Life In 19x19

daal wrote:

John Fairbairn wrote: (5 + {-1}) ÷ 2 = 2.

I get the same answer, but I don't quite follow the math. It seems to me that the span of points between black getting the play and white getting it is 6, not 4, so the value of the position should lie between 5 and minus one, in other words 2 points for black. I arrive at this by dividing the 6 by 2 which equals 3, and subtracting that from black's 5 (or adding it to white's minus one).

Everyone is in agreement; you just misunderstood what is being calculated.

As John's translation continues:

In other words, at the point in time of Problem D [shown here], in this area we can calculate that “Black has a territory of 2 points."

So the value of the position is 2 (on average Black will get two points in this area). The value of a move in this area is 3, which will bring the value of the position to 2 + 3 = 5 or 2 - 3 = -1.

dfan wrote:

daal wrote:

John Fairbairn wrote: (5 + {-1}) ÷ 2 = 2.

Everyone is in agreement; you just misunderstood what is being calculated.

So what does this equation mean in words?

John Fairbairn wrote:(5 + {-1}) ÷ 2 = 2.

dfan wrote:Everyone is in agreement; you just misunderstood what is being calculated.

daal wrote:So what does this equation mean in words?

The average of 5 points for Black and 1 point for White is 2 points for Black.

The gote move value can be calculated as (5 - (-1)) / 2 = 6 / 2 = 3. The 6 is the 'difference value', or as Sensei's would say 'the swing', or as daal would say "the span of points between black getting the play and white getting it".

When calculating 'the count' aka 'initial value of the local endgame position', (5 + (-1)) / 2 = 4 / 2 = 2 means in words that it is the average of 'the value of the local endgame position resulting from Black's play' and 'the value of the local endgame position resulting from White's play'. IOW, it is the average of the black and white local follow-up positions (followers).

Bill Spight wrote:

daal wrote:I found this video, in which the lecturer took questions from the audience, to be quite a good introduction.

Do you mean Kyle Blocher's video? It's excellent!

Yes. It would have been a bit better if one could see on the video where he is pointing, but in general, his way of making sure that the audience was following what he was saying was indeed very good.

Kirby wrote:But for awhile, I missed something: it's not the answer that's the essence of go. It's COMING UP with the answer.

Well worth repeating.

daal wrote:

John Fairbairn wrote: (5 + {-1}) ÷ 2 = 2.

I get the same answer, but I don't quite follow the math. It seems to me that the span of points between black getting the play and white getting it is 6, not 4, so the value of the position should lie between 5 and minus one, in other words 2 points for black. I arrive at this by dividing the 6 by 2 which equals 3, and subtracting that from black's 5 (or adding it to white's minus one).

As others have pointed out, you put DesCartes before DesHors. That is, you calculated the value of the move and then used that to find the value of the position. The value of the position is the place to start with understanding all of this.

Bill Spight wrote:As others have pointed out, you put DesCartes before DesHors. That is, you calculated the value of the move and then used that to find the value of the position. The value of the position is the place to start with understanding all of this.

I have to admit that I also just do not get that. Isn't the "value of a position" completely arbitrary in just how large an area you look at? If I can compute the value of a move, why would I care about the value of a local position?

bernds wrote:

Bill Spight wrote:As others have pointed out, you put DesCartes before DesHors. That is, you calculated the value of the move and then used that to find the value of the position. The value of the position is the place to start with understanding all of this.

I have to admit that I also just do not get that. Isn't the "value of a position" completely arbitrary in just how large an area you look at?

Yes, unless you are looking at the entire board.

If I can compute the value of a move, why would I care about the value of a local position?

I compute the value of a move by looking at the difference in values of the resulting local positions. (As you note, both of these position values have an arbitrary additive constant, but it is the same constant, so it doesn't affect the move value.) If you can compute the move value without using position values, go for it.

I agree that once you have the move value, you can throw the position value away.

daal: Yes, O's book is only in Japanese, but I've talked about it enough here that people who don't read Japanese beyond a few basic go characters can probably glean a lot from it.

I think you and I may be the type who lose the will to live when we have to look at numbers - I certainly am. But if you ignore all the excitable froth that the numbers people emit when they engage with the topic, there are some useful elements there. I just ignore anything that's not basic arithmetic and reduce everything else to couch-potato go. I only want people to show me how to operate the remote.

But just as you need to learn how to switch the tv on, to know where the spare remote batteries are, and to sit in the right place, e.g. out of the sun's glare, so there are a few pointers that couch-potato go players need to bear in mind.

1. When we count a position it's useful to see it all from one side (usually Black's). So we count + for Black's territories and - for White's. That way we end up with one figure (positive or negative) instead of two. For couch potatoes that's a 100% efficiency gain. But, while that is easy enough to understand, it can feel a bit unnatural for non-number types, so a bit of practice until it does feel natural is a good thing.

