9/26/2018 – In a deeply thought-out and specific proposal, IM JAN PRZEWOZNIK provides a method to train the way we think while playing a chess game. He unveils nine indicators that push us to reflect on our decisions and interprets them in terms of problem-solving cognitive strategies. In Part 1, we presented an introduction and the first three indicators; now we follow with the final six and an explanation of the "Chunking Theory".
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We boldly confront the Caro-Kann Defense with the upcoming move 1.e4 c6 2.Nf3 d5 3.d3!? With this highly strategic choice, we disrupt Black’s typical patterns and comfort zones and enter an early endgame full of chances for you.
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Analytical improvement
We continue from Part 1, where the first three indicators were laid out:
M - the number of all considered moves N - the total number of subsequent proposals to solve A - the set of alternative actions (candidate moves) considered by the subject
Indicator Dmax
Dmax - denotes the maximum length of calculated variations, the measured number of white and black moves. This value reveals how far ahead the subject is able to calculate variations, to what extent he is able to or wishes to foresee events as they unfold on the chessboard. Dmax can be a measure of an individual's skill in imagining spatial relationships and manipulating them when thinking, or as with other factors, it could simply reflect the situation on the chessboard.
Possible questions:
Did I predict the consequences far enough?
How far am I able to foresee the possible consequences?
The positions that require deep-counting were a great pleasure for both myself and my subjects. We often discovered the great potential of the respondents. During the classes of the Youth Chess Academy I used quite a cruel position, presented below. But the leading juniors, in their calculations, reached quickly enough 15-18 moves variations!
nn - denotes the overall total number of successive changes in the solving propositions. This value applies to all the proposals in the formula, but noted here is each instance of change, each new approach to the problem (including the very first letter as an instance of "change"). In the formula a-a-a-a-b-a the value of nn is 3, as the first four letter a's are treated as a single approach; while in our original example above nn = 11.
Possible questions: Is my process of thinking structured in a good order?
Here is a task that can teach a certain level of order in thinking that Alexander Kotov (1971) wrote about:
Lukow – Przewoźnik, Nałęczów 1980
Black to move
Solution: In this position, Black had to check a few logical continuations:
A. Fight for the open line! 22...Rhd8 23.Rxd8 (23.Rg7+ Kf6 24.Rxa7 Nd3+=) 23...Nxa2+ 24.Kc2 Rxd8=; B. Advance your strong pawn! 22...c3 23.Rd7+ (23.f6+ Kxf6 24.Ne4+ Kf5=) 23...Kf6 24.Ne4+ Ke5=; C. Take a pawn! 22...exf5 23.Rg7+ (23.a3 Nd3+ 24.Nxd3 cxd3=) 23...Kf6 24.Rxa7 Ra8=; D. Can you see a check — play it. Maybe it will be mate! 22...Nd3+.
Don't give 1.d4 players an easy ride — sacrifice a pawn with 3.b5 for a lasting initiative. GM Ramirez shows you clear ideas for play in every variation.
Pmax - denotes the number of re-examined solving propositions. This value marks out all the proposals considered more than once, in other words, all the first moves (moves-candidates) appearing in the decision tree for the first, and later for the second, third time, etc.
The psychological significance of Pmax can vary. It may reflect a "functional fixation," when the subject is unable to break through certain barriers during the problem-solving process, and repeatedly directs attention towards the same moves "going round in circles." A high value of Pmax could also be evidence of a difficulty in making decisions.
Possible questions:
Am I able to concentrate enough on the best option?
Sometimes the choice of certain positions informs the player or trainer whether he or she deals with the main and strongest option. There is a strong connection with the chunking theory, to be discussed shortly.
In the position below, White may concentrate on taking a pawn and calculate the consequences of 1.Qxe4. But there is another deep idea…
Pser - denotes the number of times a solving proposition is reconsidered, but only in the longest single series. From a psychological point of view, this value represents the ability to concentrate on a single chosen solving proposition.
Possible questions:
Am I able to concentrate enough on one option at one moment?
Many times, only one option requires great concentration and careful thinking. Let us have a look at the following ending
Scarcely any world champion has managed to captivate chess lovers to the extent Carlsen has. The enormously talented Norwegian hasn't been systematically trained within the structures of a major chess-playing nation such as Russia, the Ukraine or China.
Carlsen – Caruana, Sao Paulo/Bilbao 2012
White to move
White had to calculate the idea of reducing the material, what might be dangerous (draw!). So let us have a look at variations calculated by Carlsen, in order to avoid a draw.
