There are many reasons I enjoy playing go: complex gameplay arises out of simple rules, single mistakes rarely decide games, games between between people of different skill can be handicapped without changing the dynamics of the game too much, there are no draws, and I just like the way it looks. The purpose of this article is to illustrate something else I like about playing go: the ways that it provides practice in basic habits of rationality, that is, the ways in which playing go helps me be less wrong.

I've tried to write this so that you don't need to know the game to follow it, but reading a quick introduction would probably help. (ETA: A commenter below has helpfully pointed to more go info online.)   The main aspect to understand for this article is that go is a game of territory.  The two sides vie to occupy space and surround one another.  If a group of stones is surrounded without sufficient internal space to support itself, it is killed and removed from the board.

Lesson 1: Having accurate beliefs matters.

Here are three examples of a group of white stones being surrounded by black stones.  The important distinction between them is whether the white stones will eventually be captured, i.e. whether they are "dead" or "alive".

Dead white stones
Fig 1: The white stones are dead.
White stones are alive
Fig 2: The white stones are alive
White stones have ambiguous status
Fig 3: The white stones have ambiguous status.
  1. In Figure 1, the white stones are being smothered by the black stones.  They are overwhelmed and cannot escape eventual capture.  They are "dead".
  2. In Figure 2, the white stones are surrounded but have sufficient structure to protect their internal space and thus will not eventually be capture by the black stones.  They are "alive".
  3. In Figure 3, the issue is unsettled.  Depending on how play proceeds, the white stones may eventually live or may eventually die.

Accurately determining whether the white stones in situations like Figure 3 are doomed or not is essential to winning go.  There are go training books that consist of nothing but hundreds of exercises in correctly assessing the status of stones and learning the subtleties of how their arrangement affects that status.  Correct assessment of life and death is one of things besides a large branching factor that makes computer go so hard.

I once read something on LessWrong which was later labeled The Fundamental Question of rationality: "What do you believe, and why do you believe it?" I have found this useful to adapt to go: when playing, I constantly ask myself, "Are these stones alive or dead, and how do I know that?", and this practice in turn has encouraged me to ask the original fundamental question more in the rest of my life.

Lesson 2: Don't be too confident or too humble.

Overconfidence leads to bad play.  If white were to mistakenly play further in the scenario of Figure 1 in an attempt to salvage the position, she would be throwing good stones after bad, giving black the chance to make gains elsewhere.  But underconfidence also leads to bad play: if white were to play further in Figure 2, she would also be wasting her time and giving up the initiative to black. As is true in general when trying to achieve your goals, too much humility is a bad thing.  Go punishes both false hope and false despair.

Lesson 3: Update on new evidence

The status of a group of stones can change over time as play in different areas of the board grows and interacts.  Stones that once were safe could become threatened if nearby battles have a side effect of increasing your opponent's strength in the area.  It is thus essential to constantly update your assessment of stones' status when presented with new evidence (new moves), and act accordingly.  This used to be a big weakness of mine.  I often would take a strong lead during the opening and middle of the game, only to lose when a large group I thought was safe gets captured late in the game because I forgot to pay attention to all the implications of further moves elsewhere.

Lesson 4: Be willing to change your mind

Even when you pay attention diligently, it can be difficult to act in response to new information because of emotional attachment to your previous beliefs. When I launch an invasion of my opponent's territory, sometimes the battle that follows reveals that my invasion was too aggressive.  My invading stones are doomed.  But I don't want to give up.  I throw good stones after bad and in the end only end up strengthening my opponent's position.  Better play would be to 1) realize as soon as possible that the invasion was overplayed and then 2) shift from using the invading stones as part of the attack to using them to aid your efforts at containing rather than invading (this idea is called Aji).  Go rewards those who are willing to change their minds as soon as is warranted.

Lesson 5: New evidence is the arbiter of conflicting beliefs

Games usually end in a curious way: by mutual agreement.  When both players believe there are no more moves they can play that will either expand their own territory or reduce their opponent's, both pass.  The players then reveal their beliefs about the "alive" or "dead" status of each group of stones.  This is done to avoid the tedium of playing out all the moves required to actually capture doomed stones.  If the players agree, then dead stones are removed and the score is counted.  But if the two players disagree, the solution is simply to resume play.  Further moves inevitably reveal who had the more accurate belief about whether a group of stones was doomed or not.

Lesson 6: The road is long

One interesting feature of go is the broad range of skill levels at which it is played.  If you want to make a line of players such that each of them could defeat the player on their right 90% of the time, you can make a longer such line of go players than players of any other game I know.  This game is deep.  And as with rationality, it takes practice to internalize productive habits of thought and banish self-delusion.

Moreover, as with rationality, it is usually possible to appreciate the skill of those one or two levels more advanced than oneself (kind of like the way listening comprehension leads speaking ability when learning a language).  Thus, there is a constant pull, an encouragement to reach over one's own horizon and achieve a deeper understanding.

Lesson 7: Shut up and count

Go games are decided by a balance of points (roughly speaking, one spot on the board or one stone is worth one point).  Out of a few hundred points available, games between closely matched opponents are often decided by a margin of fewer than 10 points. (Different counting systems vary the absolute numbers here but not the spirit.)  This means that accurate quantitative evaluation of the board is essential to good play.  It's not probability theory, but it definitely shows how numbers can serve your goals better than feelings and hunches. No matter how skillfully you manage to read ahead the moves of a complicated tactical fight, if you pursue that fight instead of playing a simple move elsewhere that has a bigger impact on the score, you're making a mistake.

Further Lessons

Edited to add: If you find the exploration of this go/rationality analogy interesting, be sure to read the comments below, where several people have pointed out additional generalizable lessons.

In Closing

As much as I enjoy go, I feel I should finish by noting that in the end it is still just a game.  Time spent playing will probably not do as much to advance your goals as actual direct work.  Sometimes, the more you play, the less you win.

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One of the things I like best about Go is the lessons it teaches about reductionism vs holism. Success at Go requires the ability to think at several levels simultaneously. A play may be motivated by tactical considerations or by strategic considerations, or most likely by both. A well played game is frequently attracted toward a state with some similarities to what the chaos-theory-geeks call "self organized criticality", in that structures at all levels of organization become equally important.

This is a nice observation, and I think it's true about both go and rationality. Wish I'd thought of it for the post!