2. The value of a position ("how much territory have we each got?") is a different thing from the value of a move (what is the biggest next to play?) These are related but that's a posh level - pommes-frites go - so we could ignore the relationship. If we follow the traditional ways of counting territory, the relationship is far from intuitive for couch potatoes and so we do ignore it. But O's way of counting territory makes the relationship maybe not easy to understand but certainly easy to apply - basically divide by 2. So just as it's good for real couch potatoes to get exercise, we can learn to divide by 2 - our equivalent of the walk to the fridge.

3. We could stop there, but again with O's method it's so easy to try a few more steps. Here's one. How much territory do we count for Black in the corner?



It's not 5. He gets 5 points if he plays t4, of course, but we've already established that we can only assume he has a 50-50 chance of playing t4. But his territory is not worth 2.5. If the white stone on t1 was at t2, the answer would indeed by 2.5. But in this position, a White play at t4, which leaves a possible move for both sides at t3. But you will notice that this is then essentially the same position as earlier in the thread, and we already know that here that Black's territory in this new position, in the extreme corner, is then 1 point. As O says, "Once that is understood, the rest is mere calculation. From the formula: (5 + 1) ÷ 2 we derive an answer of 3 points."

These are positions with a "follow-up." As you can see, the difference is just half a point here, though there are times when it could be more. You can make a judgement for yourself whether follow-ups are infrequent enough to ignore and/or, even if they are not infrequent, to ignore them anyway. Number lovers, like Syphonapterists, like to talk about follow-ups to follow-ups and so on, or as Jonathan Swift (of Gulliver's Tales) has it: "So, naturalists observe, a flea Has smaller fleas that on him prey; And these have smaller still to bite 'em, And so proceed ad infinitum. Thus every poet, in his kind, Is bit by him that comes behind." Follow-up calculations tend to end in sixteenths and such monstrosities.

My recommendation would be to ignore follow-ups for a while until you are at home with the method, and then add just one level of follow-up. This not only saves on flea powder but it also accords with O Meien's advice not to worry about the sixteenths.

bernds wrote:

Bill Spight wrote:As others have pointed out, you put DesCartes before DesHors. That is, you calculated the value of the move and then used that to find the value of the position. The value of the position is the place to start with understanding all of this.

I have to admit that I also just do not get that. Isn't the "value of a position" completely arbitrary in just how large an area you look at?

No, it is not completely arbitrary, as go players understand. However, as go programmers understand, it is not easy to define what constitutes an independent position. In Mathematical Go Berlekamp and Wolfe suggest assuming a local position to be independent until and unless you can show that it is not. (That's not a great help in writing a go program, though, is it? )

If I can compute the value of a move, why would I care about the value of a local position?

But you are not able to compute the value of a move without computing the value of local positions. daal computed the value of the move by computing the value of two positions, the one where Black had 5 pts. and the one where White had 1 pt. He did so by counting the local scores.

However, he cannot rely upon the local positions he uses to evaluate plays to be scorable. So he needs to be able to calculate the value of non-final (non-scorable) positions, as well.

dfan wrote:I agree that once you have the move value, you can throw the position value away.

Oh, that's a great help!

John Fairbairn wrote:I've already said it several times, but I really do think any half serious go player needs O's book on his bookshelf.

I agree that O's book is the best I have seen in Japanese. It avoids the errors of traditional texts.

One of the many nice things about O's book is that he explains everything without relying on terms like reverse sente (though he does mention them in passing), and you don't need to know whether there's an R in the month to know which meaning sente has.

At least in the first part of the book he only talks about local sente in local diagrams, so he is clear about that. I don't think that that is unusual. He does not define sente, however, but trusts the reader to "get it".

Of course he relies upon terms like reverse sente (gyaku yose), and not just in passing. Gyaku yose is one of the five types of yose that he differentiates on p. 116: Sente yose, gyaku yose, gote yose, ko, and nidan ko.

I know you don't like reverse sente in English, but gyaku yose in Japanese is hardly enlightening in itself.

daal wrote:

dfan wrote:

John Fairbairn wrote: (5 + {-1}) ÷ 2 = 2.

Everyone is in agreement; you just misunderstood what is being calculated.

So what does this equation mean in words?

At this point, maybe this is overkill, but a picture is worth a thousand words. Here is a diagram with a miai that illustrates the point.

John Fairbairn wrote:If we follow the traditional ways of counting territory, the relationship is far from intuitive for couch potatoes and so we do ignore it.

Actually, O's method of calculating territory is the traditional one. He relies on a 50-50 split for gote and privilege for sente.