To create a grand unified theory of counting for captures in chess it should be either applicable in general, or, if that is not possible, then we need to be able to at least distinguish the cases where it can be relied upon from those cases where it can not. Otherwise, we are left with something that can be applied only in situations where it works but we have no way of knowing which those are.
He put a few diagrams on his blog with the question what the exact role of beancounting is in relation to these diagrams. While analysing the positions I noted that there are 5 different area's that together can describe the majority of all tactical positions.
- Chains of defenders
- Extended beancounting
- Counterattack chains
Only the first two techniques can yield you wood. Logically the vast majority of problems from tactical problemsets fall within these two categories. From these two, duplo-moves are the most common by far. All 4 diagrams of Glenn are based on duplo moves.
Chains of defenders.
Chains of defenders is a new discovered area, about which I have written only little in the past. Defenders defend a piece or a square. Undermining the defenders transits through the chain and becomes undermining the piece or the square. The undermining move is a duplo move, aimed against the defender and the subject of protection.
Beancounting comprises only a very small area of tactics: where you build up pressure against a piece. It helps you to avoid the necessity for visualisation, thus keeping the short term memory free for more useful tasks. It typically tells you if a piece is well defended or not. Most of the time there are few attackers and few defenders, so you don't need a counting method, you see it in a glance. But if there are many attackers and defenders, this is the method to settle for.
Extended beancounting - yet to invent - is meant for situations where the victim is not a piece but a square. You build up pressure to conquer a square. That can be for a positional reason, you want to have an outpost or invasionsquare, or for a tactical reason, a duplo move needs the square.
Long trade sequences should in principle always end up with equal material. Only when there is a duplo move involved you can gain wood in a forced way.
Counterattack chains have a lot in common with long trade sequences, so a new to develop version of beancounting will certainly play a role in the treatment of those. Since counterattack chains are even more challenging for the short term memory, it must be possible to get a big advantage in this area.
Answers to questions.
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?
I think I have given Glenn a clue to when to apply beancounting. The application is obviously fairly limited. When there are duplo-moves around, the outcome of the beancounting cannot be trusted.
Behind the question of Glenn lies implicit another question of course:
How can we find the key move?
The answer is: find the duplo-move and work back. I have put a lot of effort in this, without reaching a definite breakthrough though. But the answer lies within the 5 areas I described above.