I would also add something about "guessing the teacher's password".

If you do things you saw a stronger player do, but don't understand them, you will sooner or later be punished - either because you applied the move in a situation where it doesn't work; or because you don't know how to continue.

Yes, this is true, but it's also true that some kinds of imitation can take you far even if you don't understand them. Personally, I try to play with good shape, I have seen it pay off, but I don't understand most of ways that this helps me. A good parallel in rationality might be learning self doubt. This can help, even if one doesn't know the myriad ways people have of fooling themselves which it is intended to thwart.
This phenomenon is extremely frustrating to me, but I don't pretend to not take advantage of it. Part of the reason to play shape is that it's generally recognized as efficient structure; another is that it closes down options - you prune the search tree towards well-understood structures and don't have to worry or expend as much mental energy reading.
I don't know anything about Go. But the fact that following it helps you reminds me of In praise of fake frameworks: while "good shape" isn't fully accurate at calculating the best move, it's more "computationally useful" for most situations (similar to calculating physics with Newton's laws vs general relativity and quantum mechanics). (The author also mentions "ki", which makes no sense from a physics perspective, to get better at aikido.) I think it's just important to remember that the "model" is only a map for the "reality" (the rules of the game).
There is, in fact, a go proverb for this: "Learn joseki, lose two stones" (in rank, temporarily). Meaning that people who memorize joseki without understanding the reasons for the moves will be flummoxed by people who don't follow the expected pattern, since it's hard to punish a mistake if you don't know why it's a mistake.

I don't doubt that there are lots of rationality lessons in deterministic games like Go. But I think in some ways they crucially misrepresent life. When you've lost a game in Go you can always think:

"I lost because I didn't play well enough."

In games with a random element, like poker, you have to think:

"I lost because I didn't play well enough AND/OR because I was unlucky."

To become good at poker it's crucial to be able to distinguish between bad luck and play mistakes. You have to keep your cool when your opponent makes bad moves and wins anyway. You have to be able to think thoughts like this:

"That the card on top of the deck should have happened to be the only one that would let my opponent win the game is not evidence I should update on. It tells me nothing I didn't already know. It's just that Nature felt like slapping me in the face right now and there's nothing I can do about it. She'll wipe the grin off my opponent soon enough if he keeps playing like that."

In life, we are very often faced with situations where we have to analyze to what extent something is the result of our own actions and to what extent it is the result of factors outside our control.

Go has luck/chance/randomness too, unless you can read out the entire game tree. Part of go strategy is to simplify the board when you're ahead, and to try and throw the board into chaos when you're behind. And there is a sense in which you cannot win a game of go, your opponent must lose it-- and when my opponents do so, I feel lucky, especially if their mistake is something which is obvious to me.
I think this sounds like a valuable lesson to learn, and as you say, the kind of thing you couldn't get from a deterministic game. And as with go, I suspect that some lessons from poker sink in better when you experience them in play than when you just read them. I would be interested to read more about it, if you (or any other poker players out there) have the time and interest to write a post on rationality in poker or other games with a chance component. I have a feeling that there are lessons related to probability and quantifying your beliefs that could be drawn, or perhaps stories from games that can be used as illustrations of probabilistic or Bayesian reasoning.
I'd love to see such a post too but I don't really have enough experience with poker to write it myself. My gamer friends and I mostly play alternating obscure boardgames - we like exploring a ruleset for ourselves more than we enjoy improving our skill at games that already have a well understood theory. Poker does provide a very visceral lesson in 'sunk costs', I'll say that.
"quantifying your beliefs" - non-analytically, because analysis is time consuming.
You could flip coins to see who moves - if you really want randomness. You could introduce configurable quantities of randomness that way.

I think you should link to some learning resources about go in your article, for people who want to start.

Rules tutorial

KGS Go Server

Sensei's Library - wiki

Go Problems

Sorry for all the comments, I thought of some more things:

The "dark side" has an analogy in go. It is tempting to play moves that you know don't work because you think your opponent won't be able to figure out the correct response. It is usually not obvious to beginners that doing this is really holding them back.

I commonly hear beginners justify a move with the reasoning, "I played X because next I can play Y!" To which the response is, "But after you play X it's your opponent's turn. And he is not stupid and will prevent Y."... (read more)

This reminds me of the Go maxim that (for a given board position and abstracting away the parity) your best move is the same as your opponent's best move. This is rare in real life, where the situation isn't so symmetric. But it does teach you to look at things from your opponent's perspective.
Good point! I thought about including this connection between trick moves and the dark arts, actually. They don't seem quite parallel to me, but there are definitely similarities. If anybody is interested, you can read more about trick moves here.
Trick moves are a little more subtle than what I was talking about. A "trick move" in go usually has a refutation that is only a few points worse than optimal play, but if the opponent falls for the trick it can be devastating. (IOW, you risk a few points for the chance of making a lot of points.) These moves have their place in handicap go (and to some extent, even games where you are feeling out the level of your opponent). I was thinking of the less well thought out moves that beginners to medium level players play, hoping that their opponent won't see the crushing refutation. (They're risking large amounts of points for no apparent reason, often.)
OK, I see, thanks for explaining it. I'd never really heard of this difference before. I'd have to say that the more subtle moves that risk only a little and feel out your opponent sound more akin to the "dark arts" in rationality.
This line of discussion is interesting to me because if the analogy holds, then it implies that what this community calls "the dark side" vs "the dark arts" are very different from each other despite the surface similarity of the terminology. The dark side, as I understand it, is what you get when someone decides that beliefs have some value other than that derived via a correspondence theory of truth. Then they twist their mind into a pretzel and emotionally freak out when you show them evidence which violates their semi-consciously constructed "useful delusions". This is like the recovering alcoholic who has a belief that Jesus will personally intervene in their lives to give them strength where the belief powers their decision not to drink alcohol. The analogy in go would be a "trick play" where seemingly solid arguments (or lines of play) can "destroy the situation" for the person relying on the trick, but in the absence of solid refutation the move might win the game. The dark arts that you seem to be referring to just now as "subtle moves" seem to be analogous to go concepts like sabaki play, which is relatively light in the sense of putting stones on the board that are loosely connected, easy to sacrifice, but generally well placed, so that if they are attacked clumsily the other player can develop a position that is too large to sacrifice, too expensive to defend, and/or inefficient. The epistemic equivalent to sabaki play might be "sophistry", where someone is known to be highly skilled at argument and therefore it somehow "counts less" when they win because all their "fancy words" lead to a victory for reasons that are not obvious to people who disagree and/or haven't studied rhetoric. The place the analogy breaks down might be that in go "sabaki play" is in some sense simply good play, whereas in argument people have a sense (justified or not) that sophisticated argumentation is somehow "dirty". Perhaps in go the difference between trick play and sabak
I agree. I think the dark side terminology is based on the "dark side of the force" from Star Wars, which has connotations of a personal fall into temptation, and the dark arts refers to magic of evil intent or effect, perhaps from Harry Potter, where it is used by evil but not self-deceiving villains. This could explain the inconsistency.
I think you have really helped to clarify the go side of this analogy, and I'm grateful for your description of sabaki play and what makes it different from trick moves. I think the connection you draw to rationality and debate are pretty good. I'm not sure about this, but I think there's another sense in which the term "dark arts" is used on LessWrong: using one's knowledge of common cognitive biases and other rationality mistakes to get people to do or believe something. That is, fooling others, not fooling yourself. For the go analogy, I think this is most closely related to trick (non-obviously suboptimal) moves. Or perhaps the technically unsound but necessary aggressive moves used by white in handicap games to which black often responds with too much humility.
It seems to me that learning trick moves and the dark arts strengthens your overall understanding and ability, relative to just learning the proper standard moves (honte) and reasoning. Yes, both in Go and real life.

