This article is continuation from Part One.
Below, I will show how I read out a go problem by example – but before that, we should establish definitions for certain Japanese terms.
The word suji holds many meanings in the Japanese language. Originally it meant ‘muscle’ or ‘sinew’, but gradually it also came to mean other thin and long things such as blood vessels, strings, and threads. After that, it also came to mean ‘thread’ figuratively, as in a ‘thread of logic’. In go, suji holds this meaning, but its usage is limited to referring to local shape over a sequence of moves.
Suji can be translated to English fairly losslessly as ‘technique’; you can think that suji are tools in a toolbox whose contents you apply to solve a local problem.
Most western go players have probably not heard of suji but are familiar with tesuji. Tesuji is a kind of subset of suji, meaning a single particular move that solves a local problem beautifully and effortlessly. If we were to use chess terms, you could translate tesuji as ‘key move’; however, the Japanese term is widely prevalent in English go jargon.
I like to think of tesuji as keys rather than tools: sometimes you have just the right key to open a lock, and then you don’t need to reach for the hammer. If the door doesn’t have a lock, on the other hand, then the key is worthless no matter how pretty it is.
With the above terms in mind, let us look at the endgame problem I posted four days ago.
I stated that this is an ‘endgame problem’, but let us approach it as if it were a position that occurred in one of our games. In other words, let’s imagine we don’t know that we should optimise territory – we should search for the best result that Black can get, and that might involve the white group’s death.
Immediately upon seeing such a problem, our subconscious is already at work. If the shape involved is common, we may already know exactly what moves to expect; if not, we may at least compare it to similar shapes that we know to get an idea of the kind of result that should follow; and if not, we can at least get a general idea of how strong or alive the corner white group should be. The white group has five liberties, and is therefore not immediately under threat of being captured. If White gets to play t16, he also has an eight-point eye shape in the corner, which usually means a live group.
My own brain’s pattern-matching compartment – ever the spoilsport – has already spewed out the likely correct first move for me, but let us go about solving the problem systematically. But what exactly does that mean?
Some people might use a mental brute-force algorithm, i.e., literally going through every possible move inside their head. If you go about this in a blind way, since there are nine open intersections we are looking at, you need to read roughly through 9 × 8 × 7 × … × 1 = 362,880 different sequences, which is obviously too much work. However, you can tweak this algorithm a bit, removing obviously bad move candidates: for example, it should be clear that black q19 or t19 will not probably work well as the first move. A sophisticated brute-force user might only need to read through 4 × 3 × 2 = 24 variations.
I would generally advice against the brute-force algorithm. Even if you practise using it, it has very limited utility in real games, whose positions are rarely as constrained as in this problem. The brute-force algorithm is useful only if you have a very limited space to read and you are facing a shape that you have never seen before – and even then, it is probably inefficient time usage.
What we should do is open our toolbox and start from the most practical or pertinent-looking techniques. The order in which we try out the techniques is governed by heuristics that we have learned: for example, you may know that in life-and-death problems you should first reduce the opponent’s eye space and then to try to claim the opponent’s key shape point for making eyes. (If you didn’t, you should now add this heuristic in your heuristics box!)
At the same time as we are applying our tools, we should keep track of what we have read. To many players, this is one of the hardest parts of reading. It doesn’t help if we come upon the correct solution during our reading, but then promptly forget it and opt for a wrong move instead.
When reading out a position, we need to find the best result for both players. This means that, if it’s Black’s turn, we find the best move for Black; after that, we find the best move for White; and then again for Black, repeating until the end of the sequence. The tricky part is in that we have to work backwards; you cannot know what is Black’s best first move before you have read out all the possible following outcomes.
Luckily, you can save a lot of time and effort by following the ‘lower bound heuristic’. We will see this heuristic in action shortly; its principal idea is that if you for example know that one sequence at least leads to a kō fight for the defender, then you can forget about all the worse sequences where the defender got captured unconditionally.
By the earlier heuristic for solving life-and-death problems, black t16, which is the only way to limit the white group’s eye space, should be the first move we consider.
Dia. 1. Once we have Black’s move, we then flip the problem around inside our heads. Now we are playing White, Black has played t16, and our job is to resist Black as strongly as possible – in the best case, by living while also surrounding territory. When living, the standard heuristic is to first make our eye space as big as possible and then try to claim any key shape point for making eyes. White t17, then, should be the first move we consider for White.
