Sunday, January 24, 2016


The experiments with vision have lead to two important conclusions, until so far. The first is that a good thought process is paramount in order to guide your focus. The second conclusion is about the importance of visualization-I.

We will talk about thought processes later. Let's focus on visualization-I first.

Visualization-I = seeing the course of the future positions before the minds eye. It turns out that this type of visualization heavily leans on a specific subtask. If you do not master this specific subtask, then visualization-I is virtually impossible. Beyond a certain threshold of complexity, the burden on STM becomes to great and the visualization collapses. This specific type of board vision that is a subtask of visualization-I, I would like to call "aura vision". Aura = the squares that are covered by a piece. The lines or geometrical figure that emanate from the piece. If you can't see the aura of the pieces of the current position in an automatic and perfect way, you certainly will not be able too see it in future positions without an increasing toll on the STM.

I read the website of Momir Radovic (hattip to Robert). He talks about getting the chess basics right. As the chess basics, he identifies four actions a piece can do:
  • Attack
  • Restrict
  • Block (shielding the line of attack by a piece of minor value. putting it in a pin)
  • Protect

These four actions correlate with the actions I identified when a piece is under attack:
  • Annihilate the attacker (= attack the attacker)
  • Escape (= work your way through the holes in the restriction)
  • Block (= block the line of attack with your own piece)
  • Defend (= protect the piece under attack)

It is evident that we have indeed a few fundamental building blocks of the game here, and after ample thinking, I belief we have all fundamental building blocks here. Training subtasks of vision should start here. After reading mister Radivic's blog, I haven't been able to identify his solution of the vision training for each building block, until so far. Maybe one of the readers knows where he has written about that? He goes at great length to herald his solutions.

Three of the building blocks (attack, block and protect), are geared up around the pieces. Hence they are easy to learn. There are already two exercises available which are especially designed for this type of vision: point out the attacked pieces and point out the defended pieces. In practice, these three types of vision (attack, block and protect) don't pose much problems for advanced OTB players, since they can be learned by looking at the pieces. Heisman advised the attack and defence vision training especially for those who tend to leave their pieces en prise, if I'm not mistaken. Leaving a piece en prise without noticing it is uncommon beyond a certain level. And blocking the line of attack with a piece and forgetting it is pinned, is pretty uncommon too, so that's not where the problems lie. These are not the critical subtasks.

The critical subtask is aura vision. Since you don't see the aura when you focus solely on the pieces. For aura vision, you have to focus on the empty squares. From the four elementary building blocks of chess, as given by Radovic, "restrict" is related to aura vision. An example: when chasing a king over the board, you have to keep the king in an invisible cage, which fabric is made of the aura of the pieces.

Without perfect aura vision of the current position, your visualization of future positions is bound to collapse because of STM overload.

I will show you a position where that happens to me.

White to move
r1b2knr/pppp1Pp1/8/3N4/2q1P1p1/8/PB4PP/R4R1K w - - 0 1

If I try to visualize all variations of the toa, then my visualization-I collapses time and again, so I will have to restart. I hope you suffer from the same problem in this position, because then you will understand what I am talking about, otherwise, imagine as if you were failing ;)


  1. Almost every link at the right side of my blog is about exercises in this direction vision-visualisation. An exercise like supose to teach vision AND visualisation ( but with the drawback of using the coordination system and not the inner eye to "look" at the squares, thats indirect and the student has to try to visulaize the board without thinking in coordinates ). There is no doubt that a better "inner board" will help in tactics. Weak vision/visualisation causes problems. Here i did try to start a strict bottom up analysis of vision here:

  2. I did a few difficult mate in 1 at your site today. I noticed that for these mates I need aura vision. So you might have created the ideal exercise for aura vision already! Since the problem is only one ply deep, there is no interference with visualization-I (future positions).

    I have the impression we look a bit different at the speed factor. Speed should be the result of the training, not the subject of the training.

    I intend to experiment with the hard mate in 1's for a while, to see how it works out. Not worrying about speed, but focussing on the aura vision.

  3. hi AoxomoxoA, as I am not allowed to comment on your blog, may I ask you how did you come to design such visualization exercise ?
    I also agree with the coordinates parasitizing the purpose of the exercise. Would a simpler version of the exercise consist in identifying the squares attacked by a single piece ?