In a thread on Reddit about coping with the fear of death I suggestlearning to play Go and playing in tournaments (for the timed matches) as a way of getting used to managing a limited stock of time.

Robin Hanson ponders trying to stick to clear, simple methods of rationality in the hope of avoiding judgment and the biases inherent in the exercise of judgment. I comment that this has worked poorly for me and Go with the implication that it is likely to work poorly in real life because real life has even more of the nasty complication than Go.

Is it true that all of these points could be said for any goal-centered action, such as making paperclips? Or for any game? How is Go different that those other games and tasks with respect to these lessons and insights?

A good question. I think that Go provides more lessons and better lessons to an aspiring rationalist than do most other games. More lessons even than such worthwhile activities as paperclip manufacturing. The reason has to do with Go's "richness". I pointed out one aspect of what I mean by "richness" in my comment mentioning "self-organized criticality". Here I will point out one aspect of the game which I think leads to that "richness". In moving from conceptual high-level to conceptual low-level in your thinking about a game of go, you are forced to switch between binary objective thinking (I want to win!) and quantitative objective thinking (More! More! I want more!). You are forced to switch repeatedly. For example, I win the game (by three points) because the balance of territory on the left side of the board is 14 points to the good, whereas the balance on the right is only 11 points to the bad. But part of the reason I (black) am 14 points ahead on the left is because that largish eyeless white group is dead, rather than alive. But the reason it is dead is that it has only two liberties, while my opposing black eyeless group has four.
I think you're right that most goal-directed activity, especially formalized pursuits like abstract board games, encourages rational thinking. Nevertheless, I have gotten the feeling that go is particularly good in this regard, at least in my experience. I played chess for a long time, and have tried many other types of formal table and online games, and of them all, go seems to have the strongest tendency to show me how bad habits of thinking work against me. I would love to see more articles like this one explicitly illustrating how other activities can be be approached as a means of rationality practice. (Perhaps you have had experience gambling in the paper clip casino to increase your hoard, which has given you valuable practice in understanding probability?)

Thank you for writing this article.

If I can add one thing: A game of go is very long, often 250+ moves. Mistakes you make early on might take 50 or 100 moves before you start to feel their effects. As such, the game encourages long-term thinking. If you are rushing around putting out fires all over the board, you are not winning. I often find myself wishing I could teach my company's management go for this reason.

Go really does reward rational thinking. Games I play by feel and intuition are fun, but if I take my time and try to make rational decisions at each point I play much better.

For me, Go helped to highlight certain temptations to behave irrationally, which I think can carry over to real life.

One was the temptation to avoid thinking about parts of the board where I'd recently made a mistake.

And if I played a poor move and my opponent immediately refuted it, there was a temptation to try to avoid seeming foolish by dreaming up some unlikely scheme I might have had which would have made the exchange part of the plan.

The lesson I learned most effectively from Go was to acknowledge mistakes; when I was a weak player one of my worst faults was being unwilling to admit to my opponent that they had outplayed me. This is particularly clear when compared to chess.

In chess, if you fall behind in material or tempo the correct thing (in my experience; I am a weak chess player) is almost always to see what you gained in exchange and try to exploit that. If you gained nothing in exchange and the loss was significant, your play is typically irrelevant because you lost. This encour... (read more)

Losing fights sooner is an important go lesson, related to the OPs point about invasions. The sooner you realize that you've lost a fight, the less you typically lose (early detection means lots of aji). My favorite breakthrough when I was learning go, was the game that I crushed an opponent a stone stronger than me (or rather a stone stronger than I was before the breakthrough) by giving way at every fight, and then at the end of the middle game, destroying a formation he thought was safe with the aji created along the way. It was all about paying attention to what I could gain while giving up original aims, and how that would affect situations elsewhere on the board. For a while that became my style: winning by losing: lose every fight but win the game. That was my jump from 6k to 3k overnight.

Two quick comments:

The main aspect to understand for this article is that go is a game of territory.

This was interesting to me, because one of my 'viewquakes' for Go is that it's NOT a game of territory. It's more about the strength, flow, and structure of stones. I hit this around 8kyu while stuck. Territory is just a side-effect and the Japanese standard of measurement (it may be surprising to learn that there are several scoring methods, and they don't significantly change the character of the game).

The other lesson I can think of is that Go taught ... (read more)

In my experience judgement of shape becomes something that's more intuitive than based on principles. I don't think that a 10 kyu or a 15 kyu can effectively judge shape by learning the small set of principles of good shape.

