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 Post subject: One weakness of miai counting
Post #1 Posted: Mon Jan 03, 2022 12:59 pm 
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Miai counting weakness

On this page on SL is an example of the sort of problems that mathematicians can construct where they could consistently win against a top professional (by 1 point) taking either colour.
This certainly drew my attention to this area of research, but it took some time to be sure that it had minimal practical impact on the game (these examples are only 1 point difference). However, I can also appreciate that many of the ideas are good rules of thumb for the whole game. It is said that Go is just one big endgame. I'd argue the reason this is partly true is because Go is mostly positive (every extra stone has positive value for that side) and local (every stone only has local impact except for ladder breakers), though the difference is that L&D matters more earlier on.

Many of the positions in that problem I don't really understand myself. But I can work within the miai counting model. Miai counting is great for providing a reliable way to not lose by too much. This is pretty good given that Go is NP-hard to solve perfectly (iiuc).

What sorts of problems cause issues for miai counting? One that I can think of is when two endgames A, B are very similar and normally sente. However, responding to one may mean your opponent gets both endgames. This is the line that miai counting would suggest. However, deviating from this line takes a risk and may require much deeper reading.

It depends on whether the position is intrinsically in your favour or not, and whether you have enough skill to squeeze profit from that advantage. For example, playing mirror go around tengen (as in Hikaru no Go) fails for black since white curls around first and black has less liberties despite starting first locally. When your group is in atari, it is often too late because you don't have much space to escape anyway and your opponent may have an attacking advantage.

Suppose A,B are corridors where the first few moves are all sente and each defensive move settles the position and gains the following amount:
A contains threats by the opponent: 1, 2, 3, 4
B has threats by you: 1, 2, 3, 5

If the opponent starts by defending B, the you defend A, your score is -0 (A) + 0 (B) = 0
When the opponent plays in A first and you respond, your score is -1 (A) + 0 (B) = -1 (this is the line that miai counting suggests and should be at most 2pts worse than optimal, since at your first move, 2 is the gain of your largest move, namely defending in A.)
If the opponent plays in A repeatedly, then you can play in B, you get tedomari and the score is -10 (A) + 11(B)=1

So because you have an advantage (A+B>0), you may have a way to win even if the opponent plays first, but only if they make the mistake of playing in A each time. (they should have just defended B first before you could gain 5 points there). The optimal score is 0 if the opponent plays first and 1 if you play first. If the final move in B replaced 5 with 4.5, the optimal score would be 0.5 if you play first. But if replaced with 6, then it will remain at 1 (since the opponent would just take the miai counting line).

The complexity of Go compared to this model is that follow-ups don't just flow in one dimension. You may have to choose between different directions of follow ups, and follows from nearby shapes may clash. This happens most sharply when there are two important weak stones (or even groups) on the board and one move by you is a double threat and guarantees capturing one or the other. This is the principle behind a driving tesuji.

Another property that affects things is that the edge of the board is valuable because it can change colour so easily depending on which side is stronger then, by working with that colour to kill opponent stones that come near. This also helps ladders work in the opening.

Give me triangles strong enough and I can measure the universe.

When Venus transits, we can align our clocks to one event. By measuring the angle to flat Earth at two places far apart on Earth, we can compute the distance to Venus and the Sun.

 Post subject: Re: One weakness of miai counting
Post #2 Posted: Tue Jan 18, 2022 10:42 pm 

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Under some suitable go rules, solving go is O(1), i.e. constant, because there is only a constant (although tremendous) number of possible moves, sequences and decisions between the moves, or, for other go rules, a finite number of equivalance classes classifying cycles so that a constant bounds that number. Go on arbitrarily large N x N boards is not just NP-hard but, IIRC, in EXPTIME and PSPACE for some studied typical go rulesets.

You speak of miai counting weakness but what is the weakness? Miai counting does not advertise that go would be simple. It is not a weakness but it is the possibility that there are positions with difficult, or at least non-trivial, decisions. In particular, it is not always correct to play in order of decreasing-or-constant move values or to seek tedomari.

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