Comments on: Games with Graphs

By: Nathan

Nathan — Fri, 13 Mar 2009 03:12:51 +0000

Very Interesting post! found via StumbleUpon.
I would be honored to write an intelligent agent to play you in a game of Go on the surface of a buckyball.
I know this is the web, but if you had givin a talk about this in person (say at UNC Charlotte for example) I would probably beg for your autograph

By: Peter de Blanc

Peter de Blanc — Fri, 14 Jul 2006 19:49:42 +0000

You might be able to play Go on an infinite board if the value of the board were finite. A stone placed on the origin might be worth one point, and the value of a stone would decrease as you went farther from the origin. When the value of the unplayed-on part of the board drops below the difference in score between the two players, you could end the game.

Also, you can run Life on a finite grid. Usually this is done by connecting the left and right edges together, and connecting the top and bottom edges together, forming a torus, or doughnut shape.

By: Carolyn L Burke

Carolyn L Burke — Fri, 14 Jul 2006 12:48:18 +0000

I see one significant difference between Go and Life as outlined here. You’ve set up Life on an infinite board, while Go has a finite territory. If Go also had an infinite board, then the win or end state, what you are calling the goal of the game, would become moot, that is unachievable.

Can Go be played as a game with an infinite board? (By game, I mean something with an end state or win condition.)

By: pdf23ds

pdf23ds — Thu, 15 Jun 2006 22:21:06 +0000

I don’t understand “the rules of Go could specify precisely how the players think” paragraph. What do you mean by passing a goal to a player? Are we implementing them in our universe, or a Go-universe? If we specify exactly how they think, what degrees of freedom are left?

I think Nick means that, hypothetically, the rules of Go could include exact and deterministic rules governing how the players played the game, which would be anologous to the rules governing state transitions in Life, and this would make the two “games” quite similar.

By: Peter de Blanc

Peter de Blanc — Sun, 11 Jun 2006 22:43:51 +0000

Nick: Of course, it really only makes sense to speak of agents, and not games (or universes), having goals. The point of this article was to show why it doesn’t make sense to think of the universe as having a goal.

If we specify exactly how the players think, then there are no degrees of freedom left. That’s kinda the point. If we wanted to make rules of Go that determine the course of the game deterministically (as the rules of Life do), then we need to define exactly what the players do. One way to do that would be to say that the players use a minimax algorithm, and try to maximize their score as we defined it above. If you defined Go this way, then you could say that human Go players aren’t *really* playing Go, only approximating it.

By: Peter de Blanc

Peter de Blanc — Sun, 11 Jun 2006 22:28:52 +0000

I don’t think it’s nonstandard. :-)

By: Kaj Sotala

Kaj Sotala — Sat, 10 Jun 2006 21:39:45 +0000

Nitpick: Hmm, interesting. Okay. (That’s a nonstandard scoring method, though, so it might be good to note that in the main article.)

By: Nick Hay

Nick Hay — Sat, 10 Jun 2006 18:44:02 +0000

Nitpick: one can score by counting the number of stones on the board. This is equivalent to standard scoring (either by territory or area) except you are penalised for each separate live group you have. See http://senseis.xmp.net/?StoneScoring .

By: Kaj Sotala

Kaj Sotala — Sat, 10 Jun 2006 15:52:07 +0000

Nitpick: the goal of Go is not to have more stones. The goal of Go is to have more territory. (And in the first example, White should have passed as soon as Black did – playing the center stone reduced White’s points, as it ate up a point of its own territory.)

Other than that, nice write-up. :)

By: Nick Hay

Nick Hay — Fri, 09 Jun 2006 01:45:19 +0000

Hmm, there’s something I’m missing. Perhaps I’m splitting hairs.

If we view things from the outside, as games implemented in our universe, both Life and Go can have goals. In Life the initial state can be chosen to implement a goal (e.g. maximise gliders, maximise alive cells) embedded in the description of the game. Just as the players in a Go game can be designed to implement a goal (e.g. to win, to lose, to have a game of even length, to maximise the number of alive groups). With Go there is a standard goal associated with it, but that doesn’t seem significant.

Life maps much more nicely to the dynamical systems we see in physics: set the initial state (perhaps) and the dynamics’ll do the rest. With Go we have an incomplete system which doesn’t quite map so nicely. (Unless one considers the sequence of player moves, or the pair of players, as the initial state.)

Viewing things from the inside, as universes themselves… Life works but Go doesn’t seem to. Typical Go players aren’t implemented as Go shapes. I can’t work out how to compare the two from this perspective.

(Lack of suicide is my major gripe with the mathematical rules. Have likewise linked you.)