Nine Indicators to improve your chess (part 2)

by Jan Przewoźnik
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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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!

 
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1.c5+ dxc5 2.Rb4+ cxb4 3.Qd4+ Bxd4 4.Bxd4+ Kxc6 5.Bb7+ Kxb7 6.Nd8+ Kc8 7.Nc6+ Kd7 8.Ne5+ Kd6 9.Rd8+ Ke7 10.Nc6+ Kf7 11.Rd7+ Kg6 12.Ne7+ Kf7 13.Nd5+ Kg6 14.Nf4+ Kh6 15.Bg7+ Kh7 16.Bf6+ Bf7 17.Rxf7+ Kg8 18.Rg7+ Kf8 19.Ng6+ Ke8 20.Rg8+ Kd7 21.Ne5+ Kd6 22.Rd8+ Kc5 23.Be7+ Kb6 24.Rb8+ Ka5 25.Nc6+ Kxa4 26.Rxb4+ Ka3 27.Nd4 c5 28.Bxc5 Nb3+ 29.Rxb3+ Ka4 30.Rb4+ Ka3 31.Rc4#
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WhiteEloWBlackEloBResYearECOEventRnd
Patrick of Hall,H--1915

Indicator nn

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+.

But the fifth possibility, E, wins:

SHOW

It was necessary to see 35 half-moves ahead!

(Replay the rest in the game viewer below!)

 
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1.d4 Nf6 2.c4 e6 3.Nf3 c5 4.d5 b5 5.Bg5 Qa5+ 6.Qd2 Qxd2+ 7.Nfxd2 bxc4 8.Bxf6 gxf6 9.e4 Na6 10.Bxc4 Rb8 11.Nc3 Rxb2 12.0-0-0 Rb8 13.Nb5 Bb7 14.Nb3 f5 15.dxe6 fxe6 16.Nd6+ Bxd6 17.Rxd6 Nb4 18.exf5 Ke7 19.Rd2 Bxg2 20.Rg1 d5 21.Rxg2 dxc4 22.Nxc5 Rhc8 22...Rhd8 23.Rxd8 23.Rg7+ Kf6 24.Rxa7 Nd3+= 23...Nxa2+ 24.Kc2 Rxd8= 22...c3 23.Rd7+ 23.f6+ Kxf6 24.Ne4+ Kf5= 23...Kf6 24.Ne4+ Ke5= 22...exf5 23.Rg7+ 23.a3 Nd3+ 24.Nxd3 cxd3= 23...Kf6 24.Rxa7 Ra8= 22...Nd3+ 23.f6+ 23.Rd7+ Kf6 24.Ne4+ Ke5= 23...Kf7 24.Ne4 Nd3+ 25.Kd1 Rb1+ 26.Ke2 Nf4+ 27.Kf3 Nxg2 28.Rd7+ Kg6 29.Rg7+ Kh6 30.Rxg2 c3 31.f7 c2 32.Nf6 c1Q 33.Ng8+ Kh5 34.Nf6+ Kh4 35.Rg4+ Kh3 36.Rg3+ Kxh2 37.Ng4+ Kh1 38.Rh3+ Kg1 39.Ne3 Qc6+ 0–1
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Lukov,V2440Przewoznik,J23400–11980E10Naleczow

Indicator Pmax

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…

 
Ajanen 1943
White to move and win

Solution:

SHOW

Here are the main variations (replay in the game viewer below!):

 
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1.Qc4+ Qb4 2.Qc6+ Qb5 3.Qxe4+ Qb4 4.Qd3 g6 4...g5 5.Qd7+ Qb5 6.Qd4+ Qb4 7.Qd3 5.Qd7+ Qb5 6.Qd4+ Qb4 7.Qd3 g5 8.Qd7+ Qb5 9.Qd4+ Qb4 10.Qd3 g4 11.Qd7+ Qb5 12.Qxg4+ Qb4 13.Qd7+ Qb5 14.Qd4+ Qb4 15.Qd3
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Ajanen--1943

Indicator Pser

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 

 
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.

