathering territory.

Paul

I suggest we drop one dimension, so that your game becomes a 1D games of go on a 3D field with a 2D interface. Let's state that the interface is 4x4, and the field must thus be 4x4x2.




The marks could of course be skipped, but I think this makes it clearer for now.

Now, if we play:



In another few turns:



At the end of the turn, once the dead stone is removed, the field will look like this:



When playing this way, we can imagine that every move inserts a coloured stone staff into the board. If there is something in the way anywhere -- such as B4 now -- it will fail. We could extrapolate these rules to make a field that has any natural number of dimensions, and using any boards that have a natural number of dimensions (but no more than the field does). Standard 2D go is simply a 2D field with a 2D board. My 4D go is a 4D field with a 4D board.

The main problem is that I am still not sure about what number of dimensions the input must have. So far, we have observed:
Field | Board | Input:

• 1, 1, 1
• 2, 2, 2
• 4, 2, 3
• 4, 4, 4
• 3, 1, 2

I wonder whether a 5D field with 2D boards would thus yield a 3D or a 4D input... 4D, I think, but I can't prove it. In fact, I still have to demonstrate such a game can exist at all. Hm. Will look into it tomorrow.

I think we're at cross purposes here. It looks like I want to create an interesting game, and you want to write a theoretical treatise that is mathematically as sound as possible.

Anyway, it's my bedtime now. we don't have to agree on this, you know.

Paul

My goal is indeed to understand the rules you use for your game, and generalise them to be able to be used in more contexts.

I've come to the conclusion that the field must always have one dimension more than the input. The boards may have as many dimensions on the input. If the input and the boards have the same number of dimensions, the field's extra dimension is one thick, and therefore does not need to be accounted for.

I've also decided that I don't intend to write a generic engine for this at the moment. I think that if you intend to continue developing your version, it would make sense to split this discussion off into a separate thread, as it is unrelated to the first post.

Fair enough. I'll start a new thread about my version soon. I'm still working on the demo game and updating the sgf in post #22 regularly.

EDIT: I replaced the original 96k sgf with a 40k sgf as the large one was too big and wouldn't play beyond 2/3 of the way through. It's OK now with less symbols in use.

Paul