    1. The idea behind board vision exercises is to improve the awareness of what is going on at the board. As explanation: A beginner will see a Bishop at b2, then his/he eyes will go to c3 then to d4 then to e5 then to f6 and see there is a knight and this beginner will screen the whole board and all of the pieces possible moves to decide : the knight is not protected.. i should take it. A master knows already that f6 is controlled ba a bishop at b2 and is aware of all pieces if they protect f6 or not. This instant awarenes of the possibilitys of a piece at a given square will give you faster and saver calculation and this board vision skill is a/the first step to better tactical vision.
      Visualization exercise 3 is the/a logical next step: 2 pieces 2 positions and the control of squares or the ability to attack each other

    2. I see. I have seen maze looking problems (in a book and in an mobile app) where you have to find the shorter route to the attack. It is usually a 2 or 3 step route. I assume a simpler version would be "where to put the bishop for checkmate). Anyway from your experience do you think that it cold be of any help to improve board vision especially with your method of "text only" positions ?

      btw, I still don't have access to your blog, if you plan to definitively close it, may I have an export copy of it ? I strongly believe that this is a worthwhile both for its experimental value and because it's different from traditional websites on the subject.

  4. @Aox, what average #mates/minute with "mate in 1 - hard" did you reach?

    1. I never made a training with m1-hard. After i saw how difficult m1-easy is i did not see any use of doing m1-hard.
      I did start yesterday evening and today a shor session and reached a start value of ~4.5 but to get a real value it would be necessary do do some hundred sessions. Getting used to the type of exercise and doing longer session is usually good for a factor ~~2 in speed.
      Please save the tool at your pc or bookmark the link, my bog will be closed

    2. I can't understand your reasoning behind these exercises. You seem to think that you failed "mate in 1 easy" since your avg mate/minute was to low. How low was it, and how high do you think it should be?

      I think you nailed the aura vision exercise with "mate in 1 hard". The easy mate in 1's provide another bottleneck. A bottleneck that I don't consider to be very relevant when you overcome it. But being able to see the restricting squares fast, i.e. the aura, is a serious bottleneck in my problem solving skills, as I have found out.

      I copied the links to your exercises. I will add them to my site later.

    3. seemingly i am extremly bad to explain things :/ So let me try again

      1) We want to get much stronger player .. maybe an FM
      2) We have to get strong in tactics like an FM
      3) We need to be as strong as an FM in many subdisciplines of tactics
      chosing as example
      4) mate in 1

      Now i go backwards

      If i cant improve in Mate at 1.. I cant improve in tactics .. i cant become FM

      and :

      if we find a method how to improve in Mate in 1 we might be able to use this method to improve in other tactical disciplines or in chess in general

      We already know that the methods we used had not enough effect to improve in tactics but mate in 1 is only a very small subproblem so with all energy focused at m1 we should be able to improve here?

      But: by doing lots of mate in 1 there was no improvement in mate in 1.

      Like you want to use tactics as the laboratory for chess-improvement, i use Mate in 1 as laboratory for tactics-improvement.

      Now the question is: How to measure the improvement in M1? We dont have a rating for the puzzles and the score we have at these puzzles is almost 100%.

      There the results of Emirical Rabitt, Uri Blass and me about the relations between time, difficulty und score can help. If you can solve a set of problems with the same difficulty and the same score in half of the time then your strength did grow by 100-200 Elopoints.

      Now we know what to look for. I am a 1900 and want to become FM so i need an other 400 elopoints so i need to get 4-16 times faster in Mate in 1 problems... but by just solving many M1 problems i gain less then 10% of speed.

      Conclusion : Doing a lot of M1 Problems dont help .

      Other easier tasks are improvable (to master level) by simply doing a lot of them.. Fritz attack,defend,check and most of the other board and piece vision ( for example troys )

      So: The question is NOT how quick we are, the question is: can we improve significant in speed ( by a factor 2? ,4? or even more )

      My hope is/was to disect the subtasks of M1 and find a some improvable AND relevant subtasks to MAKE m1 improvable

      So what every your speed in M1-hard is you have to find a method to improve your current speed ( measured after say 1000? posiions ) by a factor 2 minimum. As long as you cant find this.. significant improvemet is not likely to happen

    4. Don't blame yourself for a bad explanation, it might be caused by my biasses.

      Maybe the chess atom M1 is too small. Some properties might be lost in the process of simplifying.

