The logic of counting
I have a set of 100 tactical problems. I use this to get a better idea of what salient cues I need to solve the problems. While investigating them I noticed different categories in which to divide the logic that is exposed by the problems. One such category is counting.
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| Diagram 1. Black to move |
5rk1/2p4p/1p1p1qpb/p1nPp3/2P1P3/1PN1B1Pb/P3B2P/2Q1R1K1 b - - 0 26
Pinho, P. vs. Gallagher, J., Gibraltar 2013
Attacking is about invasion. In order to decide where to invade, I need an overview of the focal points on the board.
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| Diagram 2. Same position. Black to move |
Red digits indicate the squares where white has the upper hand. Green digits indicate where black has the upperhand. The logic that I want to develop revolves around the invasion squares. Luring and trading and clearing and chasing etc. are the tools in the box to change the balance on the invasion squares. The salient cues are: a Queen on g2 or f1 is mate.
Although black has the upperhand on f3, he cannot make use of it due to the value of his attacker (the queen). So the first logical question is: is het possible to lure the defender of f3 (Be3) away?
- 1. ... Nd3 forking Q and R with tempo
- 2. Bxd3 Qf3 threatening mate in 1
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| Diagram 3. After 2. ... Qf3. White to move |
White must prevent the mate on g2 now.
These are the options:
- 3.Qd2
- 3.Re2
- 3.Bf1
Let's have a closer look at the position after 3.Qd2
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| Diagram 4. After 3.Qd2. Black to move |
We must first see how the balance on the focal points has changed.
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| Diagram 5. Same position. Black to move |
As you see, the balance on the focal point has shifted dramatically. This means that it is now time to look for overloaded pieces.
- Qd2 must protect both g2 and e3
- Re1 must protect bot f1 and e3
From here it is easy to see that 3. ... Bxe3+ must lead to the abandoning of one of the focal points where black can deliver mate (f1 and g2).
By focusing on the focal squares and their defenders, a logical narrative unfolds itself.
I hope I didn't make too many errors.
ReplyDelete* investigate the balance on focal squares
ReplyDelete* change the balance by working on the defenders
* see whether defenders become overloaded
Your summary comment is spot on!
DeleteMy first intuition was that this is a stock mating pattern with the White king locked inside a “kill box” by the Black bishop, h2-pawn and the Black queen and rook on the open f-file. [I looked for a named mate pattern without success. The closest one I found was Mayet’s Mate (but I didn’t remember that name).]
In this type of position, it helps ME to “count” the attackers & defenders on each potential target square. Doing this can indicate the weakest point.
On f1: [4:3] Not a B.A.D. square, but it is not safe for the Black queen.
On f2: [2:2] A B.A.D. square but it is not safe for the Black queen.
On f3: [1:2] Black has numerical superiority but it is not safe for the Black queen.
On g2: [1:1] A B.A.D. square. A possible route of the Black queen to g2 goes through the f3-square but it is not safe for the Black queen.
The most useful attack point(s) should be those where the attacker already has superiority OR the B.A.D. square(s) with the lowest number of attackers/defenders. The reason for that second option is that the fewer attackers/defenders there are on a B.A.D. square, the fewer the tempi required to “clear” that square by adding attackers or removing defenders (through attrition or diversion).
Using that criteria, Black should play 26…. Nd3, diverting the Be2 from defense of f3. It is a forcing move because of the fork on the White queen and rook. 27. Bxd3 looks like the best alternative—to a human. Black now conquers the f3-square.
After 27. Bxd3 Qf3 there is no way to avoid mate [GM Stockfish]:
D245 Mate -3 28.Qc2 Bxe3+ 29.Rxe3 Qf1+ 30.Bxf1 Rxf1#
D245 Mate -3 28.Qb2 Bxe3+ 29.Rxe3 Qf1+ 30.Bxf1 Rxf1#
D245 Mate -3 28.Qd2 Bxe3+ 29.Rxe3 Qf1+ 30.Bxf1 Rxf1#
D245 Mate -3 28.Bf1 Bxe3+ 29.Qxe3 Qxf1+ 30.Rxf1 Rxf1#
D245 Mate -2 28.Re2 Bxe3+ 29.Qxe3 Qf1#
Other moves allow mate in 1 on the g2-square.
I set up the position for GM Stockfish after I worked out the solution. It was perfectly willing to try all sorts of alternatives to capturing on d3, losing material rather than allowing the mate sequence: 27. Nd1 was “best” with mate in 9. 27. Qd2 was third best with mate in 8. 27. Bxd3 was the 20th best variation with mate in 4.