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For a pro, points are effectively money. Therefore good go needs to be highly acquisitive, profit-oriented.
There are limitations, though. Aspects of greed as a mistake come under:
- thin (over-extended)
- not willing to sacrifice (so trying to save everything)
- aji (leaving too much of it, so that one's position is unsound, rather than playing honte.)
Greedy go in general
You could divide a simple go algorithm into two parts:
1. Find the biggest point. 2. Play it.
That isn't so stupid. In fact, to a first approximation, it works in the endgame. If all endgame plays are simple non-interacting dead-end gote plays, one should evaluate each one to get a number of points. Then the best play is the numerically largest one. The greedy algorithm is strong! (See stacks of coins, orthodox play.)
Real go is full of plays that are open-ended, and coupled to other plays through interactions that may be complex to describe. It is also governed by sente/gote relationships, a sente play being roughly speaking a play that is so open-ended that the opponent must immediately close off the implications.
Some people take a sente play to be one with an immediate large follow-up, but it is quite normal for plays to be treated as sente because there are multiple follow-ups both in series and parallel, which are intolerable in combination. After all that is typical of a play threatening to steal eyes from a group, making it weak.
You could take the existence of long series of follow-ups to a play to be a horizon effect. If you have a weakish group and allow the opponent two moves attacking it, you may already be in deep trouble. One or two further well-chosen attacking plays may either kill it, or 'bounce' it off some other sensitive situation of yours. The game can then simply be out of control for you.
The importance of parallel possibilities for follow-ups is that, in the opponent's hands, this makes it all the more likely that there will be an attack somewhere with a very good direction of play. The so-called combinatorial explosion is seen in go in complex interactions, as well as in the rather more obvious branching of local reading problems.
Conclusion, in more conventional terms. Greedy go in the opening and middlegame equates 'biggest point' with 'biggest territorial point', leaving out plus values for influence and minus values for weak groups. In the opening phase one can to some extent be guided by evaluations of joseki as fair trades of territory and influence; and by the principle that one doesn't want an early weak group (there are running fight joseki, but there one doesn't want a weaker weak group than the opponent's). But in the middlegame weak group strategies must always be suspect: certainly multiple weak group strategies are very risky. The proverb urgent points before big points warns one that there are things you have to do to keep control of the game.
Greedy go in life and death
In life and death situations, don't make small nearby plays until you know that the group is alive . Sometimes this is just a matter of slowing down and considering the possibility that the group you're trying to snake into the opponent's territory might not be alive in sente.
The above might sound at first to run contrary to the proverb "Play kikashi before living". The difference is that a good kikashi play is a big sente play (typically one where gain something by making it even though the opponent counters - for example, influence - ?) or an internal threat - where if your opponent didn't respond you would very clearly make life, typically by capturing a few stones. Ignoring a vital point in your big eye and charging forward into opposing territory is a doomed play - unless you can break inside and make another eye there. If you're just pushing against the walls, trying to cut gradually across an ikken tobi or keima, this isn't likely the case.
Footnotes and discussion points
Bill: This strategy is called Hotstrat? in CGT. It has been shown to be inferior, in the sense that the potential loss from playing it is indefinitely large. See Winning Ways.
Charles Trying to get hold of the technical language here: the biggest play concept seems to be used by Bill as the play which one counts as biggest. Optimal play, which of course can't be bettered, isn't quite the same thing. Of course I wasn't intending the biggest point as the biggest play, just because I was speaking crudely about attitude here.
Bill: You say, of course you didn't mean the biggest point to be the biggest play. Does that mean you meant, the biggest Oba? That's an even worse strategy, then.
Looking at this page again, I'm pretty sure that's not what you meant. So I confess I don't know what you mean by greedy go. Maybe an example or two would help.
Charles Page needs a master edit, that's for sure.
BobMcGuigan: The greedy algorithm doesn't work in some situations, of course, but if we simply enlarge our definition of greedy it works fine in go. The algorithm above is framed in terms of always playing the biggest move. Suppose we substitute "best" for "biggest". Isn't the best move in some sense the biggest? The problem is, of course, that we can't decide what the best move is in most situations. So, as in algorithmics where optimality is too hard to achieve, we are reduced to finding good moves, not necessarily always the best moves, and this is hard enough for go players.
Bill: Well, Bob, it depends on what you mean by "fine". ;-) Good players consider playing to get tedomari at various points in the game, and whether to play a sente play early, also whether to reply to an apparent sente or play for mutual damage. All of these depart from greedy go.
And Charles, as I understand "Find the biggest point. Play it," it does not mean "ignore influence and weak groups". Also, there is another concept of greed in go (musabori), which, like greed in life, is definitely bad.
Bob: I tripped on my own facetiousness. I was redefining "greedy go" by replacing "biggest" with "best". That is, play the best move every time. Tedomari and sente/gote considerations, as the best play, would then fall under my (facetious) definition of greedy. In practice, of course, no one can play the best move every time. But, half seriously, how do we decide what is the "biggest" play? Seems to me that a move which might gain fewer immediate points than another but guarantees more in the future would in some sense be "bigger". This would mean defending weak groups or playing other urgent points might count as bigger than a simple big point.
Charles What I intended here by 'greedy go' would be a style based on pace, but taken too far. That contrasts with a style based on honte, but taken too far and simply become slow and passive. One of the things about go is actually noticing the tightrope one is walking.
Bob: Yes. Balance is all-important.
 See series and parallel principle for weak groups for weak group strategies discussed.
 dnerra: I wonder whether this page should be linked from Controversial Statements -- I think I am greedy... :-)
If you have read out that you can make a small one point gain while living, instead of just living -- then my advice would clearly be: Take the one point gain! If it turns out badly, then you have made a reading mistake, and you should know better next time!
Remember, just giving away one point every 10 moves makes you 2 stones weaker...
Of course, there are also a lot of cases where my advice would be clearly wrong. If living safely makes your position stronger, denies the opponent sente moves etc., means you can possibly attack another group later on -- then of course, you should play patiently and secure life.