The Marginal Advantage (article)

[Toge]

This got me thinking about defense in Go. It's the other side of attack to prevent attacks against own groups. If you want to be able to do this, you must read for your opponent. Once the situations is read, fight can potentially be taken to another part of the board. This is to have fighting spirit. Points you stole from opponent can be as big as points you preserved. It depends on shape. One way to win is to always strive to maintain good shape. Otake Hideo is a player with this sort of style.

[Zwergesel]

There is also the question of what is optimal play and what are optimal moves. It seems from posts above that some people are thinking they have to choose the move that makes the most points every time. This sounds like a "greedy" algorithm and in optimization theory there are plenty of examples showing this might not lead to the overall optimal result. In go there are times when it makes sense to play a suboptimal-in-points move when you still have bigger moves available. For example, you might get tedomari that way.

A greedy algorithm should lead to the best possible result in Go. The problem is that in order to determine the point-value for a move you'd have to read all possible variations up to the end of the game. This of course is impossible for both humans and computers, so if you speak of the "move that makes the most points" you're talking about an evaluation based on personal experience, theoretical knowledge and partial reading. Likewise you can assign a "risk" value to moves based on factors like fights for big groups with uncertain result due to the limited human reading. If one is ahead in a game, a reasonable strategy for a human would seem to be to always play the move that has the best points to risk ratio. This is similar to a real greedy strategy, but based on imperfect knowledge.

[gowan]

There is also the question of what is optimal play and what are optimal moves. It seems from posts above that some people are thinking they have to choose the move that makes the most points every time. This sounds like a "greedy" algorithm and in optimization theory there are plenty of examples showing this might not lead to the overall optimal result. In go there are times when it makes sense to play a suboptimal-in-points move when you still have bigger moves available. For example, you might get tedomari that way.

A greedy algorithm should lead to the best possible result in Go. The problem is that in order to determine the point-value for a move you'd have to read all possible variations up to the end of the game. This of course is impossible for both humans and computers, so if you speak of the "move that makes the most points" you're talking about an evaluation based on personal experience, theoretical knowledge and partial reading. Likewise you can assign a "risk" value to moves based on factors like fights for big groups with uncertain result due to the limited human reading. If one is ahead in a game, a reasonable strategy for a human would seem to be to always play the move that has the best points to risk ratio. This is similar to a real greedy strategy, but based on imperfect knowledge.

Interesting ideas but I think the people who talked about making the move that gains the most points each time were referring to short time-scale or even just territory points.

[dfan]

A greedy algorithm should lead to the best possible result in Go. The problem is that in order to determine the point-value for a move you'd have to read all possible variations up to the end of the game. This of course is impossible for both humans and computers, so if you speak of the "move that makes the most points" you're talking about an evaluation based on personal experience, theoretical knowledge and partial reading. Likewise you can assign a "risk" value to moves based on factors like fights for big groups with uncertain result due to the limited human reading. If one is ahead in a game, a reasonable strategy for a human would seem to be to always play the move that has the best points to risk ratio. This is similar to a real greedy strategy, but based on imperfect knowledge.

A "greedy algorithm" is jargon that has a precise meaning in the study of algorithms, and by definition it is short-sighted and does not perform a large lookahead. It doesn't mean "try to win by the most points."

[Zwergesel]

A "greedy algorithm" is jargon that has a precise meaning in the study of algorithms, and by definition it is short-sighted and does not perform a large lookahead. It doesn't mean "try to win by the most points."

You are right of course! However my point is: In a greedy-algorithm, that always plays the move that makes the most points, how do you evaluate how many points a move gives you? And the answer is: Unless you evaluate the position to the end of the game, then there's no way to say how many points you get (in general). The greedy algorithm can be applied to Mancala, because you make a certain number of points on each move and those points can't be taken from you, but in Go there are usually no points until all territories are settled in the late endgame, so a greedy strategy can only be applied to Go if we evaluate the position completely and define the point-value as the margin of victory that this move gives you. This would be "best play" in a sense that you will get the best result (win/draw/loss) that is possible for you. Whether it is a true greedy algorithm, due to the exhaustive evaluation, could be argued about.


Regarding the article:

Imho the article is inconsistent and he's partially misusing the term "marginal advantage". In the first part where he's talking about the Mancala AI he's using the term correctly as he describes the "marginal advantage" as a game strategy. And that's really what the "marginal advantage" is about Gaining a small advantage and then keeping this small advantage until the end of the game, instead of trying to win big. This works as a strategy for certain games such as Mancala or Go where the winner is determined by points. It is essentially a strategy that tries to minimize the risk of losing points to the opponent.

In Starcraft or similar RTS games however, you usually can't win without first gaining a significant advantage, because the games are designed in a way that gives a bonus to defending your base. So if you have a marginal advantage you need to grow it to a more significant advantage, instead of just keeping it or else the game continues indefinitely (or until other game mechanics force a winner, such as the depletion of resources, but then it's still not trivial to win if you only have a slight advantage).
In these scenarios what he really means by "marginal advantage" is apparently that you should not try to win immediately as soon as you have the advantage, but instead grow it steadily while, again, minimizing the risk of losing it.

The next part has nothing to do with "marginal advantage" as he describes three other factors for competitive game design, all of which I agree with. But in his final paragraph he's constantly using the term "marginal advantage", but what he is really talking about is just diversity of play. While this is of course important for game design, he's just using "marginal advantage" as a buzzword there.

Regarding Go, I said earlier that "marginal advantage" can be applied to it, but it's not necessarily a good strategy for humans, because you must be able to evaluate the points and risk of each move very accurately and small mistakes can cost you the win. For non-professional players it's often better to find a way that gives you an even larger edge on your opponent, without taking unnecessary risks. As far as I'm concerned there's really nothing wrong with using your advantage to gain more, if you see a simple way to do that.

[dfan]

Aha, now that we are on the same page, I think we're in agreement.

[Harleqin]

Aha, now that we are on the same page, I think we're in agreement.

I think that it is highly ironic that this is posting #21, starting a new page.

[shawbee]

When i read the article immediately came to my mind Kageyama's book on fundamentals. In the intro to second chapter he talks about this move made by Kano 9-dan, that caught his attention:

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He even quotes the newspaper writer: "...and Black 1 firmly captured the white stone. Had it been us, we would have wanted to expand around 'a' and swallow up the stone on a larger scale"

The commentator of the match (Sugiuchi 9-dan) said: "(...) This makes the game close. It's probably correct. If he were behind, he would try a larger move . Black 'a', for instance."

So, sure, Kano 9-dan could have gone for bigger things; or could've read if that white stone in the corner had any danger (he probably did); but he didn't try any "fancy lets maximize" my move. He played solid. Enough advantage to win, absolutely confident.
Sugiuchi doesn't say 'a' is bad... it's correct if he is losing.


Kageyama later adds: "Any strong player, even an amateur, has the right to doubt, and wonder why proffesional do not make more ambitious moves. One might even go sor far as to wonder if professionals, too, are not subject to attacks of nerves. In the end, however, it all comes down to the professional's faithfulness to fundamentals."