1.e4e62.d3The French Defence was a huge surprise to me, so I decided to
employ the same strategy that had brought me my only victory so far in the
tournament, namely push the d-pawn one square forward as early as possible.d53.Nd2Nf64.Ngf3Nc6A perfectly
reasonable way of avoiding the "fearsome" King's Indian Attack, starting with
4...c5 5.g3 and so on.5.c3Bd6Looks a little weird, but is actually quite logical. If immediately
5...e5, or 5...dxe4 6.dxe4 e5, then Black would have to reckon with the
b4-push.6.Be2It seemed to me that the bishop would have more work here
than on g2 after a subsequent dxe4 dxe4 e5, and besides, this one seemed to
fit better with ideas of pushing b4.0-07.0-07.b4
here or on the previous move, could have been well met withdxe48.dxe4a59.b5Ne5
and White has gained some space, but also weakened some squares, so Black
should be doing fine.7...a5Black had
several choices here:7...e5
would be met by8.b4and White obviously has
an excellent version of the Philidor. Whether that would be sufficient for an
advantage though, is quite unclear.7...b68.Re1Bb79.Bf1seems a little
artificial for Black.7...Re88.Re1a59.Bf1e510.exd5Nxd511.Nc4would transpose to the game.8.Re1e59.exd5Other Philidor-style moves like Bf1 or
b3 were certainly possible, but I felt like forcing things a bit.Nxd510.Nc4Re811.Bf1Bg412.h312.g3is not as accurate, as Black can playQd7when the annoying bishop cannot be kicked away with h3. I
actually once tried that in a similar position in a blitz game against
Ponomariov, who with a puzzled look in his face simply captured the pawn.12...Bh513.g3Once the e4-pawn is not there to obstruct it,
the bishop is re-deployed to the long diagonal.Going on a fishing expedition with13.g4Bg614.Qb3as the comp seems to recommend, would probably have
appealed to me on the next day against Paco, when I was in more of a
coffee-house mood.13...Nb6A decent move, made after a long period of thought. As you might
have guessed, by this point we were both way "out of book".14.Nxb6cxb615.Bg2b5?
This one however, is rather questionable, as will become apparent after a few
more moves.15...a4would have retained equal
chances.16.a4!Favourably fixing the
black queenside pawns on dark squares. b416...bxa417.Qxa4also gives
Black plenty to worry about. 17.Be3Bc718.Qb3Now the queen is active, and soon the
knight will be brought to d2 and e4, when all the white minor pieces will be
much more active than their black counterparts.h6
It's not so easy to find a more useful move for Black here.18...Qxd3?
loses immediately:19.Rad1Qa619...Qe420.Nh4Bxd121.Rxd120.g4Bg621.Bf1and the queen is trapped. 18...Bxf319.Bxf3Qxd3is possible, but even here Black has a very
unpleasant position after20.Rad1Qf521.Bg4Qg622.Rd7Rac823.Be2!
with the threat of Rxf7.19.Qc4According to a
Russian GM, this was the move of a 2nd category (1600) player.
He instead recommended19.Nh4which looks very
attractive, asQxd319...Qc8however,
bothered me a little, as after20.g4Qd8!21.Nf5Bg6it is not entirely clear what White has achieved.
20.Rad1Bxd121.Rxd1Qh722.Rd7Re723.Bxc6wins.19...bxc320.bxc3e4Otherwise, the
pressure on the queenside would quickly have become unbearable.21.dxe4I played
this and the next few moves quickly, as I couldn't wait to get to torture him
in the endgame.21.Nd4would have
been even stronger. I would have probably have considered it had I noticed
that afterNe522.Qb5Nxd3The bishop is actually
hanging:23.Qxh521...Bxf322.Bxf3Ne523.Qe2Nxf3+24.Qxf3Qd3The position has been simplified quite a bit, but I
had seen many moves ago that even in the endgame Black is far away from a draw.25.Kg2!This is much stronger than25.Rab1Qxe426.Qxe4Rxe427.Rxb7Be5when Black is pretty close to a draw, e.g.28.Bd2Rxe1+29.Bxe1Rc830.Rb5Bxc331.Bxc3Rxc325...Qxe426.Bd4Qxf3+26...Qc627.Qxc6bxc628.Rxe8+Rxe829.Rb1also gives Black a very difficult defence.27.Kxf3b628.Rab1Rac829.Re4g629...h5seems logical, in order not to be stuck with a weak pawn on
a dark square, but then after30.Rb5g631.g4hxg4+32.hxg4he might have to deal with a rook penetrating via the
h-file at some point.29...f6might be
the best way to arrange the pawns, but even here, after an eventual g4-h5,
Black will have problems on both flanks.30.g4!Fixing the pawn on h6.Kf831.h4Rxe432.Kxe4Re8+33.Kd3Re634.Be3Kg735.Rb5Bd836.h5Rd6+37.Kc4Rc6+37...f5was suggested by Caruana as a
possible improvement after the game. I was intending to keep the pressure with38.f3when Black can exchange a
couple of pawns, but is still a long way from a draw.fxg439.fxg4gxh540.gxh5±38.Kd5Re639.Bd4+Kf840.f4With the
pawn coming to f5, I felt pretty sure that I was winning. White just gains
more and more ground, and eventually Black cannot hold on to everything.Bc741.f5Rd6+42.Ke4Rc643.Rb1Ke8
Allowing a more or less forced win, but the position was lost in any case.
