Intuition Style

[cata]

I'm almost a chess master and the answer is obviously system 1. System 1 is how you come up with candidate moves; you see a shortlist of moves that "look good." System 2 is how you determine which candidate move is best.

How can that be surprising if you play Go? Isn't it the same process? It's the same process for me (although I'm not obviously not nearly as good at Go.)

[daniel_the_smith]

cata, in retrospect it is indeed painfully obvious. But I'll be surprised (again!) if I'm the only person here that finds that surprising...

[jts]

It's not clear from context what exactly they mean by "find a strong move". If they mean that everything that's going on in a grandmaster's skull during a match is system one (in other words, what happens when GM's are finding the strongest move?), yes, I find that very surprising. I would have expected something more like cata's two-stage process. Otoh, if they mean everything that happens before the GM says "hmm, what about this move, this looks interesting", then it's not surprising.

[ez4u]

While I would agree that the great majority of plays are identified this way (especially true in my case!), I would claim that one of the things that separates the title holders from the also rans is the ability to "dig in", if you will, and go beyond the short list. I do not think that Yamashita and Iyama in the recent 2-day Meijin title match games, for example, spent all their time just evaluating the relative merits of the plays that were intuitively obvious. So it is quite possible that Prof. Kahneman and I would disagree on the definition of "strong" in this context.

[shapenaji]

It's not clear from context what exactly they mean by "find a strong move". If they mean that everything that's going on in a grandmaster's skull during a match is system one (in other words, what happens when GM's are finding the strongest move?), yes, I find that very surprising. I would have expected something more like cata's two-stage process. Otoh, if they mean everything that happens before the GM says "hmm, what about this move, this looks interesting", then it's not surprising.

I think they must mean something akin to cata's two-stage (which, btw, sounds like a great martial-arts-inspired swing-y dance step).

The truth is, you rarely ever find moves by brute-force analysis. You find moves and then do brute force analysis on them. So while it is technically two-stage, the actual "finding" is divorced from stage 2.

[cata]

Personally, I find that finding sensible candidate moves is very hard for me in Go. I find that a large portion of my losses are because at some crucial moment I was unable to even identify as interesting the moves which were best -- a shape point in the middle of an enemy mass, an attachment that I have not seen before, an opportunity to hane and make a ko, a particularly resilient formation for myself.

However, I'm optimistic, since it's easy to get better at that part; just take one or two of the patterns you didn't see, think hard and roll them around in your head until you have a handle you can understand them with, and then remember them for next time.

Anyone interested in a perspective on the process of analysis should probably check out Alexander Kotov's famous book "Think Like A Grandmaster" which discusses in depth how to successfully find, analyze, and evaluate moves in chess. I suspect that it will be interesting even if you have very little chess background; much cross-disciplinary advice is presented. Let me give two brief excerpts:

On amateurish analysis (do I ever empathize with this one!)

But do you know how to analyze variations?...Let us suppose that in your game you have a choice between two moves, rook to D1 and knight to G5. Which should you play? You settle down comfortably in your chair and start your analysis...[after examining some variations] you glance at the clock. "My goodness! Already 30 minutes gone on thinking whether to move the rook or the knight!" If it goes on like this you'll really be in time trouble! And then suddenly you are struck by the happy idea -- why move rook or knight? What about bishop to B1? And without any more ado, without any analysis at all you move the bishop, just like that, with hardly any consideration at all.

On how to study pro games:

I selected from tournament books those games in which great complications had arisen. Then I played them through on a board but when I reached the crucial point where there were the greatest complications and the largest number of possible variations I stopped reading the notes. I either put aside the book or covered the page with a sheet of paper and set myself the task of thinking long and hard so as to analyse all the possible variations. All the time I tried to work myself into the frame of mind that I was sitting at the board in the tournament room. Having spent between half an hour and an hour on this task I would sometimes (especially in very complex positions) write down the variations I had examined and then I would compare them with those of the annotator...In this fashion I examined a large number of very tricky and complicated positions.

[daniel_the_smith]

Yeah, System 1 produces candidates, and System 2 considers.

