Why learn with tsumego?

Is there any evidence that solving tsumego in your head improves short-term memory? In my experience, tsumego only improve long-term shape memory and thus attempting as many tsumego as possible seems to be more effective than trying to solve all tsumego in your head.

The default assumption about learning with tsumego is probably that you have to solve them in your head completely and continue with the next one only after you're certain of your solution and have checked its correctness. But it's possible to use tsumego in many different ways. For example: you could just look at the tsumego for a short time and then quickly check the solution and move on whether your solution was correct or not. Or you could look at the tsumego very quickly and then immediately look at the solution without even trying to solve it yourself. My experience after having solved tsumego over many years is that is hasn't improved my short-term memory or my Go-specific reading ability by any significant amount and so I've come to question whether solving the entire tsumego in my head is actually useful. My Go-playing ability has improved due to solving tsumego, but that is probably solely due to their effect on my long-term memory, namely my memory of specific shapes and information associated with these shapes. This shape memory allows me to cut lines short during reading (whenever I encounter a position known to me) and thus keep their length manageable for my limited short-term memory. The Wikipedia page about fluid intelligence claims that fluid intelligence peaks around age 27 and declines after that, supporting my idea of short-term memory not improving. The conclusion is that attempting many tsumego quickly might produce a greater learning effect than trying solve every tsumego in your head.

Do you have to use tsumego to get better at playing Go? There are other learning methods: Just playing many games; Analyzing games; 1-to-1 lessons with strong teachers; Watching stronger people play; Reading books. If you do use tsumego, how exactly? The default way is probably to solve a tsumego in your head completely and only progress to the next tsumego after you're sure of your solution and have checked its correctness. But you could also just look at the tsumego for a short time and then quickly check the solution and move on whether your solution was correct or not. Or you could look at the tsumego very quickly and then immediately look at the solution without even trying to solve it yourself. The main benefit would be saving time and thus encountering a greater variety of tsumego in the same time. You can also mix these approaches.

To get better at playing Go, duh! Discussion over. But seriously, why? Or better: How exactly? I'm sure there are people with very different ideas for how to learn with tsumego or whether to use them at all. Not using them at all might seem strange to some, but there are of course other methods of learning Go: Just playing many games; Analyzing games; 1-to-1 lessons with strong teachers; Watching stronger people play; Reading books; Praying. And I know people who use one of these methods excessively or not at all. I know a pretty strong player who told me he never read a book about Go and I heard of another strong player who claims to have mostly learned it all by reading books. So if some of these named methods can be avoided entirely, that of course justifies asking whether using tsumego are necessary (or useful) at all. I can't answer that yet, but you should keep the question in mind during the remainder of the article.

Assuming that we do want to use tsumego, there are still many possible ways to use them. There are probably quite a few people who think the only useful way to solve tsumego is to do it all in your head and only proceed to the next one when you are sure of the complete solution and your imagined solution agrees with the solution given by the author. This approach is natural if you assume that solving tsumego this way trains your reading ability. But it's also time-consuming. An alternative would be to just look at the tsumego for a short time and then quickly check the solution and move on whether your solution was correct or not. And you could also look at the tsumego very quickly and then immediately look at the solution without even trying to solve it yourself. These options are of course much quicker. You can also mix these approaches and solve only some tsumego thoroughly. If you truly believe the reading ability must be trained, then these quick approaches might seem nonsensical to you.

Apart from how, you could also ask: What tsumego specifically? Old books might contain tsumego without any solution. There are different difficulty levels. There are opening tsumego, life/death tsumego, endgame tsumego, tesuji tsumego, whole-board tsumego etc. . You could try solving artificial tsumego or natural tsumego that appeared in an actual game. Even among artificial tsumego, there are realistic ones and unrealistic ones. There are ones where the solution is very long, and there are tsumego with a lot of short lines. There are tsumego where the entire difficulty is trying a single move that feels unnatural and tsumego where the solution requires finding several very specific moves in a row.

Apart from how, you could also ask: What tsumego specifically? There are many different sources. Old books might contain just the tsumego itself, without any solution. There are very different difficulty levels, from just teaching the rules and basic concepts like liberties up to problems that stump professionals . There are opening tsumego, life/death tsumego, endgame tsumego, tesuji tsumego, whole-board tsumego etc. . You could try solving artificial tsumego meant to illustrate a specific technique or natural tsumego that appeared in a game exactly as presented. Even among artificial tsumego, there are realistic ones and completely fantastical ones that would never occur in a normal game. There are ones where the solution is very long, but each move is relatively obvious, with no reasonable alternatives, and there are tsumego with a lot of potential lines, even though each line reaches a trivial position pretty quickly. There are tsumego where the entire difficulty is trying a single move that feels unnatural to an inexperienced player (e.g. an under the stones problem) and tsumego where the solution requires finding several very specific moves in a row.

