Saturday, May 13, 2023

Exercise in logic

 On my quest to obtain chess logic I'm constantly experimenting. Can you describe the chess logic that leads to the solution of this composition?

White to move. Mate in two.

8/5r2/7Q/R2q1b2/2pkpbR1/8/2P5/K2N2Nr w - - 0 9 


Escape room
The first area of attention is the escape room of the black king. The only square he can escape to is e5. So the first question that arises is: Is there a move that covers both d4 (target) and e5 (escape square). There is no need to vulture around and write an essay about what we SEE in the rest of the position. Mate ends the game. Prof. Adriaan de Groot proved that a grandmaster considers way less moves than an amateur. Grandmaster are faster because they consider less. They can't be faster in another way.

There are two pieces that can cover both d4 and e5. Namely Ng1 and Qh6.

Line of attack
The second area of attention are the LoA's. Let us start with the knight. 1.Nf3 does the job. Are there any obstacles on the line of attack? That brings us to the defenders.

The third area of attention are the defenders of the lines of attack. Pawn e4 covers a f3, which happens to be the point of pressure from where the knight must deliver mate. So the next question is: can we annihilate the defender? 
There is a whole host of methods to annihilate a defender. Lure it away, exchange it, attack, it block it, et cetera. It turns out that pinning it looks viable. This reveals another line of attack. From Rg4 towards the black king. So the story repeats itself. The process is recursive. What is the defender of the LoA from Rg4 to Kd4?
The line of attack is blocked by the black bishop Bf4. Which raises the next question, how can Bf4 be annihilated?
It turns out that luring it away looks the most viable option. How to lure away Bf4?

The fourth area of attention is the tempo battle. You can't just take Bf4, since this hands over the initiative to the opponent. So you must look for moves that are more forcing.
The hierarchy is:
  • Check
  • Threaten mate in one
There is no viable check here, but there is an interesting threat of mate in one: 1.Qd6.
This reveals a third line of attack: Qd6 (pivotal point)- Qd5# (point of pressure)
The  white queen is untouchable. Bf4 can't take it, because that would put pawn e4 in a pin. The black queen can't take it. since she must block rook a5.
Which reveals the fourth line of attack: Ra5 - e5. Remember that e5 is the escape square.

Summarizing: all logic revolves around PoPLoAFun.

d4 (target)
e5 (escape square)

LoA's (pointing to the points of pressure)
Ng1 - Nf3 - PoP's d4 and e5 
Rg4 - PoP d4
Qh6 - Qd6 - PoP's d4 and e5
Ra5 - PoP e5

Logic prunes the tree of analysis rigorously.

The following pieces play just a static role:
Rh1, Rf7
Bf5, Nd1
Pawns c2, c4
Since they play no role in effecting the lines of attack their moves don't need to be considered. No need to write an essay about during solving the problem. The vulture can ignore them. They are just time consuming distractions.


  1. Chess logic and compositions are.. not going well together. Usually you are looking in chess for CCT-Moves first, in compositions it's the opposite.
    If you know its a #2 you may start thinking if the black king is moving or not and if you come to the opinion the king is not moving you may ask yourself why the black king cant escape to e5
    So you are looking for a move which is not check, prevents Qxa5+ and disables Ke5.

    1. Your approach is very pragmatic. As always. You make use of knowledge you wouldn't have in a game. But the task now is not to solve the problem, but to build a logic model.

  2. Minuscule correction:

    "There are two pieces that can cover both d4 and e5. Namely Ng1 and Qh6."

    I am notoriously BAD at solving compositions. My System 2 immediately asks, "How in the world could this position have arisen in a game?" and gets sidetracked into irrelevance. I "know" the answer to the question - it didn't - but that does not reduce my cognitive dissonance.

    "Logic prunes the tree of analysis rigorously."

    Indeed! It is concrete logic based on the specific details of the position, NOT abstract generalized logic.

    I looked for the "box" (since it is a mate-in-2), "seeing" that the Black King is already (sort of) in it. The "box" bounding pieces are WRa5, WNd1, WPc2, BPc4 and BPe4. Only one move (without check) works to prevent the Black Queen from capturing Ra5 with check. After pinning the Black Queen, there are three possibilities for mate: Qxd5, Nf3, and Ne2 - each depending on Black's reply.