Solution:

SHOW

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The complete game with Carlsen's annotations:

 
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1.e4 e6 2.d3 The 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. d5 3.Nd2 Nf6 4.Ngf3 Nc6 A perfectly reasonable way of avoiding the "fearsome" King's Indian Attack, starting with 4...c5 5.g3 and so on. 5.c3 Bd6 Looks 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.Be2 It 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. 0-0 7.0-0 7.b4 here or on the previous move, could have been well met with dxe4 8.dxe4 a5 9.b5 Ne5 and White has gained some space, but also weakened some squares, so Black should be doing fine. 7...a5 Black had several choices here: 7...e5 would be met by 8.b4 and White obviously has an excellent version of the Philidor. Whether that would be sufficient for an advantage though, is quite unclear. 7...b6 8.Re1 Bb7 9.Bf1 seems a little artificial for Black. 7...Re8 8.Re1 a5 9.Bf1 e5 10.exd5 Nxd5 11.Nc4 would transpose to the game. 8.Re1 e5 9.exd5 Other Philidor-style moves like Bf1 or b3 were certainly possible, but I felt like forcing things a bit. Nxd5 10.Nc4 Re8 11.Bf1 Bg4 12.h3 12.g3 is not as accurate, as Black can play Qd7 when 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...Bh5 13.g3 Once the e4-pawn is not there to obstruct it, the bishop is re-deployed to the long diagonal. Going on a fishing expedition with 13.g4 Bg6 14.Qb3 as 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...Nb6 A 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.Nxb6 cxb6 15.Bg2 b5? This one however, is rather questionable, as will become apparent after a few more moves. 15...a4 would have retained equal chances. 16.a4! Favourably fixing the black queenside pawns on dark squares. b4 16...bxa4 17.Qxa4 also gives Black plenty to worry about. 17.Be3 Bc7 18.Qb3 Now 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.Rad1 Qa6 19...Qe4 20.Nh4 Bxd1 21.Rxd1 20.g4 Bg6 21.Bf1 and the queen is trapped. 18...Bxf3 19.Bxf3 Qxd3 is possible, but even here Black has a very unpleasant position after 20.Rad1 Qf5 21.Bg4 Qg6 22.Rd7 Rac8 23.Be2! with the threat of Rxf7. 19.Qc4 According to a Russian GM, this was the move of a 2nd category (1600) player. He instead recommended 19.Nh4 which looks very attractive, as Qxd3 19...Qc8 however, bothered me a little, as after 20.g4 Qd8! 21.Nf5 Bg6 it is not entirely clear what White has achieved. 20.Rad1 Bxd1 21.Rxd1 Qh7 22.Rd7 Re7 23.Bxc6 wins. 19...bxc3 20.bxc3 e4 Otherwise, the pressure on the queenside would quickly have become unbearable. 21.dxe4 I played this and the next few moves quickly, as I couldn't wait to get to torture him in the endgame. 21.Nd4 would have been even stronger. I would have probably have considered it had I noticed that after Ne5 22.Qb5 Nxd3 The bishop is actually hanging: 23.Qxh5 21...Bxf3 22.Bxf3 Ne5 23.Qe2 Nxf3+ 24.Qxf3 Qd3 The 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 than 25.Rab1 Qxe4 26.Qxe4 Rxe4 27.Rxb7 Be5 when Black is pretty close to a draw, e.g. 28.Bd2 Rxe1+ 29.Bxe1 Rc8 30.Rb5 Bxc3 31.Bxc3 Rxc3 25...Qxe4 26.Bd4 Qxf3+ 26...Qc6 27.Qxc6 bxc6 28.Rxe8+ Rxe8 29.Rb1 also gives Black a very difficult defence. 