# Does a Go variant on an infinite board exist?

I've just read the paper Better Computer Go Player with Neural Network and Long-term Prediction which seems to make a big step in direction of getting a better algorithm playing Go than any human.

Source: xkcd.com/1002

Now I was wondering how the game could be changed to something which is well-defined and where humans are still much better than computers.

Does a Go variant on an infinite board exist?

One would have to play it with a computer, of course. Having such an infinite board (of which only the parts which were looked at are calculated, of course) isn't really a programming problem.

As the boundaries seem to be important, one could add random borders to the game. The winning criterion could be an absolute / relative difference in points. What would be the implications of such a game?

Another idea would be to make a (pseudo-)fractal board.

• I wonder whether you know even the basics of Go. The finiteness of the board is essential to the game since it is decided by territory count or area count. A Go game on an infinite board would go on forever undecided. Commented Dec 11, 2015 at 9:24
• How could you possibly win? Commented Dec 11, 2015 at 10:40
• @Chenmunka I thought of an absolute / relative difference in points. Commented Dec 11, 2015 at 19:19
• @jknappen: I think the problem is more how to define the end of the game. (Internal) territory may be correctly defined as vacant points only connected along edges to stones of a single colour (contrast with dame, which are connected to both and score for neither, if we ignore Ing’s rules), and that works fine on an infinite board. It still works if we either add captives to territory or count the total area ‘controlled’ by each player (occupied+internal territory). Perhaps this is what moose means by “points” in “an absolute / relative difference in points”. Commented Dec 13, 2015 at 23:18
• I suspect that adopting forms of “fairy go” (by analogy with fairy chess) would help a programme far more than a human. I have yet to meet anyone I suspected of having an infinite brain. Our advantage comes from the way we learn about and adapt to new situations, internalise what we learn, and communicate it using a rich array of concepts such as aji-keshi or furikawari and the heuristics embodied in go proverbs such as “play at the centre of symmetry”. I think that at first humans would adapt faster, but that programmes once adapted would have an edge until humans had built up a culture. Commented Dec 13, 2015 at 23:34

There is a Go variant without boundaries (but, of course, on a finite board): Torus Go. It is sometimes played in Go clubs or as a side event on Go tournaments. On a traditional board I find it very hard to visualise.

There are variants like 3 dimensional Go, which may be interesting to you. However, from personal experience as well as seeing higher dans struggle, I'd guess humans are far worse at them than computers :)

I'm not aware of any kind of "infinite" Go that is even remotely playable. The basic problems are ladders, which need to end, and counting, which requires complete separation of space.

As far as I can tell, infinite Go could be achieved via a sequence of spaces that interact, either hierarchically or flat. You could define that a ladder may not leave its subspace etc. Play could either be simultaneous in all subspaces, or in only a selected (number of) subspace(s). While this seems borderline theoretical computing science, I believe it would provide a gameplay quite similar to the original, just with certain additions that make turns a lot more complex.

• I think it is a mistake to want to defined a ladder: it is a consequence of the rules, and the same should apply, if at all, on an infinite board. Commented Dec 13, 2015 at 23:22

With a time control, you could play on the infinite board. A player could be forced to pass when the time limit is reached. Eventually, both players pass (unless somebody resigns before) and the game is finished.

I guess, you could play on an infinite board without time control, but to make the game finite, you need to have a limited supply of stones. Basically, than would mean that a stone group that is far enough from others could be considered to be on a separate board.

Or you could keep a running score estimate (captures + territory), and once a player hits a predefined score limit, the player wins and the game ends. You just have to exclude the outside territory (that reaches to infinity) from the score, otherwise Black wins with the first move.

Another interesting approach could be, after a predefined number of steps to start game running, to have an arbiter (or a computer) to end the game after each move with a small probability. So, you never know beforehand when there is the last move, but the expectation of the game length is finite.

With either approach the game would be different from the regular Go because of lack of the usual interaction with the board edges.