And you could ask in what order they should be solved. Solve all "easy" tsumego before harder ones, or instead try a really hard one occasionally? Solve 20 with a similar theme or try them at random? Are opening or endgame tsumego useful for beginners or should they try only life/death and tesuji? Solve only tsumego you enjoy or specifically look for ones that feel unsatisfying/too hard? First become aware of your weaknesses and then solve tsumego that address this weakness? Solve the same tsumego again and again (with some time in between) ?

And since you usually don't just solve one tsumego, you could ask in what order they should be solved. Should you solve all "easy" tsumego before progressing to harder ones? Or you should confront yourself with the occasional problem that is far beyond your level, just to challenge yourself and find out your limitations? Should you try solving 20 tsumego with a similar theme in a row or should you try them at random? Is putting any effort into opening or endgame tsumego useful when you just started Go or should you focus all your effort on life/death and tesuji? Should you solve only tsumego that you enjoy or should you specifically look for ones that feel unsatisfying or too hard for you? Should you first try to become aware of your specific weaknesses and then specifically train with tsumego that address this weakness? Should you try to solve the same tsumego again and again (with some time in between) ?

To understand what tsumego could potentially do for your Go playing strength, we should first understand what is actually necessary for playing Go strongly, i.e. which abilities does a strong player have?

• Go-specific reading ability.
• non-Go-specific reading ability.
• Long-term shape memory.
• Whole-board awareness.
• Quick/estimated positional evaluation.
• Accurate counting.
• High-level knowledge of Go concepts like seki , semedori , kou and so on.
• The ability to quickly apply particular algorithms, like the algorithm for calculating the size of endgame moves or for figuring out whether a stone can be captured in a ladder.
• Your medium-term memory for all the facts you have calculated throughout the game, like life/death status of a group.
• Resource management, especially time management.
• Emotional control.

To understand what tsumego could potentially do for your Go playing strength, we should first understand what is actually necessary for playing Go strongly, i.e. which abilities does a strong player have?

