I am thoroughly confused by all of Robert's talk about the difficulty of counting prisoners. His long post made me even more confused. When I count I count 2 points for dead stones still on the board, and 1 for territory where there was a captured stone, adding on the prisoners in the bowl afterwards. Why is it so hard?

It is not hard, but, if you have never thought about it before, it is also easy to make mistakes such as those I showed. It requires thinking that initial prisoners are accounted AFTERWARDS, that the initial prisoner difference (i.e. white prisoner stones minus black prisoner stones, i.e. the difference viewed from Black's perspective) is ADDED (not subtracted), that the prisoners of the sequences for determining Black's or White's territory are (preferably) accounted NOT afterwards but for either sequence (and NOT combined with the lids' prisoners), that the prisoner difference of the sequence for determining Black's territory is ADDED, that the prisoner difference of the sequence for determining White's territory is SUBTRACTED (not added) etc. All this is easy, but if you do not know yet when to account which prisoners and which to add / subtract / not count twice, you can still make easy mistakes in particular for every consideration in bold font.

It is even easier to delude oneself into the thinking that it would be easy. While writing the book, I have made and corrected every possible easy mistake at least once. That's how not so easy it is!

It is easier if one does what typically professionals do in their teaching: pretend that the initial prisoner difference always is 0 (by showing only examples where it is not even mentioned), pretend that considering only one local territory region of only one player would suffice (instead of concentrating on whole board examples and always determining both Black's and White's territories), pretend that special cases such as remaining gote endgame options, remaining basic endgame kos or remaining teire would never occur, pretend that in the two sequences for determining Black's and White's territories always only different prisoners would be made etc.

If all this were so easy indeed, then why don't professionals just always teach it when teaching positional judgement? Since I could not learn that from professional sources, I had to study most and find out by myself. Everything is pretty easy, but it is also easy to overlook one or another of the easy aspects. Overall, it is "so hard" because one must avoid overlooking part of the one or two dozen easy aspects.

PART of what he says is correct:

"count what is definit[e] resolved territory."

Of course. The problem is: What is definite, resolved territory? Without further specification, this is only clear in the case of already tightly surrounded territory without or with only trivial remaining endgame (although, strictly, this is not definite and not resolved yet):

Click Here To Show Diagram Code

[go]$$B Black has 7 points
$$ ------------------
$$ | . X . X O . . . .
$$ | X X X X O . . . .
$$ | O O O O O O . . .
$$ | X X X X X O . . .
$$ | . . . . X O . . .
$$ | X X X X X . . . .
$$ | . X . . . . . . .
$$ | . X O . . . . . .
$$ | . O O . . . . . .
$$ | . O . . . . . . .
$$ | O O . . . . . . .[/go]

Already when it is less definite, it is unclear whether he would count territory or include it in his estimate for the rest of the board where there is not definite territory:

Click Here To Show Diagram Code

[go]$$B To count or not to count?
$$ ------------------
$$ | . X X . . . . . .
$$ | X . X . . . . O .
$$ | X X X . . . X O .
$$ | . . X X X X X O .
$$ | . O O O O O O O .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]

He also says that one must have endgame knowledge, so maybe he would count this.

However, what he says is completely unclear in situations like this:

Click Here To Show Diagram Code

[go]$$B Territory ending in moyo
$$ ---------------------------------------
$$ | . . . . . X . . . . . . X . . . . . . |
$$ | . . . O . X . . . . . . X . O . . . . |
$$ | . . . . . X . . . . . . X . . . . . . |
$$ | . . . O . X . . . , . . X . O , . . . |
$$ | . . . O . X . . . . . . X . O . . . . |
$$ | . . . O . X . . . . . . X . O . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |[/go]

Does part of the black region have definite territory? Which part? Or no part? Simply include the entire region in the estimate for the rest of the board? This is where Magicwand's suggestions are not exact at all but highly ambiguous.

"howmany points you or opponent need to cashout in order to make the game balanced."

Of course. If a player is X (or alpha, to use his preferred parameter) points ahead, then the opponent needs at least X points on the rest of the board to catch up. This is common, correct knowledge. The problem with Magicwand's application of that knowledge is that too much of a position is unclear. Because for too much he does not specify whether one should consider it definite or not definite territory, there will be a too great part "in the estimate", i.e. belong to the rest of the board for which the estimate X needs to be made.