27.Kxf3 b6 28.Rab1 Rac8 29.Re4 g6 29...h5 seems logical, in order not to be stuck with a weak pawn on a dark square, but then after 30.Rb5 g6 31.g4 hxg4+ 32.hxg4 he might have to deal with a rook penetrating via the h-file at some point. 29...f6 might 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. Kf8 31.h4 Rxe4 32.Kxe4 Re8+ 33.Kd3 Re6 34.Be3 Kg7 35.Rb5 Bd8 36.h5 Rd6+ 37.Kc4 Rc6+ 37...f5 was suggested by Caruana as a possible improvement after the game. I was intending to keep the pressure with 38.f3 when Black can exchange a couple of pawns, but is still a long way from a draw. fxg4 39.fxg4 gxh5 40.gxh5± 38.Kd5 Re6 39.Bd4+ Kf8 40.f4 With 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. Bc7 41.f5 Rd6+ 42.Ke4 Rc6 43.Rb1 Ke8 Allowing a more or less forced win, but the position was lost in any case. 43...g5 closes the kingside, but now the king creates havoc on the queenside, while Bg7 is always an issue. 44.Kd5 Rd6+ 45.Kc4 Ke7 46.Kb5 Kd7 47.Ka6 Rc6 47...Kc6 48.Bxb6 Rd8 49.Rb5 Ra8+ 50.Ba7+- 48.Kb7 Rc4 49.Bg7! Bd6 49...Rxg4 50.Rd1+ Bd6 51.Be5 50.Bxh6 Rxg4 51.Bg7 Rh4 52.Rd1 Ke7 53.Kc6! Rc4+ 54.Kxb6 Rxa4 55.Rh1 and the h-pawn will cost Black a rook. 43...gxh5 44.gxh5 Rc4 45.Ra1 Rc6 46.Rg1 Rd6 46...Rc4 allows White to finish in style: 47.Kd5 Rxa4 48.Rg4! Ra1 49.Kc6 Bh2 50.Bg7+ Ke8 51.Re4+ Kd8 52.Bf6+ and mate next. 47.Be5! 47.Rg7?? Rxd4+ 47...Rc6 48.Bg7+ Ke7 49.Bd4 Kf8 50.Rg7 and the rook penetrates with decisive effect. 44.hxg6! Reducing the number of pawns, but I had seen a more or less forced win. fxg6 45.Rh1 Kf7?! 45...gxf5+ 46.gxf5 Bd8 was certainly the most tenacious defence, and the line I had spent the most time calculating: 46...Rc4 47.Kd5 Rxa4 48.Rxh6 wins easily, despite the limited material. 47.f6! Bxf6 48.Rxh6 Rxc3! Other moves lose rather trivially. 49.Bxf6 49.Bxc3?? Bxc3 50.Rxb6 is a tablebase draw! 49...Ra3 49...Rc4+ 50.Kd5 Rxa4 51.Ke6 Re4+ 52.Be5 50.Rh7! 50.Kd5 Kf7= 50...Rxa4+ 51.Kd5 Ra2 52.Ke6 Re2+ 53.Be5 Rf2 54.Rb7 Rd2 55.Rxb6 and 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.Kd5 Rd6+ 47.Kc4 Caruana spent a lot of time on this move and the next, but in vain. gxf5 47...g5 48.Kb5 holds out longer, but the winning plan is quite clear even here: Bd8 49.Ka6 Rc6 50.Rh3! 50.Kb7 Rc7+ is less accurate. 50...Rd6 50...Kg8 51.f6! 51.Kb7 Ke8 52.Rh1 Kf7 53.Kc8 with total zugzwang. Check for yourselves! 48.gxf5 Bd8 49.f6 I played this immediately, as I had double and triple-checked the lines so many times already while he was thinking. Bxf6 49...Kg6 50.Rg1+ Kf7 51.Rg7+ Ke8 52.Rg6 Kf7 53.Rxh6 and there is nothing Black can do. 50.Rxh6 Be7 50...Ke7 51.Bxf6+ Rxf6 52.Rxf6 Kxf6 53.Kb5 51.Rxd6 Bxd6 52.Kb5 Ke6 53.Bxb6 Kd7 54.c4 Kc8 55.Bxa5 It 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. Kb7 56.Bb4 Bf4 57.c5 Ka7 58.c6 Kb8 59.a5 Ka7 60.a6 Ka8 61.Bc5 Bb8 62.Kc4 Bc7 63.Kd5 Bd8 64.Ke6 Bc7 65.Kd7 Ba5 66.Be7 Black resigned, as Bd8 followed by c7 is coming up. 1–0
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Carlsen,M2843Caruana,F27731–02012C00Grand Slam Final 5th6

Indicator T

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!