I find the concept of "aji" especially fascinating when it comes to Go. The word means roughly translated means something like "taste", and as a go concept it refers to set of possible moves and continuations that can dramatically alter the local situation. For example, if there is a weakness in the opponent formation somewhere on the board because of the mistake opponent just made, but the opponent is able to somehow defend it under direct attack, I would most likely play away from this weakness for now, and try to steer the game so th... (read more)

You can think of "don't play aji-keshi" as saying "leave actions which will close down your future options as late as possible", which I think can be a useful lesson for real life (though of course the tricky part is working out how late 'as possible' is).
Go teaches that sort of intuitions that are useful but really vague compared to LW-type of stuff. Overall you can get really strong at go if you simply decide to avoid emotional mistakes typical to zero sum game, actual reading and position analysis and planning is of much less importance.
The last part of the sentence I doubt. When I once played Go regularly, I plateaued at 15k (KGS, years ago), simply because I was too lazy to read. Beyond simple improved experience in opening and life-and-death, reading situations out is one of the most important skills to improve. In Korea schools usually heavily concentrate on reading (in the sense that compared to typical Japanese and Chinese schools they do not force "good shape" that much on pupils, but reading out the situation). This has lead to a quite aggressive style of Korean play, even at amateur level -- they play out of "shape" and "intuition", and than beat you with comparatively enormous self-discipline and speed in reading.
Which may point to another lesson. More than once, after making a move, I have had my opponent say with a frown, "I was afraid you would play there. Now I have to read[1]. This may take a while. Why don't you take a smoke break, or buy coffee, or something." An important skill in Go is to recognize when intuition becomes insufficient, and careful analysis essential. [1] "Read" is Go jargon for careful analysis - what the computer geeks might call exhaustive tree search.
This vaguely reminds me of Paul Graham's exhortation to students, "Stay upwind." [link needed and will update later if I remember to]
"What You'll Wish You'd Known" (advice to high schoolers):

I once read something on LessWrong which was later labeled The Fundamental Question of rationality: "What do you believe, and why do you believe it?" I have found this useful to adapt to go: when playing, I constantly ask myself, "Are these stones alive or dead, and how do I know that?"

I found it really important to start asking myself a bit broader question, "where do I want to play, and why do I want to play there". If, say, my answer is something like "To prepare the move X", it makes it quite straightforward to play X straight ahead, if it's any good.

"Overconfidence leads to bad play."

As an avid chess player, I can tell you that this is true in chess as well. People look at brilliant sacrifices by grandmasters (Bobby Fischer was famous for this) and think they are brilliant enough to pull off the same thing. In my experience, 80-90% of material sacrifices fail. When they do succeed, it is usually because the sacrificer is considerably better than her opponent. I've learned to subdue my desire for a sacrifice and a quick strike and work on a longterm plan instead.

  • Go and chess provide clear demonstrations of opportunity cost, the first-mover advantage (esp. go), and the importance of not wasting time on trivial moves.

  • Go provides proof of, and some understanding of, the power of human intuition. My dad can make moves that I don't think he knows the reasons for, that turn out to have amazing consequences 10 moves later when I discover eg. that a group of stones of mine is dead because, even though I have more liberties in that group than he has in his attacking group, he can use his liberties while I can't use min