I prefer to specify clearly what is "definite" (the "current territory" http://senseis.xmp.net/?CurrentTerritory) and to assess also the territorial value of moyos or of territorial regions being territory at one end but moyo at another end. Thereby the rest of the board, for which an estimate X might have to be made, shrinks to a reasonable size.

Now Magicwand and topazg cry "formula - never!". I say: The following simple formula should be used for moyos or territories ending in moyos: Count 100% of the current territory and count 50% of the 'half territory', that is, the territory the defender gets additionally by making one extra play. If you reject this formula, then you should also reject the same formula for the simplest gote endgame options: Count 50% of the territory the defender gets additionally by making one extra play.

Click Here To Show Diagram Code

[go]$$B Gote endgame options
$$ ------------------
$$ | . X X C X . O . .
$$ | X . X X . O O . .
$$ | X X X . O O . . .
$$ | X C X O . . . . .
$$ | . . . O . O . O .
$$ | O O O O . . . . .
$$ | O . X X X X X X X
$$ | O X C . . . . . .
$$ | . X . . . . . . .
$$ ------------------[/go]

Each of the marked intersections is worth 1/2 point for Black.

Formula warning! You need to divide by 2! Danger!;)

The position seems needlessly complex to show the point you are making. In any case, in the position shown the prisoner count does not change during the hypothetical play and you are only disclosing the difference in the number of prisoners.



Why would anyone conclude that if they only know the prisoner difference?



Of course not! This +100 can't be a positive number for both black and white. This kind of difficulty only arises if you are:

1. Trying to keep track of a prisoner difference.
2. Trying to make a prisoner difference count as part of a particular color's territory.
3. Somehow losing track of the fact that you made choices 1 and 2.

1) is arguably unnecessary, 2) is dubious, and 3) is just getting confused.

Keeping track of prisoner differences locally (e.g., to associate it with specific territories) is required when analyzing josekis, but I am not convinced of its utility during actual game play. Remember this is in the Beginners forum, so to me it would seem natural to go with the assumption that one applies (or computes) the prisoner difference at the end with the komi adjustment, in which case this problem is not going to arise.

It is always a problem that discussions evolve. Some become more advanced, others become more basic. Others fluctuate in both directions. It would just add unnecessary confusion if forums would be changed frequently while the same thread of discussion is being developed.



Really? I have already simplified it well. I have not wanted it to simlify it to an extent that it would entirely look like an endgame position.



Yes. I have wanted to keep things simple and start illustrating only one aspect of prisoners.



Exactly. This has advantages: 1) One needs to keep in mind only one instead of two numbers. 2) The number can be smaller in many cases; the overhead of further prisoners of both players need not be carried along. 3) The difference of prisoners is already calculated; one need not do that in future.



Because numbers and signs don't bite back and warn the player using them! If he does make such mistakes, then he needs to become aware of them by himself. He must understand whether his calculations are done correctly. Chances are that he does not necessarily notice if is already making the mistakes. It is better if he develops the related understanding before starting calculations.



It is good to see that you have enough understanding to find your own mistakes! Was your understanding also good enough to describe prisoner handling during the previous weeks, while I waited to see if somebody could describe it? Now, that I have offered some description, suddenly everybody comes and proclaims how simple and obvious everything is. I said so weeks ago:)



No. The difficulty arises also if you keep track of two different prisoner numbers (#black stones and #white stones) for every purpose. E.g., alternatively you could mentally store two numbers for the initial prisoner difference, two numbers for the prisoners removed during the imagined sequence for determining black territory, two numbers for ... sequence for... white territory. (I prefer 3 instead of 6 numbers for prisoners.)



Keeping track is necessary anyway (if we do territory counting). Why one number 'prisoner difference' instead of two numbers 'black prisoner stones' and 'white prisoner stones', see above!



How do you do it in writing? Do you prefer to state two numbers instead of one number?



Mistakes as I have described them do not occur because one expresses prisoner numbers as prisoner differences. The same kind of mistakes can occur also when one expresses prisoner numbers as numbers of black prisoner stones and white prisoner stones. Always does one have to add / subtract correctly.