43...g5closes the kingside, but now the king creates
havoc on the queenside, while Bg7 is always an issue.44.Kd5Rd6+45.Kc4Ke746.Kb5Kd747.Ka6Rc647...Kc648.Bxb6Rd849.Rb5Ra8+50.Ba7+-48.Kb7Rc449.Bg7!Bd649...Rxg450.Rd1+Bd651.Be550.Bxh6Rxg451.Bg7Rh452.Rd1Ke753.Kc6!Rc4+54.Kxb6Rxa455.Rh1and the h-pawn will cost Black a rook.43...gxh544.gxh5Rc445.Ra1Rc646.Rg1Rd646...Rc4allows White to finish in style:
47.Kd5Rxa448.Rg4!Ra149.Kc6Bh250.Bg7+Ke851.Re4+Kd852.Bf6+
and mate next.47.Be5!47.Rg7??Rxd4+47...Rc648.Bg7+Ke749.Bd4Kf850.Rg7and the rook penetrates with decisive effect.44.hxg6!Reducing the number
of pawns, but I had seen a more or less forced win.fxg645.Rh1Kf7?!45...gxf5+46.gxf5Bd8was certainly the most tenacious
defence, and the line I had spent the most time calculating:46...Rc447.Kd5Rxa448.Rxh6wins easily, despite the
limited material.47.f6!Bxf648.Rxh6Rxc3!Other moves lose rather trivially.49.Bxf649.Bxc3??Bxc350.Rxb6is a tablebase draw!
49...Ra349...Rc4+50.Kd5Rxa451.Ke6Re4+52.Be550.Rh7!50.Kd5Kf7=50...Rxa4+51.Kd5Ra252.Ke6Re2+53.Be5Rf254.Rb7Rd255.Rxb6and the tablebase shows a win in 23 moves. In fact,
the win is quite simple as soon as White captures the pawn, as was shown many
times, for instance in the recent game Grischuk-Kamsky from the Olympiad.46.Kd5Rd6+47.Kc4Caruana spent a lot of time on this move
and the next, but in vain.gxf547...g548.Kb5holds out longer,
but the winning plan is quite clear even here:Bd849.Ka6Rc650.Rh3!50.Kb7Rc7+is less
accurate.50...Rd650...Kg851.f6!51.Kb7Ke852.Rh1Kf753.Kc8with total zugzwang. Check for yourselves!48.gxf5Bd849.f6I played this
immediately, as I had double and triple-checked the lines so many times
already while he was thinking.Bxf649...Kg650.Rg1+Kf751.Rg7+Ke852.Rg6Kf753.Rxh6and there is
nothing Black can do.50.Rxh6Be750...Ke751.Bxf6+Rxf652.Rxf6Kxf653.Kb551.Rxd6Bxd652.Kb5Ke653.Bxb6Kd754.c4Kc855.Bxa5It only remains for White not to let Black sac
the bishop for the c-pawn. I (and a suspect quite a lot of other people) knew
the winning method from the famous game Fischer-Keres, Zurich 59.Kb756.Bb4Bf457.c5Ka758.c6Kb859.a5Ka760.a6Ka861.Bc5Bb862.Kc4Bc763.Kd5Bd864.Ke6Bc765.Kd7Ba566.Be7Black resigned, as Bd8 followed by c7 is coming up.1–0
T - denotes the time to solve the exercise. On the one hand, this can reflect the tested individual's superior problem-solving speed and can vary according to his/her cognitive style — reflective versus impulsive. On the other hand, the time to solve the task may simply be a function of the difficulty of the problem.
Possible questions:
How much was my solving time really worth?
Of course, the most known task is the one presented below — mate in only one move. If you do not know this problem, have fun!
