Mother of all Tactics: counting trades

After studying for 5 days the position below, it has become obvious how universal that position is. The position itself is not too difficult, you can imagine the sequence of trades well within a reasonable time. It is in fact a counting problem. It is obvious how to generalize this position. It's a matter of changing the amounts and the values of the attackers, the defenders and the victim (the piece on d4). Counting problems are extremely common.

Because counting problems are so common, I want to find a shortcut. A method which makes it obsolete to work out the actual sequence everytime. In the same way as the rule of the square in the endgame makes it unnecessary to imagine every pawn and king move in the run to promotion.

The point is that imaging a sequence of alternating moves is taxing for the short term memory. Not impossible, but taxing. Especially if you at the same time must do the bookkeeping of how much wood both black and white have gathered sofar. The fact is, that the position of the diagram below is part of a more complex position. Beginning with an added white bishop on b5 and a black bishop on g6.

I found that the addition of a bishop on b5 immediately lead to a memory overload error. Due to the fact that the load of the underlying counting-problem already has taxed the short term memory to a certain degree. Causing you to check every possible candidate move while often repeating yourself. The all too common paralysis by analyzis.

If you can solve the counting problem in the position without taxing the short term memory, you will find that adding a bishop wouldn't give you problems. Since there is enough room in the short term memory to handle that.

A counting method that handles this position after it is generalized - by changing the amounts and values of defenders, attackers and victim - will have an even broader application. In this position all alternating trades of black and white take place on the same square. In the scenario of a counterattack the alternating trades of black and white take place on different sides of the board. I'm convinced that a counting method will be applicable under that circumstances too. And if that is the case, and I'm convinced it will be, then a lot of complex middlegame positions that caused me trouble and that I have showed you in the past will be solved in a whiff (ahem). Take for instance this example of counterattacking.

See here the MOAT (Mother Of All Tactics):























White to move.

The value of the victim and the first attacker.
In this position the victim is pawn d4 and the first attacker is Ne2.
Let's generalize. There are 3 critical situations:

• The attacker has a lower value than the victim. In that case, the defender will lose wood, no matter what.
• The attacker has an equal value as the victim. All risk lies by the defender. All the defender can hope for is to keep the material balance.
• The attacker has a higher value than the victim. This means that the attacker has to invest. All risk lies with the attacker
  

After the first trade, the attacker and the defender change position. The result of the first trade is the starting point for the second trade.

There are 3 subjects: the victim under attack and the # attackers vs # defenders. This is the easiest way of looking at the position. The victim d4 is attacked 4 times and defended 4 times. So it should be defended enough. There are many cases that this way of shortcutting will do. The situation when there are an equal amount of attackers and defenders is critical. If you can solve this well, it will be no problem when there is an extra attacker or an extra defender. But there are disturbances of such utter simplicity:

The value of the pieces and the access to the square of trade. It is easy to see in the diagram above that rook d8 has no direct acces to d4 while a defender with a much higher value (Qd6) has. That changes the evaluation of the position.

Right now I'm working out the different values and the difference in access to the square of trades. It's going very slow. But I still have high hopes.