But if you think about it, System 1 is doing most of the work. To go from 300+ candidates to a handful of reasonable ones is a *much* bigger decision than going on to pick the best out of that handful. (And it applies recursively, too-- when reading, you only evaluate moves and responses produced by System 2. Only rarely do you methodically examine every combination-- there's not enough time.) This implies that if you want to be really good, you need your System 1 to understand go really well. I'm thinking that much of what we do to study--problems, pro game review, et cetera--is actually aimed at training System 1.

So, since reading that excerpt a few weeks ago (I intend to read the book eventually), I've tried, in some positions, just staring at the board without much conscious thought, in an effort to get System 1 to produce more candidate moves, which seems to work a little bit-- if your problem is lack of candidates (and if you spend all your time thinking about one or two moves, then it may be a problem you didn't know you had ).

[Bill Spight]

So, since reading that excerpt a few weeks ago (I intend to read the book eventually), I've tried, in some positions, just staring at the board without much conscious thought, in an effort to get System 1 to produce more candidate moves, which seems to work a little bit-- if your problem is lack of candidates (and if you spend all your time thinking about one or two moves, then it may be a problem you didn't know you had ).

Simply looking at the whole board helped me considerably when I was about 11 kyu. At your level, I do not know how much good it will do. However, I suspect that when pros have the time, they spend some of it just looking.

[daniel_the_smith]

Bill, it may be that much of the benefit comes just from slowing down. Also, I've been pausing in my reading and asking, "...ok, but would I play that if I were him?" and often the answer is, "... of course not!" Apparently System 1 can change its mind when you ask it a different question...

To go from 300+ candidates to a handful of reasonable ones is a *much* bigger decision than going on to pick the best out of that handful.

Some more random thoughts:

To get an idea of the amount of work System 1 performs for you, consider the case where you read a few lines 12 moves deep. Say you're inhumanly good at reading and consider 3 followups to every single move (so you consider 3^12 ~= 500,000 positions). Then System 1 contributes about 80 bits to your decision, and System 2 contributes about 17 bits to your decision. This is an enormous overestimate of how much System 2 contributes; typically I only read a couple lines that deep, nothing like 500,000. If I get that deep for about 20 lines (still an overestimate, but I read lots of lines only a couple moves deep), then System 1 is doing ~94 bits of work, and System 2 is doing 4-5 bits of work.

Say that System 2 evaluates 30 positions per minute (2 seconds per position). Then, in one minute, System 2 does 5 bits of work. In 5 minutes of thinking, System 2 could see 5*30 = 150 positions, nearly 8 bits of work. In one hour of thinking, System 2 could see 30*60 = 1800 postions, or almost 11 bits of work. I don't think anybody's System 2 operates much faster than this (2 or 4 times the speed, fine-- more would astonish me). Pros and amateurs alike. The large difference, then, must be how much work their System 1 does. If a 6 dan can read 20 moves ahead, their System 1 is doing something on the order of 160 bits of work. This explains why it's no effort for them to beat me; their System 1 does vastly more work than my Systems 1 and 2 together. They don't even have to get System 2 involved. If a pro can read 25 moves ahead, they're doing ~200 bits of work, more than the 6 dans can ever hope to do.

(On the "bits" I refer to above: the difficulty of a decision can be thought of as how many bits of information it takes to locate it within the search space. For example, if the problem is to identify a particular person on the planet, you need log2(7 billion) ~= 33 bits of information. If you know their gender, that's 1 bit (it eliminates half the population). If you know they're in New York, that's 10 more bits of information-- it only takes log2(8.7 million) ~= 22 bits of information to locate a person in New York. Every bit halves the space you have left to search. For comparison, if you needed 97 bits to locate someone on earth, that would imply that there were 2^97 people on the planet; if that were the case-- each person would have less than a square micrometer to live in. And yes, I just discovered how cool http://www.wolframalpha.com/ can be...)

(ETA: Huh, on my other computer in whatever font is being used, squiggles (~) look like minus signs (-). I'm talking about approximate bits, not negative bits above!)

[Marcus]

And yes, I just discovered how cool http://www.wolframalpha.com/ can be...)

Yeah, I love that site.

Also, nice breakdown concerning System 1 and System 2 work bits. I like the way you played it out.

[jts]

I complained about the tildes several months ago. They're actually just very small (at least on my computer) - if you blow them up, you can distinguish between them.