The perspectives vary: When determining Black's territory, then it is Black's perspective. When determining White's territory, then it is White's perspective (opposing sign!). When both are already known and the total is calculated, then, by convention, from Black's value one subtracts White's value, that is, it is Black's perspective.

Black's perspective means, if you manage two values on every occasion, to add white prisoner stones and to subtract black prisoner stones. White's perspective means the opposite: subtract / add.



Argubly, yes, because one can also do all the calculations with two instead of one value for the prisoners.



Suppose you are determining a particular player's territory. Why dubious? Are you suggesting to ignore all prisoners? Sure?;) Of course, you must consider prisoners! So, please, specify your preferred method for this case of application!



Imagine any example of territory with dead stones in atari and near the boundary of a region. When the opponent reduces that region, you create prisoners.

Proceed to a more complicated kind of examples: teire with throw-ins. You will see that simply keeping dead stones on the board would be an insufficient model in general for assessing a region's territory value.



Of course, one can pretend simplicity for its own sake;)

It might help if you stated that motivation up front. I hope your book does so. But I'll acknowledge that you can't reproduce your book here.



I don't understand. Your "correct" approach avoids neither numbers nor signs. Certainly avoiding numbers is not possible! Signs didn't come up in the example, but what if the initial position assumed there more 100 more black prisoners than white? Wouldn't you use a negative number there?




I can't speak for other people. As for myself, I didn't understand what you had in mind regarding prisoner handling. Now it is clear that you are referring to possible problems players might have with mental bookkeeping.



I'd think that's a different problem.



I'm not suggesting ignoring prisoners. I would use your "correct" method which applies the prisoner difference afterward only when calculating the total count. I dare say you did state the obvious there.



I think you should have started with that example, as I don't think the first one presents too many difficulties. But if you've seen those difficulties with your students, I suppose they are possible. I tend to classify that sort of thing on the same order of concentration problem as forgetting to account for komi, but I'm willing to consider the possibility that it's a different class of blunder.

Let's start with the boundary problem where dead stones are removed during the mental process of reading out variations to get to some kind of quiet, countable position. Before we go further, is this the kind of position where the kinds of mistakes you are referring to with respect to prisoner counting are more likely to occur? If not, feel free to modify or replace with your own example. I'm sorry of this one appears too endgame-like, but I'm afraid that with true middle-game ones one can argue too much about what the proper reduction sequences are rather than the counting itself. (That's the hardest part of counting for me, other that just speed.)

Click Here To Show Diagram Code

[go]$$B
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . O . . . . . O X O X . . . . . X . . |
$$ | . O . O . O . O X O X . X . X . X . . |
$$ | . . . , . . . O X O X . . . . , . . . |
$$ | . . . . . . . O O X X . . . . . . . . |[/go]

Edit: made slight mod to diagram.

These discussions can be tiresome but also entertaining. In this case, I do feel MagicWand oversimplifies, although not to the extent of his post where he says it is important to learn how not to lose. I eagerly await his book on that topic.

I think both views have some validity. MagicWand seems to be of the school that one doesn't have to know much to get stronger, that it's mostly experience. (He's even been so bold as to deny the existence of bad habits in go, which I think is an unorthodox view.) So I think that he accepts that a lot of examples/experience are required to get good.

Robert seems to be on a crusade to show that there's a better way than just examples, and it's clearly very personal to him. It's an ambitious agenda. I disclose that I have Robert's 3 Joseki books and I have trouble with them. He may indeed have a mental model that structures his heuristics in his own brain that works for him, but I'm not sure transplanting that will work. Some things you do have to reconstruct for yourself to understand.

It might be in the introduction, which I still need to write. An even greater motivation is: When doing positional judgement (PJ) in my games, I keep track of (only) the initial prisoner difference instead of the numbers of black / white prisoner stones. Don't you, too? It is easier having to remember only one such number!



Ah, no, that is not what I am trying to say:) Rather:

Calculations are needed for reasonably accurate PJ. They include numbers and signs. (Yes, also + or - signs.) To get good PJ, the calculations must be correct. However, when one makes them, one can also make calculation mistakes. What you write or mentally write as a calculation does not yell at you when you make a mistake. You need to notice by yourself when you do.



