RobertJasiek wrote:snorri wrote:and you are only disclosing the difference in the number 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.
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.
RobertJasiek wrote: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.
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?
RobertJasiek wrote: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:)
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.
RobertJasiek wrote: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.)
I'd think that's a different problem.
RobertJasiek wrote: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!
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.
RobertJasiek wrote: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.
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.)
Edit: made slight mod to diagram.