... (read more)
Actually, one thing I enjoy about go is that small advantages don't escalate, at least not nearly as much as they do in chess. In go, if you make a mistake early that puts you behind by, say, 30-40 points, the place where you made that mistake usually interacts with the rest of the board little enough that you're not hugely disadvantaged elsewhere, and if you play better in the time and space that is left, you can catch up. But as you say about chess, I'm not sure if this is a very generalizable idea, at least when it comes to rationality.
For most practical situations I would suggest that it does generalise. Humans have relatively little ability to compound on success in a drastic manner. Exceptions of course include situations such as if Smily and Clippy were created at the same time on the same planet. Clippy getting the first week wrong could well leave tiling the universe with paperclips instead of molecular smiley faces is completely beyond his grasp.
It generalizes to real-time strategy games, at least.
Playing a move to weaken a group by taking away it's liberties is something that doesn't happens unconsciously. Trying to play move that have a side effect of weakening the weakest group of the enemy is a lot of what the middle game is about. Then the opponent is either forced to add an additional stone to the group to defend it or you can attack that group later when it becomes to weak. Reading 10 moves into the future is also something that happens frequently in go.
I'm not talking about taking away liberties. I was thinking of a specific recent example in which I had more liberties throughout a long fight, but in the end my liberties weren't usable because the group grew out to the edge of the board in such a way that his liberties were still playable, while mine would lead to being captured. My dad has severe short-term memory loss, and usually can't remember which color he's playing. So I don't think he's reading that many moves ahead. Also - reading 10 moves ahead? Really? Are you talking about ladders or other sequences of moves that each have only 1 good response? If people could read 10 moves ahead in wide-open situations, why would they need to study joseki?
If he has short-term memory loss it's of course also possible that such a move is intuitive. When I say here liberties than I mean the amount of moves that it requires to capture a group. In a fight it's useful to have that number in mind. If you have a fight between two groups than the situation isn't really wide open like a Joseki. Reading 10 moves ahead doesn't mean that you see every possible variation but one variation that includes reasonable moves from both players. You don't want to spent time reading out the variance tree of a Joseki every time you play it from scratch. It's also not always straight forward to know what result is better. If it possible to start an invasion in the corner? To judge whether it's possible to invade a corner you might well have to read 20 moves deep. How much points is the influence really worth? Bad Joseki moves often only make you lose a single point. Lastly learning Josekis is a way to learn how stones flow in the beginning of the game. You need a bit of a feeling of how a game flows to be able to read far ahead.
This reminds me of the general rules of games... I was recently playing a game of mastermind with a friend Mastermind is considered a “solved" game, much like Tic Tac Toe, or checkers. This considered, I was given cause for thought that even though it is "solved" it still presents the ideas of "Learned Rules", "Intrinsic Rules" and "Trial and Error". For learned rules the idea is that the rules are related or taught, how one should act according to circumstance. Intrinsic rules are those rules that are obviated, that the situation itself causes the desire of a solution. Trial and error is the process of clarifying the rules, related to Occam's in the idea of using the simplest rules to solve the game. The real question is what do we do when a game situation presents us with a flip-flop such as explained in Charles Petzold's book code? (This is a basic computing concept). Are games representative of real life or are they viable only as a thought experiment? Can games be more complicated than physical reality?
I don't understand the question. By flip-flop, do you mean an electronic circuit with 2 stable states? What did you have in mind, in the game world?
Sorry for the delay. Let’s start a Fire. The Fire requires 3 things: Air(A), Heat(H) and a Combustible(C) so that: F == A+H+C. We know that there are many true statements about F: F == H+C+A F == A+H+C Etc. Let’s say that these are also true: F != A+A+A F != B+A+A Etc. We also, because of trial and error, can enumerate the false statements, starting with: F != A+H+C. Etc. Continuing with: F == A+A+A Etc. Now this is where the flip-flop comes in: The true and false of the basic circuit have an extraordinary amount of combinations for the purposes of making fire. I came up with this idea not only because people learn games through both negative and positive reinforcement, but that many times we only have a partial picture of the possible combinations for a win. This is redoubled when we think of thing in terms of arbitrary meanings such as air, heat and combustible.
I still don't understand what the idea is.
The idea is this: Not only that people can learn as much about a game from losing it as they can from winning it, but that they need to loose in order to learn how to win. The flip-flop acts as a helper in the process of trial and error. The feedback caused by the wiring of two NOR gates of the flip-flop allow this because the switches are controlled by the true and false sets exclusively; one switch is always associated with the true statements and the other with false. When we start to learn, all possibilities are indeterminate, they can be either true or false; F == A+A+A is just as valid as F != A+H+C. The flip-flop becomes sort of an ex post facto method of examining the data of the experience depending on win or loss. With a loss there can be mild sorting of possibilities, but the real sorting comes with comparing wins and losses. Let me know if how I am representing this idea is to brief, it is still in its infancy, and as I have said elsewhere in my posts, I haven’t read everything.
Yes. In go, if a game lasts 300 moves and you win by 10 points (a pretty respectable margin), then on average each of your moves was .06 points [*] better than your opponent's. (There are some problems with averaging things like this which I probably don't need to point out to you all, but it still shows that you can win the game by being ever so slightly more efficient than your opponent.) [*] 10 points / 150 moves
No, that doesn't sound right at all. You make it sound like there is linear growth and that all moves are sort of the same. When I hear small advantages escalate, I imagine something more like exponential growth. Small moves, early on, compound throughout chess and can lead to bigger and bigger advantages. From what I understand of go, this is not the same. Small mistakes early on are unlikely to be crippling.
Suggested usage: * Exponential growth: small advantages escalate. * Linear growth: small advantages accumulate.
That makes sense to me. Upvoted.
Does it make sense to talk about chaotic growth?
Small advantages bounce around? Actually, as your total advantage is growing consistently, even more slowly than linearly, you should be able to say that small advantages accumulate. And similarly, they escalate as long as the growth is accelerating. In calculus terms, small advantages accumulate while the derivative remains positive, and they (also) escalate while both first and second derivatives remain positive. So now I think that my original usage suggestion is too restrictive. Of course, if you really have a precise mathematical idea about growth, then you could just say that! So don't read too much into anything that I say.
I think this difference is just a misstatement. One thing pounded into me from Go was how a small difference in skill can produce a dominating effect. The handicap system shows the immense differences in 'strength' possible - no other game lets you give up first mover advantage AND several moves and still play on a fair level on a regular basis. Playing Go feels to me like walking a tightrope, and I'm not even dan-level yet. I would characterize it as 'small advantages escalate', but the score only measures a relative difference in play quality. Thus it looks linear. Small mistakes are unlikely to be crippling for two reasons. First, at a lower level, the other player doesn't realize how to effectively punish it, so you can get away with your mistake. At a higher level, you don't make blatant errors (too big of an error and you resign anyhow), so when you do make an error, you have enough skill to play flexibly and partially nullify the relative effect of your opponent's punishing moves.
As a (poor) Go player, linear growth rather than exponential sounds right to me. In chess, every piece you take is a piece your opponent no longer has - death is permanent. In Go, if you lose a piece, you can hope to make up for it later. You're down one piece, but it's not like losing a bishop - it can be replaced*. In Go, poorer play doesn't necessarily lead to a collapse of a figure and its complete capture, but more usually leads to simply a smaller figure. Big figures, equivalent in value to a queen, say, are almost always alive (either because they're big enough to have 2 eyes in their own right or because they can connect outwards) and can't be lost. * I ignore pawns advancing to the last rank; the promotion rule can matter a lot in chess, but it doesn't pervasively affect the whole game and rise inexorably out of the game mechanics.
In go, I don't think of mistakes as costing me stones; I think of them as costing me chunks of territory. A mistake that puts you one stone behind can turn a large group of stones from alive to dead. A strong group of stones can't move across the board like pieces can in chess, so winning is localized in go. Winning one corner of the board doesn't have a huge effect elsewhere on the board; losing a rook in chess has a huge effect everywhere.
If you lose a stone in go (as opposed to sacrificing it), you aren't only losing territory but the group that captures your stone gets an eye. That eye gives the group strength that can be used to attack elsewhere.
captured stone != eye (not always!) eye != additional strength (not always, anyway-- only weak groups need eyes, and they only need two, a third one doesn't make them stronger)
If you capture a stone and don't get an additional eye you probably not gaining a small advantage through that move but are doing an even exchange. In the end game you are right that additional strength through more eyes doesn't really exist. In the middle game it however often does. Beginner games are a bit different because beginners often overconcentrate their stones and then an added eye won't do any good.
I think you are being too general. But discussions such as this should happen about concrete positions; it's too easy to talk past each other when speaking in the abstract.
You don't really need concrete positions to discuss what gets considered as general go theory. To take the relevant proverb, ponnuki is supposed to be worth 30 points. Of course you can find examples where ponnuki isn't worth 30 points, I however wouldn't consider those relevant enough to drop the proverb. By the way, what your Go ranking?
My objection to your original statement was the specificity about gaining eyes. Yes, a ponnuki is strong, but it's not necessarily a guaranteed eye. There's more to strength than eyes. That's what I was trying to say and apparently failed miserably at. I am 1d AGA FWIW. Just for fun, I feel like guessing your level based off this conversation. :) I'm guessing you're probably between 5-10k, but 10% chance you're weaker than that, 20% chance you're 1-5k, and 10% chance you're same level/stronger than me. What level are you?
Okay, I accept that point. However the main point I wanted to make is that a mistake usually not only leads you to lose points locally but also leads you to lose strength. If the mistake would only lead to the local loss of points than I would speak about linear development. The fact that you however also get strength when you are making points (especially through actions such as capturing stones) suggests to me that the effect is larger than linear. As written above I'm 1 kyu in Germany. At least that was my ranking when I played regularly two years ago.
I didn't realize "escalate" implied exponential growth. I am now torn as to whether advantages scale linearly or exponentially in go. It may depend on how strong the players are. (i.e., do you actually know how to punish that?) It can easily scale exponentially if the player with the slight disadvantage tries something crazy to catch up. I don't think early mistakes in go are less severe in an absolute sense than mistakes in chess-- but go gives you more time to recover (and more time for your opponent to screw up), so relatively speaking they might be. 9x9 go is more similar to chess in that a single mistake is most likely game ending. EDIT: having thought about this further, I think advantage in go scales linearly. Having a small advantage does not make you more likely to gain additional advantages. Assuming correct play from opponent, etc..
Try redoing the calculation with geometric averaging: 300 moves, 150 of which are yours, suppose the final score is 80 to 70: * x^150 = 70, x = (exp (/ (log 70) 150)) = 1.028728 * y^150 = 80, y= 1.029644 * y / x = 1.00089
I don't think that's an improvement. As I said in another comment just now, I think that in go having a small advantage does not make you more likely to gain additional advantages.
Then why does handicapping work? Giving someone 3 stones on star points at the start of a game will have a much larger impact than giving them 3 stones on star points at the end of the game.
I finally saw your point-- moves are more valuable at the beginning of the game, mistakes come at a more or less constant rate, therefore the margin of victory shouldn't be divided up evenly into every move of the game. Yes. I tried to put a blanket disclaimer in my post that started this thread ("There are some problems with averaging things like this which I probably don't need to point out to you all...") in the interest of brevity but perhaps that was a mistake. There are problems with my calculation that yours does not solve. Namely, mistakes do not tend to be small and come at a constant rate. If I lose by 10 points it's entirely possible that I made a single 20 point mistake and my opponent made 10 single point mistakes. (well, for example only. In reality amateurs make a lot more mistakes than that) That said, now that I understand why you suggested it, your calculation does represent the situation more accurately. The escalate/accumulate/linear/exponential discussion threw me off, as did the fact that I was looking for an answer expressed in points (it's easier to visualize what that means), and the fact that I have seen this calculation done by stronger players than I am. Obviously an answer expressed in points can't be constant throughout the game, and I should have seen that.

