Wednesday, April 04, 2012

The hidden topology of the chessboard

In real wars the topology of the landscape has important tactical implications. If you manage to conquer a hill you have an advantage. The same is true for chess. If you manage to conquer an outpost for your knight, it gives you an advantage. The problem with chess is that the topology of the terrain isn't directly visible. Take for instance the following problem:

White to move. You can find the solution here. By solely trusting on the recognition of the constellation of the pieces, it is clear that you must have stored an awfull lot of constellations before you will be able to solve this one fast. But if we manage to develop our ability to see the hidden topology of the terrain, things might become much easier.

The focal points of the position above are g7 and g8. Why? What are the characteristics of these squares?

  • The squares are in contact with a target (the king). What does in contact mean? That depends on the attacker. If I place a queen on g7, there is contact. But if I place a rook or a knight on g7, there is not.
  • The squares are hard to reach by the defender. This means it takes a lot of moves. Both Bf8 and pawn f7 are shielding the squares off. The fact that Bf8 is immobile makes it even worse.
  • The squares are easy to reach by attackers. Especially Re1 and Qd2.
If the squares g8 and g7 would have a different color, our attention would be drawn in the right direction immediately. But they haven't. What we must learn is to look at the board in a different way. We must learn to see the hidden topology.

g1 and g2 are focal points of the second order. They are in contact with both the focal points g7/g8 and the attackers.

The skill of seeing the hidden topology of the board would be helpfull in any position. Such skill would be maximal transferable.


  1. For this puzzle, the idea comes into mind pretty fast. If it was a blitz game, and I had only a minute left, I would play Rg1 with the plan Qg2.
    I would not know that this is actually the solution, but practically this is whites best chance, isnt it?
    But because it is a problem, we want to see ahead if it is really leading to anywhere. What moves could black do in between? And black could attack, too.
    People who fail must have fallen astray and the deeper you look the more uncertain the whole thing becomes.

    From a program point of view, this is a tactic. But for us? I have somehow the feeling, this is positional judgment.

    A bit like this puzzle here:

    Here it is even more positional. I very much doubt, that the majority calculated everything through before the first move was made.

  2. It is always difficult to give a good example. What is difficult for me can be easy for you and vice versa. But do you see what I mean?

  3. Yes, I know what you mean. And dont misunderstand me - your puzzle took me very long. I am just saying, that by intuition I would play 1.Rg1, but solving a puzzle, you want to be accurate, and then (even though 1.Rg1 comes into mind under OTB conditions pretty fast) you like to seek for more substantial.

    Of the Chess-capture-threat the threats are usually hard to see in a puzzle, but they are not so hard in a real game.
    For a CT puzzle, the threat must be the winning move, while in OTB conditions, 1.Rg1 simply looks good, because you dont just want to wait till black succeeds with his attack. That 1.Rg1 is already the winning move, you would probably not really know when you play it. So for a puzzle it is difficult, but in a real game it would be easy.
    (usually it is the other way round: too know that it is a puzzle makes things much easier. In a real OTB game, nobody stands next to you and tell you "look out, here is a winning tactic possible!").

  4. This problem is one of my failures.
    Its like your last problem,.. the solution is the most natural move. There is only one piece, wich CAN move ( to a better square )and it is
    moving to the most active square. An other example how tactic-training sharpen the eyes for positional play

  5. I found a lot of these attacker-road-target problems. It is a common pattern. But usually I see only the end or the begin and forget to finish the whole pattern.

  6. I would say the pattern at the begin and the pattern at the end are not that easy for you that they come at the same time into your mind ( easily ). The capacity of your STM is to small to work with both without strong concentratione/guidance. there are some chunks missing. I would try to "learn" the chunks, you want to improve the guidance

  7. @Aox,
    not exactly. My insight in these matters is developing hence my opinion is still changing. What I advocate in this post is to extend the stored patterns of the pieces with the patterns of the squares. This is during storage time. Guidance is meant to use at solution time and since it is a conscious process my take is that that is not going to win the war.

    CT encourages the storage of patterns of the pieces. Since those are visible. For the patterns of the squares we must find a clever solution ourselves. Since they are invisible.

  8. Hm,
    -detecting the new pattern
    -creating trainingsets for each pattern

    Except point one, nothing new

  9. Beautifull, isn't it?
    It's not quite as simple though. To test the skill to see invisible squares you will have to make them visible.

  10. But i think, this is not "new" either. You need to make the traditional pattern visible too. We forget, that it did take us quite some time, to understand the traditional pattern like skewer, fork and so on.

    You will need to compare problems to find "your" pattern. These "new" pattern should be not "strong" related to the "old" pattern, so there is maybe a method to detect them(?):

    You should compare 2 problems wich have no traditional pattern together.

    This might help to see these new patterns easier(?)

  11. Finding those invisible patterns (squares) is not easy. Most of you dont.
    However, I found out, that if you do tag sorted sets, then you will see after a while square patterns which you would not if you had not done this tag-set.
    For instance I disconvered, that there are many tactics with queen and knight, where the knight is placed on the same diagonal like the queen but 2 squares of this diagonal is seperating them.
    I give you an exampl:
    white: Kg7/Qf6/Nc3
    black: Ke5

    This is a check mate pattern. But if you look at the squares, then you see, that white is attacking a lot of squares of the board. For instance the big square with the 4 corner points h8/c8/c3/h3 is almost fully covered. Only few holes in this giant square. And the square with the 4 corner points f6/d6/f4/d4 is fully covered which is why the king in the middle is check mated.

    The pattern is made of two pieces only: Queen and knight. If you are aware of it, you see this combination very often in check mate in 2 tactics. The threat of this check mate leads to some distraction/attraction puzzles.
    the wholes of the huge giant square are often filled with other pieces (black or white) enabling to check mate the black king on many other squares, too. If you know about the placement of knight and queen, you spot those check mates in the middle often and fast.

  12. Here an example of the pattern I just explained in my comment before:

  13. And here another one, same square pattern as mentioned before. Normally you would not identify the pattern, but (thanks to me) now you see it: