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
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
The next question is which piece is overloaded?
- The queen has to protect e6 and g7
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
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.