They did. (Maybe if I speak of arithmetic operations and write +8 instead of 8, you notice more easily.)



Sure.



This is one of the problems, and comes in various forms. (Thanks for suggesting the phrase!) Another problem is understanding when prisoners occur but are not counted twice.



Now, it is obvious for me. When I started writing, it was not. Describing things carefully helps:)



Yes, this is one possible kind. (A nice variety of endgame contained in the middle:) )

If you like, please tell which trouble. (Or by email / PM, if you prefer.) I am always interested in hearing feedback.

[quote="snorri"]

Click Here To Show Diagram Code

[go]$$B
$$ ---------------------------------------
$$ | . . . . . . . . . B x . . . . . . . . |
$$ | . O . . . . . O X c X . . . . . X . . |
$$ | . O . O . O . O X c X . X . X . X . . |
$$ | . . . , . . . O X c X . . . . , . . . |
$$ | . . . . . . . O O X X . . . . . . . . |[/go]

[quote="snorri"]

Click Here To Show Diagram Code

[go]$$B
$$ ---------------------------------------
$$ | . . . . . . . x W . . . . . . . . . . |
$$ | . O . . . . . O C O X . . . . . X . . |
$$ | . O . O . O . O C O X . X . X . X . . |
$$ | . . . , . . . O C O X . . . . , . . . |
$$ | . . . . . . . O O X X . . . . . . . . |[/go]

difference between two diag is 14 points
now add 1/2 points for leftover 1 point gote.
so total is 14 and half point value + alpha (alpha being less than 1 point)

_________________
"The more we think we know about
The greater the unknown"
Words by neil peart, music by geddy lee and alex lifeson

In most practical cases, a follow-up would not be gote but it would be reverse sente for the defender or sente (privilege) for the attacker.

Click Here To Show Diagram Code

[go]$$W positional judgement: black territory
$$ ---------------------------------------
$$ | . . . . . . . . 1 . 2 . . . . . . . . |
$$ | . O . . . . . O X O X . . . . . X . . |
$$ | . O . O . O . O X O X . X . X . X . . |
$$ | . . . , . . . O X O X . . . . , . . . |
$$ | . . . . . . . O O X X . . . . . . . . |[/go]

Click Here To Show Diagram Code

[go]$$B positional judgement: white territory
$$ ---------------------------------------
$$ | . . . . . . . 2 . 1 . . . . . . . . . |
$$ | . O . . . . . O X O X . . . . . X . . |
$$ | . O . O . O . O X O X . X . X . X . . |
$$ | . . . , . . . O X O X . . . . , . . . |
$$ | . . . . . . . O O X X . . . . . . . . |[/go]

When determining Black's territory and, by assumptions of no relevant outside aji and local reduction plays being local sente, letting the defender reply by defending in response to the reducing attacker, then...



...an alpha is not needed here! Considering only this suitable locale...

Click Here To Show Diagram Code

[go]$$B locale
$$ ---------------------------------------
$$ | . . . . . . . C C C C . . . . . . . . |
$$ | . O . . . . . O B W X . . . . . X . . |
$$ | . O . O . O . O B W X . X . X . X . . |
$$ | . . . , . . . O B W X . . . . , . . . |
$$ | . . . . . . . O O X X . . . . . . . . |[/go]

...and comparing the counts by calculating the territory count, that is, Black's minus White's territory, (incl. either sequence's prisoner difference) in that locale after either reduction sequence, we get the positional judgement's territory count -7 - (-7) = 0 points. (In the locale, when determining Black's territory, White makes points; when determining White's territory, Black makes points. Therefore we have negative values from either defender's perspective.)

When you calculate a value like 14 points (including sente follow-ups considered as privileges), then that does not express a positional judgement's territory count, but expresses an endgame value: the so called deire value. Expressed as a miai value (per excess plays, here: 2 because either Black plays 1 play more or White plays 1 play more), the endgame value becomes 14/2 = 7.

