Life In 19x19

Osvaldo wrote:I think I disagree with you palapiku. I think it is more a question of style/popularity than it being that research has established that for the first few stones, there is optimal and sub-optimal play. It's not about where you play the first few stones, it's about how you use them afterwards.

For example, the chinese opening was very popular at one point, and then lost its popularity among pros, and now it has resurfaced as the most popular opening.

This is because of the necessarily imperfect manner in which the search for perfect play works. A line is developed, refuted and abandoned as inferior - until someone finds a refutation to the refutation. Some backtracking is necessary, but this doesn't mean there's no progress.

There is no "optimal" way for an artist to lay his brush on a blank canvas...

But there is an optimal way to play Go. And the motivations of the professionals developing new openings are based exclusively on the perceived success rate of a line, not on any artistic value.

palapiku wrote:But there is an optimal way to play Go.

I guess this is the philosophical question that is at the heart of our disagreement-- whether or not we are approaching an "optimal line of play"

How can there possibly be an optimal way to play go? In the first few moves, there are many options (openings) that are reasonable for black, though of course it depends on what white plays. Then the course of the game is dictated by how black can make use of those moves, relative to white's moves. Every move becomes good or not in an increasingly complex relationship with all of the other moves on the board. Since there are more possible game combinations in go than there are protons in the universe, it is for all intents and purposes and truly infinite game... since it is infinite, there is necessarily an artistic aspect because it can't be solved. Top players play with a combination of knowledge and feeling.

Of course the collective understanding of the game progresses, and some extreme openings can be ruled out as too 1-dimensional, but I don't think top professionals will ever agree that for example playing a 3-4 and 4-4 is more powerful than playing two 4-4's. The chinese/mini-chinese/micro-chinese/kobayashi openings are very popular and powerful indeed because professionals have been studying them very deeply. They try to get an edge by using the research they have dedicated countless hours to. Once playing nirensei regains popularity with rise of some young star who has done his own research on some deep variations ensuing from that opening, I expect it will regain popularity.

Yes there is progress, but progress is almost insignificant when the path is infinite...

anyways we might just have to agree to disagree. But be sure to post it on here in 100 trillion years when you find the perfect opening hehe jk

There is indeed at least one optimal line of play in go. This is a mathematical fact that cannot be disputed. See: Zermelo's Theorem Unfortunately, there is no practical way of computing that optimal line of play.

However, there are very few lines of play in the opening that can be proven to be suboptimal. Lines of play that were considered terrible often become acceptable as the innovators show how to use them effectively. Even pros admit that what is considered "best" often changes with the style of the strongest player. Heck, sometimes trends may change because the top player got tired of playing a particular opening. To say that the nirensei opening for black has been refuted seems like an exaggeration. It is far more accurate to say that it is currently out of style.

There are many moves that were universally considered unthinkably bad by pros in the past, but became acceptable once the innovators showed how they could be used. This tells us that pros update their knowledge. However, it also tells us that an opinion that is strongly believed by 99% of pros can be overturned by a single innovator. Also, because pro's constantly update their knowledge, the refutation of an opening may be refuted itself in the future. This is because there is no practical way to refute ALL continuations from an opening. What is refuted is the currently popular way to continue from that opening.

lemmata wrote::w1: There is indeed at least one optimal line of play in go. This is a mathematical fact that cannot be disputed. See: Zermelo's Theorem Unfortunately, there is no practical way of computing that optimal line of play.

I wonder, do you know what prevents Zermelo's theorem from being extended from finite games to infinite games?

It seems like, if you add an additional condition that the moves must eventually exhaust the space (Which can be done in infinite games, you just have to allow for the occasional "half/quarter-infinite" move), then the theorem should still be true.

shapenaji wrote:I wonder, do you know what prevents Zermelo's theorem from being extended from finite games to infinite games?

It seems like, if you add an additional condition that the moves must eventually exhaust the space (Which can be done in infinite games, you just have to allow for the occasional "half/quarter-infinite" move), then the theorem should still be true.

If the game is guaranteed to finish, then it's not infinite, and if it's not guaranteed to finish then of course Zermelo doesn't hold.
I suspect that "an infinite game where moves must eventually exhaust the space" is a contradiction in terms?

Well, Zermelo's Theorem (what is usually called that name, anyways) uses backward induction in its proof. Backward induction is a method of solving the game backward from the last move. In games with an infinite number of periods, not all possible paths of play have a last move. An infinite number of moves in a finite period game would not prevent the application of backward induction, so infinity matters more in the time/move dimension. If the infinite game is shown to be meaningfully isomorphic to a finite period game after removing some redundancies, then we can use backward induction to show the existence of solution. shapenaji might be suggesting one of those cases. This is not a generic property of infinite games though.

I just wish everyone would remember that when we talk amongst ourselves about having a "winning strategy" or finding an "optimal line of play", that means one thing, and when game theorists talk about those things, it means something else entirely.

jts wrote:I just wish everyone would remember that when we talk amongst ourselves about having a "winning strategy" or finding an "optimal line of play", that means one thing, and when game theorists talk about those things, it means something else entirely.

You're making me remember why I don't like words...they have too many meanings.

lemmata wrote:Well, Zermelo's Theorem (what is usually called that name, anyways) uses backward induction in its proof. Backward induction is a method of solving the game backward from the last move...

For Go, how would we establish the final position from which the 'proof' proceeds?

ez4u wrote:

lemmata wrote:Well, Zermelo's Theorem (what is usually called that name, anyways) uses backward induction in its proof. Backward induction is a method of solving the game backward from the last move...

For Go, how would we establish the final position from which the 'proof' proceeds?

It's in the premises of the proof. If [i] the game must end and [ii] one of the players must win (at the end of each branch), then there exists at least one final board state that can be reached by legal play where one of the players has won. That's all you need to know about it, for the purposes of the proof. The position on the board doesn't matter at all, just that someone won.

(Now, technically Go is not apt for the strong version of the Zermelo theorem, because even with komi you can still get a triple ko. But if the technical meaning of "optimal play" doesn't deter the would-be game theorists, surely this wrinkle won't either...)

ez4u wrote:For Go, how would we establish the final position from which the 'proof' proceeds?

Like most proofs of this ilk, you don't have to establish anything specific.

There are a finite number of board positions (legal or illegal). All paths of play start from an empty board and move from one position to another. With a superko rule that says that any repetition of position results in a draw, the possible length of every path of play is bounded above by #Positions+1 (This is a very loose upper bound). This says that a final position will be reached in less than #Positions+1 turns, no matter what. We don't have to show what that final position might be.

For practical purposes, an optimal strategy for go, although it exists, is not something we can figure out. I do have some confidence that A1 is not a good first move for black.

Can somebody maybe give a brief summary of what "dictionary of basic fuseki" says about niresenei and sanrensei in general? I don't know this series, so if there's a content preview with some sample site feel free to post the link here too.