## Wednesday, August 29, 2007

To speak to the invasion subject of last post. The invasion square is often at a crossroads where it interacts with multiple pieces. I wonder if there is value to mapping some of these fields of force. Ct-Art does this as part of their hint section. Do you think there would be any value in doing this?

Yes, I'm inclined to think that that would be very valuable. Let's investigate an example.

White to move and win.

It is miraculous how every problem in Polgars Middlegame book seems to revolve around invasion and overloading. I just took the next problem.

The first question I ask myself is where do my pieces converge?
• Q+B: g7
• Q+R+R: f8
• R+R+pawn: f7
You see that I neglect at the moment that the long diagonal isn't cleared yet.
The next question is what are the defenders of these potential invasion squares?
• g7: Q+K
• f8: N+R+K
• f7: B+R+Q+K
Especially important is the value of the defenders. The higher the value the worse the defense. Thus g7 has the least defense.

The next question is which piece is overloaded?
• The queen has to protect e6 and g7
It's remarkable how often it is the queen that is overloaded.

Based on these data you can make a plan. First you have to decoy the blockader of e5 away since you have to clear the long diagonal in order to give the bishop access to g7. So the main line will be
1.Bh3 Bxh3
2.e6 Bxe6
3.Rxe6 Nf8
4.Qf4 attacking both Rb8 and Rg7 and black is lost.

There alot of other lines of course, but you get the idea. You see how the other tactical themes seem to revolve around the basic themes invasion and overloading. The decoy of the bishop, the clearance of the long diagonal, the discoverd attack e6 etc..

I stress again the importance of the value of the defenders of the invasion squares and the overloading of those defenders.

1. Based on these data you can make a plan

I don't mean to put down your method, but so far what I have seen is that you can explain a winning tactic with the data about invasion squares and overloading. But it is a whole different thing to really construct the winning plan based on these ideas.

For example, I had the same ideas about invasion squares that you had, but came up with the wrong line. I came up with:
1. Rxe6 Qxe6
2. Bh3 Qe7
3. e6

White is threatening Rf7 where Rxf7 exf7+ Qxf7 Be6 wins. However, black can just play 3. ... Rf8 and this plan seems to be refuted quite easily.

2. What you might have missed is that 3.e6 is a discovered attack winning the exchange. After 3. ... Rf8 4.Rf5! white is still winning. The reason why your plan is refuted is because of 2. ... Qxa2, but even then white is in good shape after 3.Rf2

But besides that, I get your point. I will think about it.

3. As usual, my mistake comes from not having the right idea. I missed Qxa2 because I believed the queen was needed to guard g7.

After reading your reply, I think I can restate my problem. In many positions, the same weaknesses that help find the winning move (Bh3) can help us find candidates that don't work (Rxe6). The only way to distinguish between them is very difficult calculation. Finding Qf4 and the end of the line you gave is pretty tough from the starting position. As is how to deal with 1. Bh3 Re8. At least, it's hard for me :-).

Even though I can recognize where the weaknesses are and what I should be trying to attack, it is still quite difficult for me to actually determine which is better between two candidates like Rxe6 and Bh3.

4. Loomis,
that is why this work is mentally so demanding. It's a hard job to formulate why Rxe6 doesn't work and Bh3 does. Beyond a description of the mere lines, that is. But I'm sure that once I manage to do that, the position will look much simpler to me. And that is the goal of those narratives. It must make a complex looking position look simple.

I will try if I can come up with something.