 
L. Kubbel
White to move and mate in one

Solution:

SHOW

How long did it take you to get the solution?

 
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1.d8Q is played very often by subjects. :) 1.Qa3# 1.dxc8Q+ 1.Qxe5+ 1.Nf5+ 1.Nc6+ 1.Bd6+ 1.Bh4+ 1.Ng6+ 1.Rxe5+ 1.Qg5+ 1.Qd6+ 1.Qc5+ 1.Qb4+ 1–0
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L. Kubbel - Mate in One--1–0

Indicator V

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:

 
Karpov – Kasparov, Moscow 1985
White to move

Are you sure your solution is correct?

Solution:

SHOW

This novelty was prepared by World Champion Anatoly Karpov and used against J. van der Wiel, Brussels 1986.

 
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1.e4 c5 2.Nf3 e6 3.d4 cxd4 4.Nxd4 Nc6 5.Nb5 d6 6.c4 Nf6 7.N1c3 a6 8.Na3 d5 9.cxd5 exd5 10.exd5 Nb4 11.Be2 Bc5 12.0-0 0-0 13.Bf3 Bf5 14.Bg5 Re8 15.Qd2 b5 16.Rad1 Nd3 17.Nab1 h6 18.Bh4 b4 19.Na4 Bd6 20.Bg3 Rc8 21.b3 g5 22.Bxd6 Qxd6 23.g3 Nd7 24.Bg2 Qf6 25.a3 a5 26.axb4 axb4 27.Qa2 Bg6 28.d6 g4 29.Qd2 Kg7 30.f3 Qxd6 31.fxg4 Qd4+ 32.Kh1 Nf6 33.Rf4 Ne4 34.Qxd3 Nf2+ 35.Rxf2 Bxd3 36.Rfd2 Qe3 37.Rxd3 Rc1 38.Nb2 Qf2 39.Nd2 Rxd1+ 40.Nxd1 Re1+ 0–1
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Karpov,A2720Kasparov,G27000–11985World-ch31-KK2 Kasparov-Karpov +5-3=1616

Karpov and Kasparov in 1988 | Photo: Rob Bogaerts / Anefo [Public Domain] via Wikimedia Commons

And do not choose your wife or husband with this method, please. Follow your heart.

The indicators described above (M, N, A, Dmax, nn, Pmax, Pser, T, V) are summarised in Fig. 15.

Click or tap to expand

Chunking Theory

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:

 
Chunk No. 1

Solution:

SHOW

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":

 
Lasker vs Loman, USA simul, 1903
What should white play after 1…Rc3?

Solution:

SHOW
 
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1...Rc3+ 2.Kf2 2.Kg4? Rc4+ 3.Kg5 Rh4! 4.Kxh4 g5+ 5.Kxg5 Kg7-+ 2...Rc2+ 3.Ke1 Rc1+ 3...Rxg2 4.h8Q+ 3...Rxg2 4.h8Q+ 4.Kd2 1–0
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Lasker,E-Loman-1–01910Londyn - symultana

Having in mind this idea we are able to solve the next task very quickly:

 
Alekhine – Szyszko, Moscow 1919
Black to play

Solution:

SHOW

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.


 
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1.Rxf5 Kxf5 2.g4+ Kf4 2...Ke5 3.Kg2 Kd5 4.Kxf2 Kc5 5.Kf3 Kb5 6.Kf4 Kxa5 7.Kf5 Kb6 8.Kxf6 3.Kg2 Ke3 4.Kf1 1–0
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Alekhine,A-Szyszko-1–01919Moscow

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.
  • Ross, Ph. (2006). The Expert Mind. In: What Makes a Genius.
  • Saariluoma, P. (2001). Chess and content-oriented psychology of thinking. Psichologica, 22, 143-164.
  • Zlotnik, B. (ed., 1990). Shakhmaty. Nauka, opyt, masterstvo. Moscow: Vysshaia Shkola.

An 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.

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