As some commenters have mentioned, we should be able to derive lessons of rationality from any game (such as Backgammon or Chess), not just Go. After all, rationalists should win, so whatever helps us be rational will help as win, at games as at life.

However, just because being rational helps with the game, that doesn't mean that students of the game will learn this. (After all, being rational helps with real life, yet many students of real life miss these lessons entirely!) Each game (at least each that has long been widely played) has its own literatu... (read more)

I like this point. Actually it is more common in life to learn the value of being hypocritical, instead of being rational. E.g. most people act as if there was no afterlife, which is rational, but maintain that there is an afterlife, which is not. What games, or real-life situations, punish hypocrisy and not just irrationality?
Approximate quote from Taleb: "Nature doesn't tell you how many slots there are in the roulette wheel".
Right on - I hear a lot of twaddle about the benefits of martial arts practice, especially in their marketing or articles, but rarely do students actually accrue those benefits if they aren't specifically trying to. This probably generalizes.
This reminds me of a recent correlational study discussed on the dual n-back mailing list, about comparing Go experts with non-experts. (Have to scroll down.) The Go experts had, if anything, lower IQs; the spatial mechanisms that the Go experts seem to be drawing upon for their performance don't seem to generalize. Like chess, Go may stress WM and IQ early on, but eventually domain-specific stuff comes to dominate.
You however have to know that a lot of go experts also usually spent less time on other task that can improve mental skills. Korean go professionals for example don't have a normal school education but instead spend that time of their life with learning go.
Yes, but while schooling gives an IQ boost, it isn't that much of one. At least, I vaguely remember the one study I've heard of which shows causality only showing a few points. That might offset the observed decrease, but given that I naively expected the Go experts to have average IQs 20 points higher or so, is still a deeply counterintuitive result.

Comment to 7: Important in Go, as in real life, is that taking the most recent change way more into account than reasonable is very easy to happen, and most times a very bad thing to do. (I think this may not be clear for non-players from the description.)

Beginners (that includes me) usually have a model of the game, see the opponent's move, and concentrate 90% (or more) of their thinking time a few points around the move. It's similar to the priming problem, and it's similar to how our emotional state is influenced by things that just happened, whereas everything in the past gets more and more muddled up.

And I'm too lazy to pull out the corresponding links.

Do you mean the idea of "playing away"? eg. focusing on the global rather than the local situation?
Yes, exactly. An example to hopefully resolve any remaining ambiguity Usually you know what has been the last move of the opponent. On the computer, the last move is usually marked with a circle on the stone, in live play you see it being set, and most (all?) rule-sets require your opponent to point out the last move when asked. When using something like a play-by-mail server (like DGS), it is easy enough to forget the board position between each move. One could write a script to replace the marked stone with the circle by a standard-stone, without any markings. To decide on the next move then you have to evaluate the board as a whole. As Go is a full-information game, and the chronological ordering of the moves is irrelevant to the strength and function of any stone on the board, this is at it should be. However, as like most beginners, when I play there I look for the circle, and place my move in the neighborhood. Bad.
As a player on DGS, I'm pretty sure it does mark your last move and also your opponent's move. (I do much the same thing. I sometimes ask Gnu Go for its opinion on a turn, and am routinely surprised by when it suggests playing somewhere far from the last few plays.)

Interesting article!

I think you're overstating the difficulty of Go to computers. The latest wave of Monte Carlo programs -- when run on fast multicore machines -- are able to beat professionals with a modicum of handicap on 19x19, or at even games on 9x9; they're certainly now better than the average club player.

Seven stones is a large handicap. Perhaps they're better than the average club player in English-speaking countries, but I think the average Korean club player is stronger than Zen.

The position in Figure 3 looks alive to me. One eye in the center, and miai for eyes at the two points diagonally below.

