Boundary plays - O Meien's method

[mitsun]

In the notation used so far, I suppose the calculation for diagram 4 would be:

B territory = 50%(5)+50%((50%(2)+50%(0)) = 3.0

[Marcus]

This is very interesting, John! I especially like that you want to encourage people to discuss. I admit, though, I'm more of a Tigger than an Eeyore ...

I think I can follow the thought process.

For those having trouble counting the first diagram, I suggest trying Steve Fawthorp's counting lessons here. It's taken me a few times going through them, but it's started to work in my brain, and some of the meat of those lessons made it easier for me to succeed in the count.

Diagrams 2 and 3 sem to build a foundation for counting contested areas, which is interesting and new to me.

My own spin on describing this counting:

In both diagrams, the possibilities all revolve around a single spot on the board. Two possibilities: a) Black plays there, or; b) White plays there. OM seems to be saying that you can count that area as an average of the possible black points (using negative points for white).

So, for Diagram 2:

Black plays: 2 points
White plays: -0 points

Since there are only those two outcomes, we get (2-0)/2=1.

For Diagram 3:

Black plays: 5 points
White plays: -1 points

Average becomes (5-1)/2=4.

Diagram 4 is interesting. I'll copy it here:

$$ Diagram 4 - Page 27
$$ . . . . . . . . . . |
$$ , . . . . . , . . . |
$$ . . . . . . . O . . |
$$ . . . . . . . . . . |
$$ . . . . . . . O . . |
$$ . . . . . . . . . . |
$$ . . . . . . . O O O |
$$ , . . . . . , . X a |
$$ . . . . X . X . X O |
$$ . . . . . . . . X b |
$$ . . . . . . . . X O |
$$ --------------------

Click Here To Show Diagram Code

[go]$$ Diagram 4 - Page 27
$$ . . . . . . . . . . |
$$ , . . . . . , . . . |
$$ . . . . . . . O . . |
$$ . . . . . . . . . . |
$$ . . . . . . . O . . |
$$ . . . . . . . . . . |
$$ . . . . . . . O O O |
$$ , . . . . . , . X a |
$$ . . . . X . X . X O |
$$ . . . . . . . . X b |
$$ . . . . . . . . X O |
$$ --------------------[/go]

This situation revolves around two points, not one. My guess is that we'll be able to apply the same idea here. Let me try it. EDIT: Hidden, just like mitsun did, in case people want to try before reading.

With point a, Black or White could reasonably take the move.

Black point a: 5 points
White point a: Still unsettled

Okay, we don't care about point b when Black takes point a, but if White takes point a, we need to evaluate point b.

Black point b: 2 points
White point b: -0 points

Average point b: (2-0)/2=1 point

Going back to point a:

Black point a: 5 points
White point a: 1 point

Average point a: (5+1)/2=3 points

This makes at least a bit of sense to me. Diagram 4 is worth more (in theory) than Diagram 3 because White needs two moves to get the maximum swing in Diagram 4 (instead of only one in Diagram 3). In both diagrams, Black only needs one move.

Does that make sense to anyone but me?

[Bill Spight]

This is not a practical way to find the value of the corner region, but a demonstration that the value people have found is correct.

(;FF[4]AP[GOWrite:2.2.21]CA[ISO8859-1]GM[1]ST[2]SZ[19]FG[259:]GN[ ]PB[ ]AW[ss][sq][so][ro][qo][qm][qk][qi][qg][qe][re][se][sc][sa][aa][ac][ae][be][ce][cg][ci][ck][cm][co][bo][ao][aq][as]PW[ ]PM[2]C[The four copies of the position are miai. They have a definite value, which is the same regardless of who plays first. From that value we can determine the average value per position.]AB[ra][rb][rc][rd][pc][nc][ba][bb][bc][bd][dc][fc][bp][bq][br][bs][dq][fq][rp][rq][rr][rs][pq][nq]
(
;B[sd]
;W[sp]
;B[ap]
;W[ad]
;B[ab]
;C[Black gets 12 points in 4 positions, for an average of 3 points per position.]W[sr]
)
(
;W[sd]
;B[sp]
;W[ap]
;B[ad]
;W[sb]
;B[ar]C[Black gets 12 points in 4 positions, for 3 points average per position.]
)

)

OC, the demonstration depends upon the play being correct.

[daal]

This is not a practical way to find the value of the corner region...

While it may not be generally practical, in this fortunate example where there are exactly 4 possible outcomes, your diagram completely and excellently unfuddles the issue.

[flOvermind]

What Eeyore would like to know, is why, in Diagram 3, we are told to take the approach of counting Black territory as 2 points rather than taking the approach of saying Black has 2.5 points (half chances of getting 5 points) and White has 0.5 point (half chances of getting 1 point).

Does it really matter? 2.5:0.5 and 2:0 is the same, in both cases black wins by 2 points. And since it doesn't really matter, it makes sense to prefer the version where you only have to remember one number instead of two

[Stable]

Hrm...
I was consistantly getting 3.5 points, but...

