I think that this is an interesting article that also applies to Go (even though it mainly mentions various computer games):

The Marginal Advantage

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A good system naturally covers all corner cases without further effort.

For the SC fans, Sean Plott is Day[9] . I'm a huge fan of his high-level analysis on SC2, and you can find a lot of parallels between SC2 and Go.

It sounds like an interesting idea. Can somebody say from experience that trying to win by a marginal amount works well in go?

My fear is that, if I have only a marginal lead and then make a mistake down the line - which seems inevitable, I lose that marginal lead.

If I try to play in a way that maximizes the lead, if I made a mistake down the line, I might have a cushion. Maybe I'd feel the same way about Mancala if I played it.

Apparently this may not be the case... Can somebody with experience in applying this to go explain to me how they deal with the fear that I have explained here?

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be immersed

This is basically the way that the new Monte Carlo bots play - they are always trying to play the move that gives them the maximal chance of winning, not the move that maximizes their score.

I need to try this.

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That which can be destroyed by the truth should be.
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My (sadly neglected, but not forgotten) project: http://dailyjoseki.com

Wow, who'd have thought the day that Day would be more famous than his brother, to even appear on a Go forum?

I'm not sure if this answers my concern. If I try to only keep a marginal lead, I don't feel like I am maximizing my chances of winning because, if I make a mistake down the line, I could more easily lose the lead than if I play to try to maximize points.

If I get a point cushion, then I feel like mistakes won't affect the result of the game.

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be immersed

I am not sure either! I was just trying to point out that it works for some "people."

But, maybe more relevantly, I think this is just a generalization of the principle "don't pick fights when you're ahead." If you're up 20 points on the board, you can afford to play safely and not totally optimally. For those of us who are not pros or computers, it's probably not a good idea to try to coast to a 1.5 point win though

Interesting article. It reminds me of a couple things I've read about some pros. Since I tend to take second-hand analysis with a grain of salt, I don't know if they're true or accurate. Even if they're not, I find them to be at least useful parables in how I approach my play.

Once I read about Phil Ivey (Pro Poker Player); I'm especially skeptical of any comment of conservative in poker. The article said that Phil's style was based on the fact that he knew he was better than the other players. As a result, he'd be willing to walk away from big pots w/ lots of risk to slowly take smaller pots consistently, allowing him to win in the end. It minimized the gambling aspect (busting out when risking it big), and allowed more control of the situation. At least in a casual sense w/ friends, this style has worked for me well.

I also read that Lee Chang Ho would be willing to play suboptimal local plays if it allowed him to limit his opponents' options. This in turn meant he could read further through less branches. As a result, get a longer term large advantage while potentially sacrificing in in the short term. At a superficial level I contrast this with Lee Se Dol games, often described as large wild fights, in what feels more like an all-or-nothing game than controlled and measured (but that may just be a severe lack of understanding). My reading and board assessment isn't strong enough to guarantee this to work for me, but it does help me to not make reckless plays.

I do think marginal advantage looks (and sometimes feels) less exciting. But I enjoy the thought that if I can consistently play a couple points better than my opponent, I'll win. I don't need the big kill, I just need the slow steady death of a thousand cuts for my opponent.

Actually, I think that this is a major insight that can help your Go tremendously. I thought on different occasions that I had finally got it, but it is an eternal struggle. The point is not that you try to win by a marginal amount, but that you work to keep your advantage instead of trying to expand it even further.

I know the feeling that having a lot of points in advantage somehow feels more secure than having less points, but actually, it is better to work for thickness and for settling the game.

I recently had a game in which I got ahead early (around move 50) because my opponent mistreated a corner, and the whole rest of the game I managed to play for thickness. I made some mistakes, but I managed to keep about 10 points ahead throughout, at several points choosing a line that gave my opponent points, but also settled the game. Of course, since the game seemed still countable, my opponent did not resign. With my second to last move, I finally blundered for a swing of 15 points (overlooked trivial damezumari), and with my last move, I overlooked a similar blunder by my opponent which would have made a swing of about 6 points, and finally I lost by 4½ points. This can happen (and I fear that I am building up a bad reputation of having a bad temper when this happens to me), but it is much easier to avoid such blunders than to get unscathed through a needless middle game fight.

"To crush your opponent, see his weak groups driven before you, and to hear the lamentation of his cramped shapes"---yes, but this is Go, all stones are made equal, and each player makes one move on his turn.

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A good system naturally covers all corner cases without further effort.

It seems that Monte Carlo programs do make plays calculated to give them the maximum score by the end of the game--at the very least, relative to their opponent's. For example, A move that has the highest chance of getting the largest amount of territory, but a corresponding risk that the opponent can invade, is not necessarily the territory-maximizing move. It just depends on the risk. Granted, this is an oversimplification.

The bigger point is that, if a move has a higher chance of getting more territory, but also a lower winning percentage, the territory conceded in the losses offsets the territorial gains in the wins (it should in theory, anyway).

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.

I have heard Day9 (Sean Plott, the author) talk about this topic on different occasions, both in his shoutcasts and his forum posts, and you can tell its a little pet topic of his. I'll try to explain a little clearer what he means by marginal advantage.

The most important gist of his idea is that when you are ahead in a game, you should not be "going for the kill", but rather think about the safest, surest way to parlay this small advantage into a slightly bigger advantage later on. The goal is to control the flow of the game and inexorably expand your advantage, such that the game will be naturally won without you having to push things.

To use a game of Starcraft for example, say you've won a small skirmish defeated your opponent's army, thus granting you a military advantage. Many players would be tempted to press the attack and try to end the game in final, decisive battle, even if it means fighting on adverse terrain. While this may win you the game right there, you might also lose your army due to superior opponent control, your own micromanagement mistakes. This would cause the game to be even, or you might even be in a losing position after that. If we follow the principle of marginal advantage, what you ought to do is to pull back, and make use of your superior military by securing more resources and map control while matching your opponent's military production. You should aim to make your advantage in one aspect (military) translate into an advantage in all respects (military, economy, technology, map control). Soon this will result in an even larger military as well as economy until eventually, your advantage is so large that there is no conceivable way your opponent can beat you in a battle, even if a monkey takes your place.

A corollary of this is that when you are ahead in a game, you should be risk adverse, and if you are behind, you should swing for the fences. By following up on the first Starcraft example, after you have advantage, you should aggressively scout what your opponent is doing, either for hidden expansions or tech switches. This way, you will remove all counterplay and prevent him from forcing an "all in " situation. While you are behind however, you should take crazy risks like establishing resource bases without defense (hoping they won't be found), harassing aggressively while leaving only token defenses at home, or completely neglect economy to try and win with a burst of military advantage in a game ending battle.

I find a lot of these principles to be relevant and often quite well known in Go already. One thing that struck me in particular is the importance of counting - if you are ahead, you shouldn't start a fight involving huge groups that have an unclear result. Or say, if your opponent made an early joseki mistake that gave you too much corner territory for insufficient thickness, then you shouldn't be trying to take even more territory, but simply solidify your existing groups and try to match him in the balance of power. The idea is to avoid risk, try to use your one advantage and obtain clear, if slight advantages in all aspects of the game, and then safely expand upon those advantages even further. This will create a "natural" win where you never had to take significant risks at any point in time.

My understanding is that they do not attempt to maximize the difference in score, they attempt to maximize the probability that the difference in score is positive.

I thought "a rich man should not pick quarrels" was already accepted Go wisdom?

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.

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.

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.