Glenn commented on my previous post (in blue):
(Tempo said:) what point are you making with the quiz-questions?
My point is that to evaluate the tactics in a given position one must evaluate the tactics in the given position. Shortcuts must be used with extreme caution. That subtle differences in the position make a significant impact on the usefulness of counting for the position.
Beancounting is valid when there are no duplo-moves around. That equals the statement above.
My last example illustrates that in the original position the (accidental) fact that the Q was at f2 instead of g4 was an important characteristic of the position to make Nxd4 playable. Start with the Q at g4 instead and the "counting" aspects of the position stay the same (same number of attackers and defenders of d4) but the evaluation of Nxd4 changes quite a bit but for subtle reasons.
When you create positions where duplo-moves do play a role you stress that beancounting isn't valid when there are duplo-moves around. To which I agree.
I believe that your statement:
(Tempo said:) This means that this position can be judged in a glance without any necessity to see the move sequences before the minds eye ... is, at best optimistic and possibly just incorrect.
Beancounting is incorrect when there are duplo-moves around. So there we agree again.
The study of beancounting in this position in extenso has made that I understand this position very well. So when you make some slight modifications in the positions, by toying around with duplo-moves, I now can see in a glance what the effect will be. That is new. In the past I had to re-evaluate the whole position. It is this difference that I'm interested in.
Could we have predicted or expected the move via counting? If counting should not apply in this position or for this capture how can we know? What changes in the position by moving the Queen from f2 to g4 to alert us that in one position it works and in the other it does not?
No, we cannot predict or expect the moves when there are duplo-moves around. Only in the very beginning of studying beancounting I toyed with this idea. But I abandoned it as soon as I discovered the role of duplo-moves. Given Glenn's comments I obviously must have made the impression that I thought otherwise.
Don't get me wrong -- there is some value in counting as a technique. But in the immortal words of Lewis McClary: Things that are different are not the same.
The value of beancounting I would summarize as follows:
Within the 4 restraints (take with lowest piece first, no queens in front of rooks or bishop, victim is not a pawn defended by a pawn, no duplo-moves around) you don't have to worry about the actual sequence of the captures, since it doesn't change the outcome. In that way it reliefs the short term memory, which then can be used for more important tasks, like thinking about possible duplo-moves.
(Tempo said:) It was my hypothesis that a grandmaster solves this kind of positions without calculating. I believe that is actually not possible to solve this kind of position without calculating.
Even a grandmaster has to calculate the duplo-moves, of course. Please look at the green text above to what I mean with this hypothesis. Glenn, I hope you don't feel ridiculized by my comments. That is not how I meant it. I'm very grateful with every contribution since it forces vague thoughts to cristallize. For instance in reaction to another comment of you on my previous post, I came up with this little gem:
"The only point of worrying for both sides are the duplo-moves. Those are the only ways to gain or lose wood by force. No duplo-moves: matter stays equal if you count it or not."
This means that it might be possible to go beyond counting. My next post will be about that.
20 hours ago