Dia. 2. Now we return to Black’s point of view. Black can no longer reduce White’s eye space, so it is time to attack White’s eye shape instead. One standard suji is to play the first-line atari of t18 which forces white s17: this way, the potential eye at white s17 is removed.
Dia. 3. Following, Black’s stone only has two liberties while the white stones have three, so for now Black cannot hope to win a capturing race. Also, White seems to have an unremovable eye at q19, so the best Black can do is try to create an eye for herself, aiming for a seki.
Dia. 4. Black 5 and white 6 achieve this. Instead of 6, White can consider playing s18, but then black 6 starts a kō fight for the life of the white group. Since White can only capture three black stones in the kō while Black can capture ten white stones, the kō is hardly fair – therefore, White should prefer the seki.
Now we have established a lower bound for Black after white t17: Black can at least form a seki in the corner. Stronger readers may want to consider the sub-problem involved: does Black have a better move available than t18? In this case, however, we can omit this part of the reading while still getting to the correct solution.
Since white t17 in Dia. 2 leads to Black at least getting a seki in the corner, White should consider his alternatives. Here we can apply the heuristic, ‘your opponent’s good move is often your own good move’ – we should consider if white t18 instead is better.
Dia. 5. Although white 2 may not be instantly obvious to the eye, it actually does follow logically from the local shape – the Japanese would say it is part of the local suji. In our previous reading, black t16 and t18 together formed a set to limit the white group’s eyes; it therefore makes sense for white to try to claim the apparent key point of t18 for himself.Dia. 6. Upon seeing white t18 and considering Black’s choice for a moment, we realise that there is not much Black can actually do. Moves at ‘a’ and ‘b’ have become miai, meaning that White will get to form two eyes with one of the moves no matter what; and so the best Black can do is just to reduce a bit of white territory by exchanging 3–4. The outcome is now that White has five points of territory while Black keeps her sente. It is difficult to conceive White getting a result better than this – we already saw that white t16 instead of t17 didn’t work –, so now we have read out black t16.
T16 in Dia. 1 is not Black’s only possible starting move – just the most straightforward one. Since limiting White’s territory to five points does not look like a very significant gain, we should entertain the idea of other starting moves. We actually have a hint from our previous reading: since white t18 in Dia. 5 was a good response to black t16, we should next consider starting from t18 ourselves.
Dia. 7. In response to t18, White has limited options. White has to prevent Black from connecting under with ‘a’, as then White would find it impossible to form two eyes inside the remaining space.
Dia. 8. Also, it again turns out we have already done a part of the reading involved: if White plays 2, Black responds with 3, forcing white 4, and the sequence proceeds to the seki we have seen in Dia. 4.
Dia. 9. It follows, then, that White mainly wants to consider playing 2, himself. Now black has an isolated stone with three liberties against White’s chain of five liberties, so a capturing race is again out of the question; Black instead strengthens her stone while reducing White’s eyes with 3.
Dia. 10. Now White can descend to ‘a’, to which Black responds with ‘b’: both players’ stones have formed an eye, and the outcome is a seki. Alternatively, White could play ‘b’ to which Black plays ‘a’, and this shape, too, is a seki. In fact, when you think about it, White does not need to play at all and the shape is still a seki.
Note that this seki is better for White than the one we saw in Dia. 4. This time, White at least gets the turn to play elsewhere, whereas previously Black could reduce White’s potential corner territory to zero for free. Whether this result is better for Black than reducing White to five points in sente is another question, and sometimes depends on the game – however, mathematically speaking the seki result is one point better (why this is so is a topic for another time).
We have now read out Black’s starting move of t18 and established a new lower bound for Black: Black can play t18 to form a seki inside the white corner as in Dia. 10, removing all of White’s potential territory. At the same time, we have exhaustively looked through the t16–t18 suji of this particular shape. We don’t actually yet know if t18 is Black’s best move available; but we do know that it is better than t16, and that if Black wants to do better, he has to try a different tool in the toolbox.
If Black were to hope to achieve more in this position, he would have to forget about the territory-oriented moves of t16 and t18 and instead see if there wasn’t a way to more severely threaten the life of the white stones – probably by attacking its liberties.
The remainder of this problem is left to the reader as an exercise.
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