Also for this calculation referring to privilege follow-ups, an alpha is not needed. However, now I get at least a rough idea of how you suggest usage of an alpha during endgame calculations when suddenly follow-up values drop dramatically. Before your last message, I had guessed that you would suggest a pretty different usage of an alpha: as an assumption by means of a separation line between a moyo's assumed safe territory and its insecure potential territory, for which one would not calculate territory at the moment but include the insecure intersections in the alpha to see which player is alpha behind on the whole board and needs at least alpha on the insecure / open rest of the board to catch up.

EDIT: corrections, in particular: twice replace 6 by -7

In my previous message, I did not consider the endgame values too carefully. Let me do this now. I.e., the following is endgame value calculation - it is not for positional judgement during the middle game.

Click Here To Show Diagram Code

[go]$$B endgame locale
$$ ---------------------------------------
$$ | . . . . . . C C C C C C . . . . . . . |
$$ | . O . . . . . O B W X . . . . . X . . |
$$ | . O . O . O . O B W X . X . X . X . . |
$$ | . . . , . . . O B W X . . . . , . . . |
$$ | . . . . . . . O O X X . . . . . . . . |[/go]

For endgame calculation of determining move sizes, this locale is suitable.

Click Here To Show Diagram Code

[go]$$B Black move, 2 = pass
$$ ---------------------------------------
$$ | . . . . . . 4 3 . 1 . . . . . . . . . |
$$ | . O . . . . . O X O X . . . . . X . . |
$$ | . O . O . O . O X O X . X . X . X . . |
$$ | . . . , . . . O X O X . . . . , . . . |
$$ | . . . . . . . O O X X . . . . . . . . |[/go]

If Black moves first, then he gets the gote move 1 and its follow-up privilege 3, which White 4 must answer.

Click Here To Show Diagram Code

[go]$$B resulting position, prisoner difference = 3
$$ ---------------------------------------
$$ | . . . . . . O X . X C C . . . . . . . |
$$ | . O . . . . . O X C X . . . . . X . . |
$$ | . O . O . O . O X C X . X . X . X . . |
$$ | . . . , . . . O X C X . . . . , . . . |
$$ | . . . . . . . O O X X . . . . . . . . |[/go]

In the locale, Black makes 5 + 3 = 8 points for himself.

However, there is the remaining basic endgame ko, which (under territory scoring) is worth something for White, i.e., it is worth something negative for Black. Using Magicwand's symbol, let us call that alpha. So, to be precise, Black makes (8 - alpha) points.

Click Here To Show Diagram Code

[go]$$W White move, 2 = pass
$$ ---------------------------------------
$$ | . . . . . . . . 1 . 3 4 . . . . . . . |
$$ | . O . . . . . O X O X . . . . . X . . |
$$ | . O . O . O . O X O X . X . X . X . . |
$$ | . . . , . . . O X O X . . . . , . . . |
$$ | . . . . . . . O O X X . . . . . . . . |[/go]

If White moves first, then he gets the gote move 1 and its follow-up privilege 3, which Black 4 must answer.

Click Here To Show Diagram Code

[go]$$B resulting position, prisoner difference = -3
$$ ---------------------------------------
$$ | . . . . . . C C O . O X . . . . . . . |
$$ | . O . . . . . O C O X . . . . . X . . |
$$ | . O . O . O . O C O X . X . X . X . . |
$$ | . . . , . . . O C O X . . . . , . . . |
$$ | . . . . . . . O O X X . . . . . . . . |[/go]

In the locale, White makes 5 - (-3) = 8 points for himself. (The sequence's prisoner difference is negative because it is white prisoner stones minus black prisoner stones. Since we are determining White's points from White's perspective and the prisoner difference is expressed from Black's perspective, we must subtract the prisoner difference.)

However, there is the remaining basic endgame ko, which is worth something for Black, i.e., it is worth something negative (to be subtracted) for White, let us call that -alpha. (Negative sign in front of alpha because it is the inverse of the alpha used in the black points calculation.) So, to be precise, White makes (8 - (-alpha)) points.

Now, we have Black's (8 - alpha) points in the locale and White's (8 - (-alpha)) points in the locale. Both players' values together amount to

Deire value = (8 - alpha) + (8 - (-alpha)) = 8 + 8 - alpha + alpha = 8 + 8 = 16 points.

The miai value is 16 / 2 = 8 points.


EDIT: major corrections. I hope, it is correct now.