• Go-specific reading ability, i.e. the ability to use your short-term memory to reason about different variations of Go moves quickly and accurately, i.e. imagine hypothetical positions in your head, study these positions, and draw conclusions from them.
• non-Go-specific reading ability. Mentioning this might feel pointless, but short-term memory is something every human has and uses every day and not everyone is equally good at it. Go-specific reading ability probably comes from this non-specific ability, but improving your Go reading doesn't have to improve your ability to do other things with your short-term memory, like mathematical computation, memorizing and recalling sequences of numbers, memorizing and recalling stories, memorizing and recalling a path through space, memorizing and recalling audio sequences (e.g. melodies) . Short-term memory would be classified as part of what some people call fluid intelligence , as opposed to crystallized intelligence. My assumption is that people with a superior non-Go-specific reading ability will be able to learn Go faster and achieve a higher strength.
• Long-term shape memory. After having seen particular Go shapes again and again, you are likely to memorize facts about these shapes automatically and be able to later recall these facts without having to think long about the shape. One example would be knowing that the L group is dead or knowing that a second line attachment is a good way of dealing with the Small knight's enclosure . This shape memory is always combined with reading in real games, because shapes never occur in isolation in real games and memorizing whole-board shapes is impractical.
• Whole-board awareness. Something that novice players usually lack is the ability to look at the entire board and understand how the different parts fit together and influence each other. Lacking this ability is a good way of running into a devastating suprise attack on one of your groups.
• Quick/estimated positional evaluation. Quickly understanding whether one player is ahead in a position and by approximately how much is very important for making strategic decisions like whether to start an invasion or to avoid it, especially in quick games. This is probably the vaguest but also most important ability that separates strong players from middling players. I do not know of any tsumego or other training techniques specifically for improving this ability, so most players probably learn this subconsciously during play.
• Accurate counting. If you have enough time, estimating the winning chances is not good enough, you should count both player's territory as precisely as you can. You can probably train getting faster at doing this, but there are limits and thus in blitz games you probably can't use this ability. And even if you do count, only solid territory is easy to count. The value of influence, strength and weakness are much harder to value precisely, unless you are an AI.
• High-level knowledge of Go concepts like seki , semedori , kou , me ari me nashi , overconcentration , tewari and so on. All of these concepts can be derived without outside help, but it's unlikely that you will do it in a short time over the board. And without understanding these concepts, applying them correctly is hard to impossible. Just look at how the AI Aya handles kou - it just doesn't understand that it can't win two kous and will waste all of its kou threats in the futile attempt of winning both kous. Luckily the number of Go concepts is finite and thus learning them all is possible, but some are quite hard to understand and even harder to apply correctly. Just knowing them is good, but it's not enough, you have to practice using them. Some high-level concepts, like liberties, are absolutely essential for playing Go strongly and it is clear that humans have the innate ability to abstract away from the potential complexity: We know instinctively that only the number of liberties matters, in most cases the order in which they are filled is irrelevant. AIs have some trouble with that and consequently sometimes make catastrophic mistakes in "complicated" semeais with many liberties. The problem for AIs in this case is that the number of potential move sequences for filling liberties rises faster than exponentially with the number of liberties. For humans a semeai with 20 liberties isn't harder than a semeai with 10 liberties.
• The ability to quickly apply particular algorithms, like the algorithm for calculating the size of endgame moves or for figuring out whether a stone can be captured in a ladder. In my experience, most amateur Go players never bother to learn this. In Go the number of important algorithms is relatively small, but in Chess, this is much more important, as essentially every Chess endgame type requires its own specific algorithm. This goes beyond just memorizing shapes, because the number of Chess endgame positions of a specific type (e.g. rook, pawn and king against rook and king) is huge, but the same algorithm can be applied to all of them. You could argue that an "algorithm" is really just a set of specific patterns, but to make good use of them, you have to understand how they all fit together and do so quickly and without error.
• Your medium-term memory for all the facts you have calculated throughout the game. Solving a particular life/death problem in your game should ideally be something you do only once and then remember the result until something in the vicinity changes and forces you to recheck your solution. If you can't remember the solution, you'd be forced to solve the problem again after every move, which would be extremely time-consuming. Also remembering how many points you counted for both sides is important, as is the status of ladders, potential cutting points, the viability of invasion spots, and so on. This is another area where AIs are lacking, as they usually recalculate almost everything after every move, making them less efficient than humans. Of course this ability can also be an Achilles heel. If you remember a fact that isn't true anymore, you might make detrimental decisions based on that. I remember one of my opponents forgetting that one of his groups inside of my territory was captured and so he played an endgame move based on the assumption that this group was still alive. He noticed the mistake immediately afterwards, but the stone had already been played.
• Resource management, especially time management. Some people use hardly any time at all, others get into time trouble frequently, and my experience is that under serious time pressure, the number of severe mistakes goes up sharply. Thus anticipating your future time budget and the time budget of your opponent is important. The same goes for your stamina and health in general. For example spending endless amounts of time trying to turn around a hopeless game might exhaust you and reduce your chances of winning the next game.
• Emotional control. I have lost many games due to making not very rational decisions and I know most other players have as well. This is one of the first things taught to new players, as it should be easy to understand and easy to fix for a disciplined mind, but the battle against making emotional decisions never really ends.

Which of these abilities is influenced by training with tsumego? The assumption is probably that Go-specific reading ability or even non-Go-specific reading ability is improved by training with tsumego. Long-term shape memory is probably improved as well. I'm unsure whether any of the other abilities is improved by solving arbitrary (as opposed to specific) tsumego. Improving my reading ability by solving tsumego would be lovely, but I don't know scientific evidence showing that. My experience was that neither my Go-specific nor my non-Go-specific reading ability has improved. The Wikipedia page about fluid inteligence says that it peaks around age 27 and then declines. Professionals usually reach their peak around age 30 and rarely win titles after age 40. It seems it's similar for Chess grandmasters.

Which of these abilities is influenced by training with tsumego? Most people's assumption is probably that Go-specific reading ability or even non-Go-specific reading ability is improved by training with tsumego. Long-term shape memory is probably improved as well. High-level concept understanding might be improved as well, but probably only by studying with tsumego that contain that particular concept. Application of algorithms might be improved as well, but I have not seen anyone attempting that in Go, only in Chess. Whole-board awareness might be improved, but likely only by using whole-board tsumego. I don't think any of the other abilities will be influenced measurably by solving tsumego alone.

