4D Go

yawnguy · Post by **yawnguy** » Wed Apr 27, 2011 9:19 am

I've got a Go 4x4x4 software version online now. I used the cell-linking function in a spreadsheet. There's an Open Office Calc one and a 97 Excel one.

On the left in green is the playing grid. A stone played there will automatically place the appropriate 3, 4 or 5 stones on the 4x4 boards on the right. The legend to the right shows what will map where. The characters used are more or less arbitrary.

I haven't worked out all the rule tweaks yet. Maybe someone else will be interested in it too and will come up with something workable.

I figure that once a stone is played in the green playing grid, it's a done deal. When a stone or group on the 4x4 boards on the right is captured, it seems best to mark it as captured using the format cell background feature* (I colour it red) and then imagine a permanent empty space there. This works like an eye for both sides. Kos are impossible, of course.

For a move to be legal, it has to show as legal on all 16 4x4 boards. I have been using a different character to show the tentative move, while it is checked out to make sure it is legal throughout. If OK, then the move is made permanent and the usual symbols are used (X and O, or B and W, or whatever).

What often happens is that what looked like a great move on one board turns out to be really bad on another board, but I figured the best rule was once you have made a tentative move you're stuck with it as long as it is legal. You can only undo it if it is illegal on one or more boards. I found it useful to put nb, nw or nn in the move squares to signify points that would be illegal moves for Black, White, or both as they get checked. It saves re-checking next time. And it also shows a safe position on a board, in that if Black can never put a stone adjacent to a white stone, that white stone can never be captured, even if it has no eyes at all.

I've played through about 3/4 of a game. It's quite interesting. It is playable, and I can see glimpses of various strategies. I haven't got down to the nitty-gritty of scoring yet.

I don't know if I'll make a 4D board, but using simple spreadsheet software looks like the way to go if I do. The only real thing lacking apart from a pretty interface is an automatic prevention of illegal moves.

Paul

EDIT: Highlight the square(s) concerned, then Format > Cell > Background > Select colour

yawnguy · Post by **yawnguy** » Wed Apr 27, 2011 9:22 am

Sevis wrote:Yawnguy, I am not sure how you are treating the extra dimensions, but I it is not the way I am treating it.

Just saw this. I'll answer it later. Dinner time now.

Paul

Abydos1 · Post by **Abydos1** » Wed Apr 27, 2011 10:17 am

Sevis wrote:Yawnguy, I am not sure how you are treating the extra dimensions, but I it is not the way I am treating it.

...

Reviewing your post, I think the reason you're treating things this way is because in tic-tac-toe, things really work that way. I would argue that in go, they do not: 2D go is not merely `a number of 1D go games'. Adding a third and fourth dimension simply add connections up, down, strangewards and charmwards (the terms I use for the fourth dimension), and thus on the single, `unsplit' goban, every stone has at most eight liberties, and will live or die according to them. How many liberties a stone has when you cut things into cubes, slices, and rows is irrelevant for it.

Agreed, the extra dimensions add more connections; it's only one game of go you're playing.

yawnguy · Post by **yawnguy** » Wed Apr 27, 2011 12:05 pm

Take a look at the dynamic spreadsheet I've given links to and toss some moves into the green-bordered bit. It should give a bit more life to my explanation. Sheet2 of that spreadsheet gives the numerical basis for the mapping. I used alphabetical characters on the top sheet because they take up less space.

I agree that in theory one could just play "one game," where in 3 dimensions a stone in the middle has 6 liberties. What is that like as a game? Is it playable? Can I play it online without being a Linux nerd? I've shown you mine — will you show me yours?

If you want to look on your version as the proper one, and mine as an upstart, that's fine by me. It's a big universe!

Paul

yawnguy · Post by **yawnguy** » Wed Apr 27, 2011 4:12 pm

Oh! I finally got it through my thick head about the diagonals. Thanks. It's bed time now, so I'll nuke them tomorrow.

EDIT: Now uploaded without diagonals.

Paul

Sevis · Post by **Sevis** » Thu Apr 28, 2011 10:35 am

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.

yawnguy · Post by **yawnguy** » Thu Apr 28, 2011 2:19 pm

[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

Sevis · Post by **Sevis** » Thu Apr 28, 2011 2:35 pm

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

yawnguy · Post by **yawnguy** » Thu Apr 28, 2011 3:42 pm

Sevis wrote: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.

-----

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.

-----

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

Sevis · Post by **Sevis** » Thu Apr 28, 2011 4:11 pm

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.

yawnguy · Post by **yawnguy** » Thu Apr 28, 2011 4:39 pm

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

Sevis · Post by **Sevis** » Fri Apr 29, 2011 11:32 am

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.

yawnguy · Post by **yawnguy** » Fri Apr 29, 2011 11:42 am

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

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