      As far as I have seen lately, there are two main causes for me being slow in solving tactics. The first cause is that I spill my time, 85% or so, by doing the wrong things. This means that I can become 6-7 times faster by omitting this waste of time. For that, not a single neuron needs to fire a millisecond faster. I would become become faster, not quicker. This waste plays no role in M1.

      The second cause that I loose time, is that my visualization of future lines collapses beyond a certain complexity. Which is probably caused by bad aura vision.

      M1 easy doesn't have aura vision as it's main bottleneck. M1 hard does. So my main causes of being slow, play both no role in M1. At least not in M1 easy.

      The first thing we need to know, is how fast is a FM at M1 easy? Only then you can compare your own speed with the speed of a FM. Maybe you are already as fast as you need to be in M1. You can't possibly know without a calibration point.

    5. I dont need to calibrate with an "FM" I am already calibrated by ChessTempo, so i know i have to increase my speed by something like a factor 4. My Performance at Chesstempo in Mate puzzles is "typical" for my rating of a 1900, even my perormance in Mate in 1 at chesstempo is typical.
      Your mate in one performance is "too" low in compqarison with your mate in 10 performance. As longer the line as better your performance, you seem to have a relativ deep calculation strength. Your mate in 10 performance is even higher than mine while your mate in one performance is 230 points lower than mine.

      So m1-easy is a bottleneck, maybe m1-hard is a bottleneck in a different way too. Maybe at the end we will see that these both bottlenecks are in real the same..
      Now we need to find improvable subtasks

    6. Translating rating to speed at CT followed by a translation of speed at CT to a speed at M1 easy is a tricky business. You end up with relative speeds, and you don't know how that relates to absolute speeds. It is all based on a series of assumptions. Plausible maybe, but assumptions nonetheless. It is done by simplification of real world phenomena into mathematics. You don't know how much information is lost in the process.

      Without a calibration point, you cannot possibly know if your conclusions have a solid base or not.

    7. As if your ideas would be not based on assumptions, as if you would not work with simplifications and you seem to have a serious phobia against math.

      naa i give up. I get the feeling you simply dont want to understand me.

    8. @Aox, sorry, I didn't mean to irritate you. I'm an irritating guy, who isn't easy to convince when there is any stretch possible in the interpretations. Being convinced doesn't come without a price tag for me. If I'm convinced, I must apply my conviction. To prevent wasting my time, I'm overly critical. I love math. At the same time I know I can proof anything with it when I'm biased. I've no math phobia but a bias phobia. I have doubts about your reasoning, since the few questions I implied remain unanswered.

      Sorry, it's nothing personal.

      And indeed, I work with assumptions and over simplifications too. But my own reasoning falls victim to my irritating habit to continue to ask questions too. I have the irritating habit to proof that I'm wrong. It's all for the greater good: the final unbiased truth.

  5. I have also blogged about some of Radovic's ideas. One concept he picked up from a research paper was three levels of vision: bottom up (seeing a piece and all squares it can move to as one unit), top down (the functional relationships between the various pieces), and an interconnected system (of 5-6 groups of pieces with interconnected relationships). He seems to have removed this from his website since I cannot find it anymore.

    One idea that is missing from his function list is that of coordination of allied pieces. This would be the corollary to restricting enemy pieces. I found in using these concepts to train my son that five of the six functional relationships can be demonstrated by a pin (with a line piece behind the pinned piece). Only the concept of restrict is not demonstrated, unless you use queens on the same color square on opposite sides of the pinned piece.

  6. I have solved about 100-110K chess mate in 1 (easy version). At first I scored about 38-40 MPS (mate per second) and the highest score I have achieved so far - has been about 47-48 MPS. I do not believe anyone can break 50 MPS unless he is a canidate master level player (CM, FM, IM or GM). And it close to impossible to solve 60+ MPS as some positions are quite far away from the standard (regular) ones. Try to imagine anyone who has not learnt by heart (remembered these) the puzzles - to solve EACH of these in a speed of ONE second per puzzle. Moving the mouse to the square and pressing the key is about 0,3-0,5 second. And the recognition of mate takes about 0,2-0,4 second time (at the best scenarios). You cannot improve the speed of M1 easy by a factor of 3, 4 or 6 if you have already reached the speed of 40MPS. It sounds ridiculous - at least to me.