Black first is 5 points, so black has a 50% chance of 5 points
In the other 50% black has again a 50% chance of 2 points
So from the original position black has 50% 5p, 25% 2p = 5/2 + 2/4 = 2.5+0.5 = 3

OK, I think I get it now.

[John Fairbairn]

Does it really matter? 2.5:0.5 and 2:0 is the same, in both cases black wins by 2 points. And since it doesn't really matter, it makes sense to prefer the version where you only have to remember one number instead of two

This is at the heart of quite a few hotly debated topics in go. It does not make sense to me to use one number in said of two. I can see the equivalence, of course, but I feel more comfortable, in the uncomfortable situation of dealing with numbers, in having maximum information available to me, i.e. two numbers instead of one. Reducing two to one always strikes me as sleight of hand and leaves me feeling uncomfortable. On the other hand, I am perfectly at home with fuzzy words like excellent and sportsmanship.

The world seems split into numbers people and non-numbers people. This thread is meant in part to be a chance to bridge the gap, both ways.

[flOvermind]

But you don't really have more or less information available. You have two numbers anyway. Either you use 2.5 and 0.5, or you use 2 and 0. It really does not matter from a correctness point of view, you can use what you feel comfortable with. But the advantage of using 2 and 0 is that you have to *remember* only one number, because the other will always be 0. In that example it doesn't seem like that matters much, but when you start calculating with these numbers, it will get complicated very fast. I'm not saying that either way is correct or wrong. It's just that one way is more complicated than the other, and it's understandable that O (and I guess pros in general) uses the faster method.

For example, let's take Diagram 4. You can try calculating it both ways. I'm sure the result will be the same, but it will be less work when using only one number instead of two.

I think the point here is this: You have to try to reduce the raw data you have, while preserving all the (interesting) information. After all, that's what counting does. You have a board with stones on it. But what you really want to know is whether you're ahead. This information is hidden in the data of the stone positions. Therefore you count, reducing the huge amount of data to a few numbers. So you've already thrown away lot's of irrelevant data. There's no harm in throwing away a bit more

Of course that's all speculation on my part. I don't actually *know* why O chose this method over the other. It just seems logical to me...

[RobertJasiek]

All: Is this thread about endgame only or also about middle game? Double sente and sente have their practical good meaning in the middle game. So I doubt that disregarding them entirely is the best practical option. Maybe they could be ignored in the endgame though; convince us if so!

When the phrase "boundary plays" is used, then what is the boundary? Is it a sort of hot area between Black and White? Is there an assumption made on multiple threats not existing and all studied endgame regions (or their smaller boundary regions) being pairwise separate in that sense?

He does not evaluate double sente at all. In fact, he does not evaluate sente, but reverse sente. That is eminently correct, as it is reverse sente that gains something. [...] Technically, it does gain something, but that something is not some number of points.

Could you explain these statements, please? Why may one not evaluate double sente at all? Why and how can sente be evaluated in terms of reverse sente? Why is not evaluating sente correct? What exactly does it mean that reverse sente gains something (some points?) and that sente does not gain any points? What (other than points) is it that sente can gain? Does it not rather waste something (aji) than gain anything? And why might wasting it be advantegous nevertheless?

[flOvermind]

"Boundary play" is a more accurate translation of yose. It means moves that settle the border between territories, opposed to other moves that attack, defend, build moyos and so on. Basically, it means "endgame move", but avoiding the confusing term "endgame", because yose moves can also happen in other phases of the game, like the middle game.

That should also answer your first question: The thread is about yose moves. It doesn't matter whether they occur at the end or in the middle of the game

[Bill Spight]

He does not evaluate double sente at all. In fact, he does not evaluate sente, but reverse sente. That is eminently correct, as it is reverse sente that gains something. [...] Technically, it does gain something, but that something is not some number of points.

Could you explain these statements, please?

I have done so at some length on SL. I will give some brief replies here.

Why may one not evaluate double sente at all?

"Double sente", like other natural language terms, has more than one meaning. In an informal sense, you can talk about the value of a double sente. However, when you try to use the term technically, you run into problems. You can see this in Ogawa and Davies' book, The Endgame, as well as in Kano's Yose Dictionary, both books from the 1970s. Kano attempts to explain double sente in terms of "necessity", but then gives an example that is a not very large simple sente. Recent books have shied away from the term, and OM finally goes all the way. The key is the proverb, "Sente gains nothing." It follows that double sent gains nothing for either player, which is true in the technical sense. Example: seki.

Why and how can sente be evaluated in terms of reverse sente?

That is how it has always been done. When we say that a move is a 5 point sente, we mean that the reverse sente gains 5 points.

Why is not evaluating sente correct?

Because beginners (and some others) misinterpret and think that sente gains points.

What exactly does it mean that reverse sente gains something (some points?)

It means exactly what it means that a gote gains some points.

and that sente does not gain any points?

"Sente" is ambiguous, too. In a technical sense, when a sente is played with sente, the result is the same in terms of points, on average. (This is standard, BTW. )

What (other than points) is it that sente can gain?

It prevents reverse sente. You cannot measure the value of preventing reverse sente in terms of points.

Does it not rather waste something (aji) than gain anything?

That depends.

And why might wasting it be advantegous nevertheless?

That depends, too.