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Greedy Go
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    Keywords: Strategy

Well, why not?

It's a good question. You could divide a simple go algorithm into two parts:

1. Find the biggest point. 2. Play it.[1]

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.)

Forgive me if I meditate aloud on the other side of the argument.

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.

I suppose that some people take a sente play to be one with an immediate large follow-up, but I think 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 what I was calling 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[2]. The proverb urgent points before big points warns one that there are things you have to do to keep control of the game.

Charles Matthews


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.


[1]

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.

[2] See series and parallel principle for weak groups for weak group strategies discussed.



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This is a copy of the living page "Greedy Go" at Sensei's Library.
(OC) 2004 the Authors, published under the OpenContent License V1.0.