    1. You can not improve at M1 with a factor of 2 when you are already at a speed of something like 50 mates per minutes because there is to much other stuff slowing us down like mouse/hand/eye coordination so this method of measuring the skill does not work at such speeds propper anymore we would have to substract the offset. But if you cant improve your speed at all then this is a hint that improvement of m1 is a bottleneck.
      The recognition of a mate is done by an grandmaster in 145? ms at average That was a finding of "Saariluoma, P. (1984). Coding problem spaces in chess"
      but i dont have the paper here and im not shure about the 145 ms , it was something close to 100 ms. fact is : as better the player as quicker the recognition if it is a mate or not.
      The "program" M1-easy can only be used to measure/estimate the speedimprovement up to 40 but not realy above 40 mate / minute

    2. Was the mate already manifest on the board and had the gm only to confirm if it was mate or not? Or had he find the move that leads to mate too?

  7. I can't imagine that anyone can go beyond 50 mates per minutes. The limited hand speed starts to stand in the way. I don't belief a FM can do it, until I see him doing it.

    1. Solving #1 puzzles (easy) above 50MPS is possible, but ONLY when you have technical additions - for example: touch screen (monitor) and very fast internet connection. This way you can go up even to 60. However solving puzzles with the speed above 60 (MPS) is not possible in my opionion. At least unless you memorize the puzzles. I have BIG difficulty at reaching the speed of 50 MPS (and I consider myself pretty fast at solving #1 puzzles - not to mention that I have solved over 100K Aox's mate in 1 puzzles).

  8. Yesterday, I did a few hundred M1 hard and got avg #1/minute. After another thousand or so, it was #4/minute. Have I 4x, 2x or 0x multiplied my speed?

    1. @Aox, If I take 4#/minute as my baseline, will I have proven that it is possible to improve with M1 hard when I reach 32#/minute? Would that be a FM performance for me?

    2. One day you are fitter than the other. At the beginning you improve fast, you get used to the pieces, get used to the board, get used to the goal to find a mate in 1, get used to : that its always white get used to just click at the destination square asf. As long as you have to think about these things you cant reach your maximum speed. This takes a few hundred (or 1,2,3?thousand ) attempts and usually 5,7? days.
      Now the "improvement" gets slower, the return diminish. One day you have say 5m/m next day 3m/m next day 4m/m again... And here it gets interesting is it possible to get a decisiv improvement in speed after this pont.
      Lats say you already reached your baseline with 4m/m then based on the hypothesis that you are a 1700 and not already an extreme mate in 1 genius in your rating group ( the CT-Statistics seems to indicate that you are not )you need to improve your speed ~~8 times to get into the FM class. Of couse we need to substract your hand-eye-mouse time and a few other delays, so it would be good if you first try to find out how fast you can click squares ;) I for example know that is can find & click about 60 meaningful squares per minutes ( like attackers and defenders..) .
      I would guess that 4 (+-2??) might be your baseline

      An improvement to 16 m/m would show that M1-hard is improvable for you, even 8 would be phantastic value

    3. I've been steady at 4M/M for five days in a row, so I take that as my baseline. I've done M1-easy at 12M/M and my hand/arm started to fatigue after a while. I'm a slow mover. But with some training, a hand speed of 16 should be doable. So if I will fail to become a M1-hard master, I can't blame my slow hands. My training speed is between 1-3M/M because I focus on aura vision and not on speed.

    4. If you focus on aura vision then you use a thinking process ( even if you do it as aftermath ) and you do a training by repetition af a smaller and easier element of mate in 1 positions.
      As soon you are able to realy improve in m1 then you should be theoretically able to improve in tactics in general, you just repeat this method at all other types of tactic pattern.
      But i would guess that improving at m1 could be already enough to improve in all other tactical motivs too.
      Masters can memorise complete positions in a high speed because they understand or see the interactions of the pieces instantly.
      In the time we try to find the king at the board they found the mate and memorised the whole position.

    5. The video shows the importance of "meaning". Chunks are remembered because they are meaningful. Hence you are right with working on your thought process. A TP is meant to give a position meaning. Even now, when focussing on aura vision, I can't get around integrating a thought process. As you can read in my latest post.

  9. You need a disciplined mind for those M1 exercises. The training mode should be different than the measurement mode. The training mode should be slow, otherwise you don't learn anything from the positions.

    It is tempting you train too fast. The speed is a by product of the lessons learned. Nothing learned, no speed increment.

  10. Diagrams are the best way to illustrate ideas in summery form. What is the diagaram software used for this? Is it creately ?

  11. For diagrams with arrows and coloured squares etcetera I use Lucas Chess.