There' s kos, or maybe just the order of play - but then if 3 is "unsettled" in this way, then so is 2. [EDIT: figures 2 and 3 have been updated since this comment was written]
I don't understand this comment. [EDIT: Also, I agree with the GP: figure 1 is dead, figures 2 and 3 are alive.]
Do you mean you think there is no possible way for black to kill white in 2 and 3 - no matter what the situation is on the rest of the board? [EDIT: figures 2 and 3 have been updated since this comment was written]
There is no way to kill those groups if white is trying to save them and does not make any mistakes. This is the usual meaning of "alive" in Go.
Right - but they might possibly yet die if white is trying to win. I was trying to find a sympathetic reading for describing 3 as: "the issue is unsettled. Depending on how play proceeds, the white stones may eventually live or may eventually die". There is one - but it also applies to 2. [EDIT: figures 2 and 3 have been updated since this comment was written]
Ah! You are suggesting that black can make a ko threat against the live group in figure 3, and that white might choose to ignore the threat. True, but the usual convention in this case is to call the group alive, rather than unsettled.
I came to the comment section to say this, but you saved me the trouble. As it is, though, it's not really important to the point of the article.
Thanks for the feedback. You're right: for players with more than beginning skill, I agree that Fig 3 is alive (and Peter de Blanc is right that Fig 2 is not "unconditionally alive") in the original versions of the figures. I've revised Figures 2 and 3 accordingly. (So the rest of you shouldn't worry if this comment thread seems confusing! If you're interested, the original versions are here and here.) In choosing examples, I was aiming for arrangements that visually conveyed the three states of close surrounding, surrounding with internal structure, and something intermediate. The goal is to be able to talk about "life" and "death" as alternative states the game might be in, like alternative hypotheses of reality, to serve the go/rationality analogy, without having to explain the rules. I hope the revised versions still do this, while making their labels more correct.
White is still alive in the modified figure 3. Sorry. One full eye and two half eyes.
Again, thank you. I've made another fix. As you can see, life and death problems are not my strength!
I agree. But on the other hand I wouldn't worry about it too much. You get the point across to newbies, and veterans already know what you're talking about without the pictures. The only real danger is somebody who has read the rules but has never played games. (But since you linked to a site with the rules, maybe that is a danger after all!)
Don't worry: I don't know the rules of Go; I went to the site linked; and I could only find a link to a link to a video tutorial, not a list of rules, so I stopped trying.
Well, that's a shame. Read these or these if you're interested, but only after reading the OP, of course!

Go teaches: don't always respond to what your opponent does. Instead, survey the situation and make the best move.

I was quite pleased to see that an article had been written on Go's effect on rational thinking. It's a subject I had been thinking about quite a bit recently. #3 and #4 are the most relevant to my experience of Go and it's effect on my level of rational thinking in general. After playing Go for quite a while, I noticed that it promotes a sort of soft game/decision theoretic strategy to approaching everyday problems and more importantly it makes that approach feel natural. The equilibrium position becomes the natural one.

An additional benefit to playing go, especially on an online server that shows a detailed plot of your rank (as KGS does, for example), is that you can use it as a proxy for brain function when you are doing self-experimentation. I mean, it's rather more fun to play go than to time yourself solving simple arithmetic problems (Seth Roberts' method for measuring mental performance). For example, I noticed a marked increase in performance after I started standing up for most of my workday. More obviously, I lost a stone during a time when I was exhausting ... (read more)

I find backgammon to also be a good analogy for life in general, though I don't really have the time to get into all of the details... perhaps the most important lesson, though, is that if you always take the "safest" move, you're almost guaranteed to lose! You need to take risks - smart risks, where the payoff is worth the danger and the danger is non-fatal, but risks nonetheless.

And sometimes, even if you do everything right, you still lose. That's life.

Oh, and another (cynical) lesson: there are times (when you're likely to get gammoned or even backgammoned) when you can't win, you can't break even, and you can't even quit the game. You actually have to play it out to the bitter end, just to see how bad it's going to be.
There's an interesting essay by William Pinckard that contrasts the philosophical perspectives of the gameplay of three ancient games; backgammon, chess, and go, which says in summary: backgammon is man-vs-fate, chess is man-vs-man, and go is man-vs-self.

Go teaches: behave differently when you are winning - don't take risks, consolidate, play conservatively. Also, to figure out how you are doing - so you can adjust accordingly.

It also teaches "if you're behind, try to rock the boat", which probably isn't great life advice.
Well, a similar lesson may well apply in cases where you are losing, and have got to win. Society might want to try and arrange things so not too many people feel that way, though.
Same advice in Sirlin's Playing to Win

On the other hand, there are some ways of thinking which are useful for Go but not for real life. One example is that damaging my opponent is as good as working for myself.

Another example is that, between equal players, the sunk costs fallacy is sometimes sound reasoning in Go. One form is "if I don't achieve goal X I've lost the game anyway, so I might as well continue trying even though it's looking unlikely". Another form (for stronger players than me) is "if I play A, I will get a result that's two points worse than I could have had if I played B earlier, so I can rule A out."

Is that really the sunk costs fallacy? I think it's valid reasoning-- play the moves that give you the best chance of winning even if that chance is looking slimmer. I think the sunk costs fallacy is more like a failure to be flexible-- e.g., insisting on making some stones live when you could have a larger benefit elsewhere by sacrificing them. (And that thinking is punished quite harshly in go.) I don't think that's sound reasoning; you could have made a mistake since having played B, and A might be the best current option. FWIW, I'm a reasonably strong go player - it's easy to lie with tewari analysis, which is what it sounds like you're talking about.
The first is certainly valid reasoning in Go, and I phrased it in a way that should make that obvious. But you can also phrase it as "I've spent so much effort trying to reach goal X that I'm committed now", which is almost never sound in real life. For the second, I'm not thinking so much of tewari as a fairly common kind of comment in professional game commentaries. I think there's an implicit "and I surely haven't made a mistake as disastrous as a two point loss" in there. It's probably still not sound reasoning, but for most players the best strategy for finding good moves relies more on 'feel' and a bag of heuristics than on reasoning. I'm not sure I'd count that as a way that Go differs from real life, though.
I agree. I think that this phrasing significantly changes the meaning of what you said originally, which was: I interpret this as assigning +infinity utilons to winning the game, and asserting that goal X must be achieved to accomplish that. I think it's completely valid, but the goal structure in life is so much more complicated than it is in go that it doesn't really transfer. Your rewording sounds more like the sunk costs fallacy to me, but I think that it's terrible reasoning in go as well as life. And on point 2: Which would make it valid reasoning. It might not be useful reasoning for life in general (as it's much harder to tell if you made a mistake than it is in go) but I think it's still valid.
Fair enough. I should have said "there are ideas which are useful heuristics in Go, but not in real life", rather than talking about "sound reasoning". The "I'm committed now" one can be a genuinely useful heuristic in Go (though it's better if you're using it in the form "if I do this I will be committed", rather than "oh dear, I've just noticed I'm committed"). "Spent so much effort" is in the sense of "given away so much", rather than "taken so many moves trying".
Thanks to go, I've learned NOT to think like this, but to adjust according to the new information that flows in. It seems rather weird that you can get two totally opposite lessons from the same game.
Right. That's because Go is a zero-sum game while real life is not.

