Friday, August 17, 2012

Seeing vs calculating

White to move.
You can find the solution here.

I always say that we should seek speed in doing something different and not by trying to do what we already do at a higher speed. You can move faster by changing from walking to using a bike. You can never speed up walking to the same extend as riding a bike.

Especially in a position like the above, I feel that it should be possible to actually see the solution right away in stead of calculating it.
Allthough the problem has a rating of 2282, and people found 19 moves that go astray, the problem is rather clean and straightforward.

The tactical elements are easy to spot:
  • Discovered attack Qd1, Nd4
  • Discovered attack Re1, Ne4
  • Pin Bg5 => Nf6
  • Knight fork Nxf6 => Kg8, Re8
One of the discoveries while doing high rated tactics is that I always neglect the defenders. But the defenders often give a clue where to start the combination.

In order to see the combination, it is necessary to see the essence of the position. This essence consists of seeing the tactical elements and seeing which pieces defend which. In stead of seeing the bare pieces, you can see the function of the pieces. What they are actually doing.
  • Qd8 is defended by Re8.
  • Re8 is defended by Qd8, Ne5 and Nf6
  • Ne5 is defended by Re8
  • Nf6 is defended by Qd8 and Bg7
This gives an idea of the load of the defenders:
  • Qd8 defends 2 pieces.
  • Re8 defends 1 piece.
  • Bg7 defends 1 piece.
  • Ne5 defends 1 piece.
  • Nf6 defends 1 piece.
So the queen is overloaded.

All this you can see in one mental picture. That means:
  • Seeing the pieces.
  • Seeing the attacking elements.
  • Seeing the defenders.
It is possible to see this all at the same time. To mentalize it is maybe a better word.

Of course you might not be able to see it right away, may be you should do first some trial and error in order to reveal the tactical elements and the defensive elements. But once you have listed these elements, you can mentalize them. It may take you a while before you are accustomed to the picture. Once you become familiar with it, you will be able to look around in the picture and see more details. It is for instance possible to look at Bc8 and Ra8 and see that they don't play a role in the combination.

You can compare it a bit with looking at a stereogram. At first you will have trouble to focus. But after some exercises you will be able not only to focus, but to look around in the picture while maintaining focus. Just like you would look around a normal 3D object.

The queen is overloaded, so that gives a clue where to start the combination. The idea behind overloading is to attack one of the pieces that is defended by the queen so that she has to commit herself and leave the other piece that she defended without defence. Knight f6 is already under attack.
First you must get rid of the second defender of Nf6 which is Bg7. An exchange will do that. But with what piece should you start? My instinct is inclined to start with the knight, in order to keep the pin. But Nf6 is subject to two attacks: a knight fork and a pin. It is good to keep the strongest threat, which is the fork (since the King is the target). So you start with 1.Bxf6 Bxf6

Then you must look at the other piece that the queen defends : Re8
Re8 has a second defender too, so you must get rid of that too by a knight sacrifice:

Here black has two responses: 2. ... Qxd1 or 2. ... Nxc6
After Qxd1 you see why is was important to keep the stronger threat Nxf6. Since you attack the king which prevails over the tackeback of the queen.
After 2. ... Nxc6 3.Nxf6+ the queen is forced to abandon Re8, so white wins the exchange.

You see that again a high rated problem is made simple. This is the technique:
  • List the attacking elements.
  • List the defensive elements.
  • Mentalize the position with pieces, attacks and defenses until you can look around in it without loosing focus.
  • Apply some straightforward logic, starting by the (lack of) defenders.
This is what I'm dabbling around with lately.


  1. You made a list of the tactical elements: why is the unprotected rook at a8 no tactical element? Underprotected pieces are often involved in tactics.

  2. I wrote down all elements that are relevant for the combination.

    A tactical element according to my subjective definition is always one of those:
    A duplo attack (2 targets, 1 move)
    A trap(1 target,1 move,lack of space)
    A removal of a defender.

    Ra8 would is part of the following tactical elements:
    Double attack Qd5 attacking Kg8 and Ra8.
    Discovered attack with Qf3 or Bf3

    Since I judged that these weren't going to manifest anytime soon, I left them out.

  3. If you know the right combination than its "easy" to detect the tactical elements involved and then its "easy" to create a path of thought to "conclude" the right combination. But that is reverse engineering. To "shredder" ( is of couse hopeless exagerated but it sounds so nice ) a car is not to build a car. You will need to find an algorithm to "concentrate= minimise the numbers" of the tactical elements without erasing the relevant ones. then you might start your logical reasoning.
    ( was it SAT and NP-Hard ? The complexity might not be reduced )

  4. @Aox,
    That are side issues which might distract you from the core.

  5. About the nature of a difficult puzzle this is a typical example: equal pieces fork equal pieces.
    Here the Nc6 forks the Ne5 (=equal piece) and the queen.

    But the rule "equal pieces threat" fails with the bishops. If you take with 1.NxNf6 BxNf6 then the Bg5 still pins the Bf6 (which is an equal piece). By knowing it is a difficult puzzle, my instinct told me it should be rather Nxf6 in order to keep the pin.

    I actually had a look at the move 2.Nc6 but for some strange reason I though Bc8-g4 counter attacking the queen would save black, while conect the black rooks with each other. Bc8-g4 is a rubbish move though. Just didnt count the material afterwards correctly somehow.
    But it shows, that even the Bc8 played a part in my calculations, and before I did not look at the solution, how can I be sure to exclude it?
    Same with the Ra8. A queen fork Qf3 attacking the point f6 and Ra8 looks like a good idea, and probably led to most fails?

    The puzzle is indeed not that difficult, if you look at it afterwards. But the rating does not make me really wonder, because it has a lot of elements and variations that can mislead you.
    If it had been a 1900, I would not have been surprised, but the 22xx rating seems o.k. to me, too.

    What really makes me wonder is the rating of puzzles like this one:

    It is rated 2000 in Blitz, but rated 800 in Standard.

    Or how about this? It even is a clear pattern!

    Last one (and I could not believe I failed it on the same day, after I was arguing with tempo about sample A and B. --> You remember that, tempo?):

    I still dont have any good excuse how I ever could fail it after thinking 1 minute about it?
    Why didnt the patter got fired here?
    That can make me start to doubt about pattern recognition, but probably it can be explained with: we see what we expect to see. The standard ratings are much lower in rating, which means, if you take your time, you will see it and the pattern gets fired. OTB anyway, because there you expect all sorts of blunders, whereas you would not expect such puzzles in the range 2000 and above. (We only see what we expect to see.)

    Last word: I liked this post of Tempo very much. I guess it is a good advice to count how often one piece attacks and defends an other piece. In that way you can find overloaded pieces and get your thought work around that piece. It definitly helps, and I guess that is the main point Tempo wanted to make here.

  6. The main point I want to make is that you can replace (a considerable part of the) calculation by seeing the combination. That is not an argument but what I experienced.