    I'm (obviously) confused: IMHO, the logical process you've described (based on identification of the PoPLoAFun) starts with the vulture's eye view (an overview), identifying the salient surface features of the position. As each salient feature (PoPs, LoAs, and Funs as well as other factors such as tempo) is consciously and logically identified and connected with each other, the vulture circles lower (drills down) toward the final target - mate. As soon as the vulture starts the descent from up high, the vulture's eye view narrows its focus to the essential features, i.e. its essence. Otherwise, the vulture is flying blind as he nears the target (as if he has closed his eyes as soon as he starts his diving attack), which makes no analogical sense to me.


    1. The spiralling of the vulture is an activity of system 1. But the darn beast is uneducated! We must first educate it before let him try to SEE anything. If we now let him fly, it will just start dreaming about SEEing. Which means we are blind now.

      What is the best way to educate the beast? By letting him look over the shoulder of system 2 when it is applying logic to the game. We start simple, with mate in two. If we can find the logic that governs mate in two, only then we will be ready for more complex matters.

      There are two ways that tactics can arise in a game: blunders, or concessions to avoid mate. So it is quite logical to start with mate in two before anything else more complicated. Assuming you are already able to find a mate in one within a reasonable time.

      The the first logical question is: is my king in check? Since if it is, we must first solve that.

      The second question is: what about the killbox? Is it already tight and squeezing? Otherwise our first action must be to chase the king in a more tight area and to start the squeeze.

      The third question is, when the killbox is tight enough: what about the points of pressure? Which are naturally the square where the king is and the escape squares.

      The fourth question is: how about the lines of attack? Can our attackers reach the points of pressure and are the lines of attack free of obstacles?

      All these questions are abstract logical questions which are valid for any mate in two. The work for system 2 is cut out: find the concrete answers to these abstract questions. While the vulture looks over your shoulder and works its miracles.

      May the logic be with you!

  3. Another pruning shears for the tree of analysis is the tempo battle. As long as you give a check, nothing else matters. Unless your attacker clears a line which puts your king in check. Hence I divided the pieces in two types, dynamic and static. The pieces that might have an effect on the lines of attack are dynamic and the ones who cannot have any effect are static. Only the dynamic pieces can play a role in the tree of variations. The tempo battle has its own separate general logic.

    If there is no viable check, the next move in the hierarchy of the tempo battle is to threaten mate in one. But since that is not forcing, you must look whether your opponent can give a check and start a counter attack.

  4. Trying to make use of compositions is an experiment of course. I have selected only 14 compositions. Sofar I find it very enlightening. It helps to make the logic model more robust, since a composition makes use of the most extreme situations. It might be a good idea to separate the tasks. Building the logic model and exercise its application. For the first task, compositions might play a role. While for the second task more realistic positions from games might be better. Maybe.

  5. An aside, only tangentially related to the current topic:

    My antipathy to compositions/studies is limited to those which are obviously impossible to reach by any sane approach to playing the game. Mister Lasker in Lasker’s Manual of Chess has some observations on "made up" problems and how to go about making your own composed problems. He cautions against doing very much of it, and strongly recommends learning from actual games, preferably your own games. The notion that “struggle” is the sine qua non of learning permeates his writings. He even wrote an entire booklet in 1906 titled Kampf (Struggle), expounding his personal philosophy toward life. It can be found on the Internet Archive at:


    I regularly revisit GM Yuri Averbakh's outstanding book Chess Tactics for Advanced Players. Last night, I did a quick survey of examples in that book, and found that approximately half of his examples are studies from outstanding artists in the composition genre such as A. Troitzky (fabulous endgame studies!), L. Kubbel, H. Rinck, G. Kasparyan, V. and M. Platov, R. Réti, and even Em. Lasker himself.

    Realistic positions that “might” have been reached in a struggle between two players OTB are excellent training for working out concrete solutions via calculation/logic.

    Obviously, we CAN learn from ANY example, provided we are willing to suspend disbelief in the impossible. I personally have a hard time doing that – I’m too much of a ‘realist’ for my own good, I suspect.