Lately I've been looking into various board games (in a broad sense--there doesn't have to be a board) that are good practice for good thinking. Anybody here have any recommendations?

It would be interesting to know if people have learned anything about resigning from go.

...ignore sunk costs?

Go teaches: prioritisation and time management skills.

Go teaches: hide your thoughts from your opponent - control your speech and body language.

IMO, there's a lesson in the Japanese rules of go. These have complications that lead to a shorter game. I think the lesson here is: don't adopt other people's culture and then start making changes before you have understood it all properly.

AFAIK the Japanese rules of Go have complications for historical reasons. However, those complications usually only affect the best of the players, ergo, ignore them, if you're not a Pro, and try to change them, if you are. Nothing to learn for normal life here.

Go teaches: trade! If you gain points while threatening one group, and your opponent responds by gaining points while threatening another one, sometimes trading one group for the other one is the best thing to do.

But the really important thing about trade in the real world is that it can be win-win. Since Go is a zero-sum game, its lessons about economics will be distorted. (As will be its lessons about war.)
I don't think he was talking about a lesson in international economics. It was more of a lesson against forming sentimental attachments to things that have been in your possession for a long time.

What's your playing strength in Go? The article reads a bit like it's either too much targeted at people without understanding of go or is written without by someone with a playing strength >5 kyu?

But if the two players disagree, the solution is simply to resume play. That true for some Go rule sets but it isn't true for Japanese style rules.

I'm 1 kyu.

I'm about 12k on KGS. I definitely aimed the article at people who knew nothing about go, but I think it's also interesting that you could tell that I'm not a very strong player myself. I would be interested to know if you have found generalizable lessons which only came after you achieved a deeper understanding of the game. According the wikipedia article on rule sets' treatment of the end, all the sets actually say that you should play things out, capturing dead stones. I guess I've only ever played with the more convenient practice of mutual agreement about dead stones. It happens this way in every club and internet server I've ever played at, even when using Japanese rules. So in this sense, the actual experience of playing go does reinforce the idea that new evidence is the arbiter of conflicting beliefs.
In practice when the situation can be played out one usually plays it out till the opponent is convinced. There are however situations where you can't play it out. Under Japanese rules certain local shapes are per definition dead when the game ends. Bent for in the Corner is one example. If there are nonremoveable ko threads on the board those shapes don't die in Chinese rules or other rule sets that require playing out.
No, it's only the Wikipedia rule set which says this. Then the article says So none of the rule sets used in practice agree with Wikipedia's Rule 9. This is from lower down on Wikipedia (more there): So if neither player is good at distinguishing live from dead, then both may lose! (So much for a zero-sum game.) I am not fond of this feature of the Japanese rules; I much prefer the idea that one solves disagreements by playing them out. But then I am an even weaker player than you, so what do I know? (^_^)
Plenty of stronger players feel much the same way. The Japanese rules do mean the game is sometimes over quicker, though - since they avoid filling dame.
0ChristianKl is a fine report that deals with transfering Go concept to thinking about military strategy. Strategy is about thinking "What should I do?", while rationality is about thinking "What should I believe?". I think the two questions are similar enough that one can transfer a lot of what David Lei writes.

Awesome, I've voted it up simply for bringing this subject to LW. I've always wanted to learn about Go. I've already got a book, but what I'm missing is someone/thing I can play with. I know computers are no good at Go yet, but I wonder if there are programs for beginners to play against before bothering humans with their lack of sophistication? I'll have to check out the link provided in the OP. Thank you.

Did you try GNU Go? That should be hard enough for most beginners. Side-note, Wikipedia has a nice article on computer-Go; it's gotten a lot better, but still... with all the discussions on AGI on LW, it's sobering to see how difficult even a constrained well-understood domain like Go can be dealt with using today's methods.
The problem with GNUgo is that it teaches a style that would not be effective in beating humans. Generally, you have to build up moderately difficult situations, where you have a deep sequence of forcing moves. These kind of deep but simple to prune trees are very easily read by humans, but GNUgo sucks at them, especially if they are on the interaction boundary of bigger fights. Still it can be valuable learning tool, but one will learn a different skill set to playing with humans.
That's because, as Minsky said, no one has tried to make a general intelligence first, and then teach it Go.
Computer go uses more interesting methods than computer chess, but they're very obviously not generalizable to any AGI.
One aspect of go which is present on LW but not true about rationality in general (and so not part of the article) is a culture of welcoming and mentoring. Good players are honored by teaching beginners, and the handicap system facilitates interesting teaching games. You should not worry about bothering (go playing) humans with any lack of sophistication. Not all players have this attitude, of course, but surprisingly many do. The place on the internet I've found best reflects this welcoming culture of go is the Kiseido Go Server. Also, I should note that I've been advised by strong players on a few occasions not to play against computer opponents much, especially those set to easier difficulty levels, because it can build bad habits.
I agree. KGS is very friendly, and I certainly managed to make 15k before buying any books. The computer is just for getting some very raw mechanics down. Do it a max of maybe 30 times and start playing humans! I'm about 2k now and I still suck at playing Igowin on 9x9.
Only because the game is so deep. Best programs are going to massacre you mercilessly. Internet go is extremely popular, ranking systems to find players of comparable strength are pretty good (once you learn the basics at least), and it's really easy to find a match. Just go for it.
Maybe there should be a LessWrong email Go games? There are a fair number of people at SingInst who play Go.
That would probably be fun. Someone also advertised this new email-go server to me just recently.