On this DVD, Grandmaster and worldrenowned commentator Maurice Ashley reviews some of the most interesting patterns with examples meant to educate and entertain.
V - denotes the value of the solution, i.e. 1 or 0.
Possible questions:
How much is my solution worth?
Here, of course, a million examples can be given. Let's choose something mysterious:
12.0-0? is a famous mistake (Black has compensation for the pawn). Only 12.Be3! gives White a clear edge, for example after 12…Bxe3 13.Qa4+! Nd7 14.Qxb4 Bc5 15.Qe4+ Kf8 16.0-0 b5 17.Nc2.
This novelty was prepared by World Champion Anatoly Karpov and used against J. van der Wiel, Brussels 1986.
Our experts show, using the games of Botvinnik, how to employ specific openings successfully, which model strategies are present in specific structures, how to find tactical solutions and rules for how to bring endings to a successful conclusion
Mikhail Botvinnik said:
Capablanca didn't make separate moves — he was creating a chess picture. Nobody could compare with him in this.
This is a smart introduction to the so-called "chunking theory".
A chunk is defined as a familiar collection of more elementary units that have been inter-associated and stored in memory repeatedly and act as a coherent, integrated group when retrieved (Tulving & Craik, 2000; Tulving, E., & Craik, F. I. M. (2000). The Oxford handbook of memory. Oxford: Oxford University Press).
"Chunks" are seen as an important basis for building mastery in chess!
For years, chess players trained typical positions, having in mind not only the structure on the chessboard, but also possible actions. Example: White may see this characteristic structure as some kind of "chunk": Qc4, Nh6, Kh8, Wc8, p. g7, p. h7:
The final position can be seen as another "chunk", but without actions attached to it:
Chunk No. 2
Note that in our diagrams "chunk" sometimes means a pattern in which the pieces may be placed not exactly in the same position. In our example, the white queen may be placed on a2, b3, d5, e6 or f7. The idea is the same: checkmate after a sacrifice on g8.
Let us finish the idea of "chunking theory" with the famous "Loman's Motif":
Checkmate. That's the aim of the game. There are numerous ways to checkmate the enemy king, but there are common patterns that recur over and over again, and having these at our mental fingertips is essential for when we want to finish the game.
And finally, you will solve the last task within a few seconds, having incorporated "a chunk" in your mind:
Troicki 1899
White to play
I wish you a successful combination of the two ideas while training: the "Chunking Theory" and the Nine Indicators in calculations.
References
Chase, W. G., Simon, H. A. (1973). Perception in chess. Cognitive Psychology, 4, 55-81.
De Groot, A. D. (1965). Thought and Choice in Chess. The Hague, Paris: Mouton & Co.
De Groot, A. D. (1981). Thought and Choice in Chess: An Overview of a Study Based on Selzean Theory. W: N. Frijda, A.D. de Groot (red), Otto Selz: His Contribution to Psychology (192-255). Hague.
Kotov, A. (1971). Think like a grandmaster. London: Batsford.
Gobet, F. (2001). Chunk hierarchies and retrieval structures: Comments on Saariluoma and
Laine. Scandinavian Journal of Psychology, 2001, 42, 149-155.
Gobet, F., Clarkson, G. (2004). Chunks in expert memory: Evidence for the magical number four… or is it two? Memory, 2004, 12 (6), 732-747.
Przewoznik, J. (2003, 2011). Mysl - Dzialaj - Zwyciezaj! Psychologia szachów w praktyce. Gorzów Wielkopolski: Integracja.
Przewoznik, J., Soszynski, M. (2001). How to think in chess. Milford: Russell Enterprises, Inc.
Jan PrzewoźnikAn International Master from Poland who was the Polish Champion in 1979, and also a psychologist and lecturer at The West Pomeranian Business School in Szczecin. He has written 25 books on chess and psychology of chess, communication, creative problem solving, selling skills, professional customer service, adult education, and social economy.
This interactive video course of over 8 hours, provides an in-depth exploration of the Pirc Defence, a favoured opening for people looking to play for the win with the black pieces.
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The Pirc Defence Powerbook 2025 consists for a greater part of engine games (168 000), to which has been added high value material from Mega and the Correspondence Database (115 000).
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Whether it’s a weak pawn, a vulnerable king, or poor piece coordination, this course will teach you how to pinpoint the critical targets, prioritise your attack, and execute a clear, effective plan.
The Cozio Variation (1.e4 e5 2.Nf3 Nc6 3.Bb5 Nge7!?) is an underrated weapon that takes White out of well-known theory.
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