Improving my Go-specific reading ability by solving tsumego would be lovely, but I have never seen scientific evidence for that and after seeing over a thousand tsumego, I can't say that my Go-specific reading ability has improved. My non-Go-specific reading ability definitely hasn't improved. The Wikipedia page about fluid inteligence says that it peaks around age 27 and then declines. I can't say that my experience contradicts that. I only started playing Go at age 25, so my results might have been different had I started much earlier. Professional Go players usually reach their peak playing strength around age 30 or even earlier and rarely win titles after age 40. It seems it's similar for Chess grandmasters. In fact, the strength peak might have moved to earlier years over time. Around the end of the 19th century, Chess players were still able to compete at the highest level above the age of 40 (the first 4 Chess world champions lost their titles long after their 30th birthday, 3 of them significantly after their 40th) . But maybe I'm just imagining this.

My Go-specific reading ability was always bad. Go positions in my mind are usually incomplete and fuzzy, which leads to reading errors. I usually have to re-attempt reading a position 3-4 times before I can be certain, in particular for positions where stones are captured and recaptured. Some under the stones shapes are well known to me, but most aren't. If no stones are captured, it is much easier. The problem gets worse the longer the sequence of moves. No matter how many tsumego I solved, none of this has changed. There are techniques like the method of loci , but that's for memorization, not computation. If my reading ability hasn't improved, how could my playing strength have improved at all and what role did tsumego play in this? The answer is that I always take short-cuts: When I encounter a known position, I just use my memorized knowledge about that position. This cuts many lines down to a length that is manageable for my short-term memory. Of course this does not apply if I never encounter a known position during reading, like in positions that are essentially random arrangements of stones. And so the primary effect of tsumego on my Go-playing ability is through their effect on my shape memory. Remembering a shape becomes much easier if it occurs in many tsumego in a row, probably due to humans' general pattern recognition ability.

My Go-specific reading ability was always bad. When I try to imagine Go positions, these imagined Go positions are usually incomplete and fuzzy in my mind. That leads to errors like miscounting liberties. I usually have to re-attempt reading a position 3-4 times before I can be reasonably certain that I didn't make any mistakes. Particularly troubling are positions where stones are captured and recaptured. Some under the stones shapes are well known and easy to recognize, but capturing and recapturing stones is part of most complicated problems and I can't memorize all involved shapes. If no stones are captured, it is much easier, because the imagined position remains largely unchanged and so I only have to think about the small difference between the on-board position and the position in my head. Obviously the problem gets worse the longer the sequence of moves. No matter how many tsumego I solved, none of this has changed. I thought about training my short-term memory independently of Go, but I couldn't find any scientific evidence for methods that are proven to improve short-term memory significantly. There are techniques for making better use of short-term memory, like the method of loci , but that is for memorization, not computation. The method of loci makes use of particular biases in our brain, namely that we are able to remember facts like stories, paths through space, faces, etc. much more easily than things like random sequences of numbers or letters. And unfortunately, Go positions and move sequences do not seem to be among those facts towards which our brain is biased. And of course memorization techniques are not guaranteed to bring any advantages for computation. During reading in Go, the position to consider quickly changes multiple times while simultaneously previously considered paths have to be remembered as already checked. The method of loci instead tries to keep a fixed sequence of facts and tries to use your short-term memory in much the same way as your long-term memory. If reading in Go were more like brute-force search, i.e. going through all possible paths in sequence, memorizing previously visited paths would be much less onerous, as you would have to remember only the current path and could use a regular traversal pattern (e.g. left-to-right and then top-to-bottom) to go to the next path. But unfortunately the number of paths to check is much too high and so this is impractical for games with a reasonable amount of thinking time.

If neither my Go-specific nor my non-Go-specific reading ability improved, how could my playing strength have improved at all and what role did tsumego play in this? Well, during reading, I always take short-cuts (and I assume other players do, too) : As soon as I encounter a known position, I stop reading and just use my memorized knowledge about the position. This cuts many lines I read short from 20-30 moves to maybe 3-10 moves, which is still manageable for my limited short-term memory. Of course this does not apply if I never encounter a known position during reading. This is particularly obvious when presented with an essentially random arrangement of stones, as is sometimes done in tsumego. Many people do not explicitly try to create such positions during games, but some do. And usually when I encounter those positions, I fail and make catastrophic errors. And so the primary effect of tsumego on my Go-playing ability is through their effect on my shape memory. I know that my long-term memory is relatively good, much better than my short-term memory, and this can mask most of my reading shortcomings, especially for opponents who don't know me. I often need to see a position only once to remember it for years (but that's not always the case) . This effect is of course reinforced through repetition, which is why I occasionally repeat important tsumego.

