Tuesday, February 07, 2017

King chase

If the hostile king is already contained in a box, the PLF (PoPLoAFun) system can be used to guide the attention towards the right cues. But when the king isn't boxed in yet, it would be nice to have some guidance too. What are the potential boxes we can chase the king into? How do we decide between them? Of course everything can be decided by actual calculation, as gm Watson has argued comprehensively. But can we formulate some help to get the mind thinking in the right direction? I'm not sure yet.

Diagram 1. White to move
2b3k1/pp5p/1q1r2p1/1Np1Q3/2p5/1P4P1/P4P1P/6K1 w - - 0 1

1.Nxd6 seems to be the obvious move. However, the immediate recapture of the rook isn't very advantageous. We have a few forcing moves up our sleeve. We can postpone the recapture for a while, and retake under better, decisive conditions. Right now, we contain the black king in a box existing of 3 squares: g8, f8 en f7. When the knight recaptures, it covers the invasion square f7. To let the knight and queen work together, we must try to bring the queen in contact with f7, with tempo.
In order to recapture, the queen must stay in contact with d6. On e7, the queen can do both: staying in contact with the invasion square f7, where the knight and the queen converge, and stay in contact with d6, which is necessary for the recapture. And the white queen can get there with tempo via 1.Qe8+ Kg7 2.Qe7+.

Now there are two boxes the black king can choose from.

Box 1. White to move

Box 2. White to move
Now it is the right moment to take the rook. And black must sacrifice his queen to prevent mate.
And here the reasoning stalls. The invasion square has guided my attention via the invasion square. But how to prevent  T&E (Trial and Error) mode from here?


  1. PART I: (What?!? You thought it was going to be “sweet and SHORT”? Ha! Ha! Ha!)

    2079.8 - solved in just under two minutes - which is TOTALLY IRRELEVANT to the discussion/investigation at hand.

    As you indicate, the first two moves are relatively easy to find. The hard part is deciding what to do afterwards to "corral" the Black King into one of the two available boxes.

    1. Qe8+ Kg7 2. Qe7+

    At this "stepping stone" position, it seems "obvious" (maybe only to ME!) that the White Knight is needed to help close the "box." The assault motif advises to proceed while using threats. There is an immediate threat available (while also restoring the material balance somewhat) because the BBc8 is "loose" and we all know (right?!?) that "Loose Pieces Drop Off." In this case, we are simply interested in getting the White Knight a little closer to the Black King with tempo, because Black must waste a tempo saving the BBc8. So, we can expect that the logical way to proceed is:

    3. Nxd6

    We are again at a stepping stone position, and we can split the two potential solutions into "box" 1 and "box" 2.

    "Box" 1:

    Visualizing "box" 1, we can see that White threatens to check on the "new" PoP f7. If Black can be forced on to h8, then the White Queen can mate with Qf8#. The Black Queen has too many functions to perform (protect the BBc8 A-N-D prevent the mate on f8), because there is no square available from which the Black Queen to cover both threats. Black can throw away the Queen with 3. ... QxN, which is hopeless. The only possible "salvation" is promotion of a Pawn, which is just too far away from that goal.

    So, one "solution" for "box" 1 is 3. Nxd6 Qc6, followed by 4. Qf7+ and 5. Qf8# (presuming Black does NOT "dump" the Queen to defer mate. Black can resign.

    There IS an alternative after 3. Nxd6. Black can just decide to "dump" the useless BBc8 and try to wiggle out of "box" 1 by opening up the area around his Queen-forsaken King, hoping that he can do something (ANYTHING!) with his potential passed Pawn and his Queen: 3. ... h5. Well, where there's life, there's hope. Not really: White clamps down on a new PoP at g7 with 4. Ne8!, ignoring the BBc8. At this point, Black is chirping crickets; it's all over except for the fat lady singing.

    We need to keep this alternative line in mind while exploring "box" 2; it "might" prove to be useful.

  2. PART II:

    "Box" 2:

    This one ate up most of my time.

    At first, I could only "see" trying to use the Knight to force the Black King up the board, perhaps using 4. Nf7+. Strangely, it just "felt" wrong. Black just ducks back to g7, and nothing has been accomplished toward the goal of closing the "box." That was when it hit me that the Knight could go to e8 and close the "box" for the square g7. Ah, 4. Ne8! is much better: now White threatens to mate next move on h4.

    Let's give Black an "E" for effort, and allow him to get the "bright idea" of running around on the white squares (and potentially escaping from "box" 2) toward the opposing King.

    3. Nxd6 c3 ("going for the gold" [goal] of pawn promotion) 4. Ne8! and now the Black King "dreams" of escaping via h5 and g4 and (maybe) even f3. Alas, those dastardly Knights have a way of providing protection for Queens AND closing off "boxes": 4. ... g6 (else 5. Qh4#) 5. Qg7+ Kh5 (almost out of the "box"!) 6. Nf6+ [So sorry, Charlie!] and Black must throw the Black Queen back into the piece box to stop mate. After 6. ... Qxf6 7. Qxf6 c2 8. Qb2, Black can end his misery and resign with a clear conscience. If necessary, White can leisurely stroll over with his King and stop the Pawn promotion, while the Queen will eventually go on a raid of the Black position.

    I picked the variations with "box" 1 as the first to be investigated simply because it "looked" simpler to solve. There were two pieces attacking and no available defenders. I didn't have any "magic formula" to guide me. As it turns out, one of the key ideas (4. Ne8!) became useful while contemplating the solution to "box" 2. I seem to recall a similar "bleeding over" of key ideas from one variation to another in a lot of other complicated solutions. Or, maybe that's just an hallucination.

    If you can decipher any generalities from that overly long description, you are much better at doing so than I am!

  3. It seems that we must guide our attention towards the squares where pieces converge. The queen and the knight, the queen and the pawn(s) and, just to be complete, the knight and the pawn(s). Those convergence squares are a kind of dynamic PoPs.

  4. "Those convergence squares are a kind of dynamic PoPs."

    As usual, you zoom right out to the key concept - dynamic PoPs. I love that description! The idea of PoPLoAFun so far has been somewhat static; the PoPs, LoAs and Funs are relatively fixed in place while analyzing a specific position for its unique characteristics. This idea adds a much-needed dynamism to the concept, considerably broadening the scope of applicability. Well done!