Stretching the limits (part II)

continuation from part I. . .

In general: a duplo attack can only be parried by a move with a "duplo-effect".

An "ordinary move" with no such duplo effect can only lead to postponement of the execution of the duplo attack.

Since moves with a "duplo-effect" are not common, this gives a sort of stability to the material evaluation of a position. If you have two attacks and your opponent can only make "ordinary moves" he can only parry one of the two attacks, or he can use the tempo for a single counterattack, which only postpones the execution.

If you have 5 attacks ongoing while your opponent has only 3 attacks ongoing, and he can only make "non duplo effect moves" or "ordinary moves" or "mono-effect moves" or as I will call them from now on "mono-moves", he can only postpone the execution of the 2 extra attacks. But with mono-moves he will never be able to prevent it.

This may look far-fetched, but it is what I found time and again during the study of complex middlegame positions.

So far, the beancounting method only applies to trade sequences on one square. Typical of trade sequences is that they consist of mono-moves. If a duplo move could be made during a trade sequence, the beancounting method would not work.

We Knights are all specialists in duplo-moves. Since that is what the circles are all about. Duplo-moves and traps. So we don't have to be afraid that we wouldn't recognize a duplo-move when there is one:)

The power of the beancounting method is that it eliminates the need to worry about the move order. It eliminates the need to visualize the sequence before the minds eye. It prevents the short term memory from overloading. It's my hypothesis that the beancounting method can be stretched beyond trade sequences. As long as there are no duplo-moves around!

First I will try to describe the ordinary trade sequence in terms of attacks.
Take the following diagram:






















White to move.

White attacks the pawn on d4 three times. How does that compare with a duplo (triplo) attack?

A duplo attack is stretched out in space. It is a tempo or time problem for the defender. He can only parry one attack at the same time. The defender can only save the day if he finds a move that does two things at the same time.

In the 3-fold attack in the above diagram, the attack is stretched out in time. In space it can be seen as just a single attack. Beancounting shows you that the mono attack will not yield fruit in this case.

Reformulation with this new knowledge:
A multi-fold attack of a single piece can be seen as a mono-attack. Beancounting decides if the piece is well protected or not.
A duplo attack consists of 2 mono-attacks. Only a duplo-attack against two unprotected pieces will yield you wood. As long as the defender cannot find a duplo-move.

Summary:

• If a mono-attack is against an unprotected piece or against a protected piece can be found by beancounting.
• Only a mono-attack against an unprotected piece counts. Since an attack against a protected piece will never be succesfull.
  
• If you have 5 mono-attacks ongoing, while the defender has only 3, all mono-attacks are executed until you have 2 mono-attacks while he has zero.
• Mono-moves can only act as a means of postponing the final execution.
  
• If you have 2 mono-attacks more than your opponent you will gain wood. Since he can adress only one mono-attack at the same time. Or he must find a rare duplo-move.
  

This shows that the beancounting will work when applied to trades on multiple squares. That was the first step to make.

Hello, are there still any readers out there who made it to the end? Hard to imagine. Maybe I should flick in some Cum-Sums to attract more readers.

to be continued. . .