One effect that is noticeable is that I hardly remember anything about unrealistic tsumego (my brain might just filter them out automatically due to perceived irrelevance) and that remembering a shape becomes much easier for me if the same shape occurs in multiple tsumego in a row. For example, I would assume that I would remember the monkey jump much more easily if I had seen it 20 times in a row in tsumego as part of the solution or part of a refutation. I can't check, because I learned the monkey jump so long ago, but for other shapes (whose name I don't know) that repetition effect is quite obvious. This is probably just an expression of the usual human pattern recognition: Things that appear repeatedly within a short span of time are much more likely to be recognized as a pattern than things that occur apparently randomly and/or stretched out over a long time.

The conclusion is that actually solving tsumego might be irrelevant (at least for me) and what matters is seeing the solution, understanding it and memorizing it. And since solving tsumego is time-consuming, going through tsumego faster would increase the learning effect. The usefulness of doing that might have become obvious only due to the Internet and its abundance of information (e.g. here ), whereas in the past the number of easily accessible tsumego was small and thus engaging with each tsumego for a long time made much more sense. This is probably hard to swallow in the West, but in East Asia, letting even young children rote-memorize large amounts of information is likely seen as less unusual. And given Asians' continued dominance in Go, we might want to take a page from their book. I'm not advocating for relying on rote-memorization exclusively, but most of my Go-playing ability comes from it and I feel I can still become stronger through more of it, whereas attempting to improve my short-term memory feels pretty hopeless by now.

Let me hear your opinion about this topic.

But if that's true, then that leads to the conclusion that actually solving the tsumego yourself is irrelevant. The only thing that matters is that you see the solution, engage with it and understand it so that it is committed to your long-term memory. And since solving tsumego is time-consuming, going through tsumego faster would increase the learning effect as more tsumego are seen during the same amount of time. If that is the case, why wasn't this idea mentioned centuries ago, given the long history of Go? I assume it has to do with the paucity of available good tsumego in the past. When every tsumego has to be created painstakingly and then printed, without access to the Internet or some similar trove of knowledge, going through thousands of tsumego would have been difficult and thus it might have made more sense to spend more time with the tsumego that were available to maximize their learning effect. But nowadays, with billions of people connected via the Internet, an essentially endless supply of tsumego can be found, alleviating this limitation. For example, check this collection .

This idea may be hard to swallow in the West. But China and generally East Asia doesn't seem to be bothered by the idea of drilling endless amounts of rote-memorized information into the minds of 7 or 8 year old children. And given that the East Asian Go players still outclass all Western players significantly, we might want to take a good look at their teaching techniques and apply them ourselves. Over time I have played against several Asians who hadn't played Go for a long time, but apparently had little trouble recalling shape knowledge they had learned over a decade earlier as young children. It is obvious in those players that shape knowledge alone is not good enough to become a truly strong player, but on the other hand most Western players can't claim to still play Go at a single-digit-kyu level after having learned it early and then paused for a decade or more. I'm not advocating for relying on rote-memorization exclusively, but most of my Go-playing ability comes from it and I feel I can still become stronger through more of it, whereas attempting to improve my short-term memory feels pretty hopeless by now. The same Wikipedia page that claims fluid intelligence declines after around 27 years of age also claims crystallized intelligence only declines after around age 65 and so improving my shape memory seems like a realistic goal.

I would always prefer realistic tsumego, tsumego that don't tell you the expected result (i.e. "find the best move", not "find a kou" or "kill the group") and series of tsumego revolving around a common theme. I'm not sure what level of difficulty would be appropriate for me and so I attempt all tsumego irrespective of difficulty. And like I already said, I think repetition is important (3-4 times, not 100 times) and so would attempt the same tsumego again after some time has passed. Apart from that, I would like to solve a good mix of opening, life/death, tesuji, endgame and other tsumego, but unfortunately the sources I have focus strongly on life/death and almost completely ignore the other areas. Fortunately, publicly accessible game records together with AI should make it possible to create new tsumego in large amounts without too much human labor and so I think this paucity of tsumego will eventually be resolved.

I would like to hear your opinions. What are your strengths and weaknesses in Go and what are the strengths/weaknesses of your opponents? What learning techniques have you tried and how have they influenced your abilities?