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What is Calculation?

In his generally thought provoking, deeply intelligent and beautifully human book Think First, Move Later Willy Hendriks talks about various concepts. One is calculation, another is combinational vision and a third is seeing. But when reading the book I did not get the impression that the author had a clear definition of all of those; especially calculation.

In order to have a meaningful conversation, it is good to know if you mean the same things with the words you use. We can all think of words that have two opposite meanings, with my personal favourite being the word original, which prior to around 1750 meant “as it was in ancient Greece” or something to that effect; a permanent truth. After this of course it has meant “not seen before”, which is the way we use it today.

When discussing things or explaining complex points, it is good to agree that a cat purrs rather than barks. I have often made the mistake of believing that people would understand what I meant, when I used common terminology, only to find that this was not the case. A recent example was a review where my book Positional Play apparently did not deal with dynamics. As one of my three questions is: which is the worst placed piece, I found this confusing, but rereading it today, I see that the reviewer is a bit all over the place:

Adams-Giorgadze 29.h4!

Taken from Adams-Giorgadze, Groningen 1997. The correct move is 29.h4! to put further pressure on the hook (a type of weakness) on g6. The reviewer insists that the tactical point that 29…Bxh4 is refuted by Bxg6 and Qh6 (in either order) is dynamics. Something very similar in Hendriks book is called calculation.

Let me give my own definition of some of these words (which others are by no means forced to follow!). Hopefully they will be meaningful and helpful to those reading this blog.

Dynamics: The immediate aggressive potential of the pieces. e.g. a dynamic advantage means your pieces are ready to do harm, while the opponent is uncoordinated.

Tactics: Operations based on very concrete variations.

Combinational vision: The ability to spot well-known tactical patterns.

Seeing: To me this includes something like why 29…Bxh4 does not work. It is definitely because of a tactic. But what it is not (for me) is:

Calculation: Forcing yourself to look for moves/variations either a) beyond your natural horizon or b) outside of your intuitive spectrum.

Obviously, the last two are subjective. What a GM sees, others will have to grind their way through with gritted teeth (calculation). When you work on your calculation, you will automatically improve your ability to see. You are slowly (very slowly) pushing your horizon away from you.

Sorry if this post is a bit technical, but it will all make sense when I discuss Hendriks book a bit more intimately next week, specifically Chapter 14, in case you want to read it in advance.

(A final note on the review: To make some sort of point, the reviewer puts the black king on g7 in a comparative diagram, to make a point I don’t fully understand. Obviously chess is not an entirely static game; the pieces move! But at the same time, chess is also a static game, so those armed with poor understanding and a computer will struggle to understand quite a lot.)

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  1. Patrick
    April 22nd, 2013 at 16:08 | #1

    Jacob,

    Maybe I’m just confused. Your definitions of “Tactics” and “Calculation” appear to be 2 different statements saying the same thing, like six of one or half a dozen of the other, or the glass being half empty or half full.

    Maybe a concrete example can clarify this. I had a recent miniature on Saturday against an 1850 player, playing White in the following line: 1.d4 Nf6 2.c4 e6 3.Nc3 d5 4.Bg5 Be7 5.e3 h6 6.Bxf6 Bxf6 7.Nf3 O-O 8.Qc2 b6 9.O-O-O Bb7 10.cxd5 exd5 11.g4 c5 12.h4 g6 13.g5 hxg5.

    Ok, so now the “obvious” move is 14.hxg5, sacrificing the pawn and dragging the Bishop away from g7/h8. The “natural horizon” or “intuitive” move.

    I, on the other hand, first looked for, then observed, and actually played, a different move, 14.h5, going for g6 instead, seeing that taking h5 is losing, and advancing g4 doesn’t work as 14…g4 15.hxg6 gxf3?? 16.g7 loses on the spot (in the actual game, he went for the other Knight in the same manner, and the game ended abruptly after 14…cxd4 15.hxg6 dxc3 16.g7 1-0). However, other variations I determined were also better for White, the best 2 for Black being A) 14…Bg7 15.hxg6 fxg6 16.Ne4 and taking on g6 as 16…Bxe5 loses to 17.Qxg6+ Bg7 18.Bd3 Rf5 19.Rh8+ Kxh8 20.Bxf5 Kg8 21.Be6+ Kh8 22.Rh1+ Bh6 23.Rxh6#, or B) 14…Nc6 15.hxg6 Nb4 16.gxf7+ Rxf7 17.Qg6+ Rg7 18.Qh6 and White has got to be better here.

    So what is all of this? Calculation? Or just mere Tactics? Is it possible that there is no “clear definition” of Calcuation?

    In the Mid-90s, Andrew Soltis in his book “The Inner Game of Chess” said that “Chess isn’t 99% Tactics, it’s 99% Calculation”, so he sees the two as different entities.

  2. April 22nd, 2013 at 18:12 | #2

    Jacob, the title of the book is different from what you write!

  3. Phille
    April 22nd, 2013 at 18:33 | #3

    I understand it like this: Of course you often have to use “Calculation” to work out a the necessary “Tactics”. But sometimes, when the tactic is short or standard and/or your “Combinational Vision” is well developed, you just “See” it.
    So “Calculation” is one possible mode of making out the “Tactics”, but not the only one.

    Alas, I think that many players think only of combinations when they talk about “Tactics”. That’s probably a more likely source of misunderstanding.

    Another possible misunderstanding: For me being good at “Dynamics” means accurate assessment of violent positions, so it’s a kind of positional understanding and relatively separate from “Tactics”, “Calculation” and all that.

  4. Borwas
    April 23rd, 2013 at 00:01 | #4

    I recently read a book by Dan Heisman which is a significantly expanded version of what I think was his first serious written work on Chess, so the original text refers to what was considered positional theory in the mid seventies.
    In this book the author does a very nice job in defining what are pure chess elements for positional evaluation: things such as mobility, speed, flexibility, vulnerability, coordination. Those definitions of pure elements are then used to clarify and define the compostite nature of chess concepts like development, potential, strenght/weakness, etc. relatively to chess pieces in a given position and to pawn formations as in the traditionally (mid 70s) considerd weak doubled pawns, isolated pawn. And so on: you get the idea.
    That book is done with an approach which shows the mathematical background of the author, when definitions are really “definitions”, and I found it quite interesting: it brings a clarity which is very often missing in chess literature.

    Just to say: being technical and rigorous with chess terminology is necessary, if you want to be understood, and I’m sure not to be the only reader which welcomes precision and clarity in these matters, even sometimes at the cost of a little bit of repeatability.

    p.s.
    Re-reading what I just wrote, it came to mind that my comment might seem a bit of a commercial for the book I use as an example. (Or maybe it has the opposite effect?!).
    I just spoke about it in order to explain what I meant in welcoming the technical clarifications, but if you feel like not publishing this message of mine, I understand perfectly and I don’t feel at all offended (lol):
    I’m NOT going to start trolling your website with censorship complains!

  5. Borwas
    April 23rd, 2013 at 00:46 | #5

    BTW, as an additional interpretation, so that you guys can make a poll of it and give percentages.

    If some removal of the guard is a “tactic” present in a position (i.e. the actual application at the board of a tactical motive), then the thought process when you visualize the moves you play in order to remove the guard and win material is “calculation”.

    So, step by step:
    (1) you “see” that a piece is weakly protected in a given position, hinting at some prerequisites to try removing its guard and winning material,
    (2) then you “calculate” the actual moves, and, if your calculations confirm the effectiveness of the tactic you saw the prerequisites of,
    (3) you finally play those moves realizing a little “combination”, which works thanks to the “tactical motive” of guard removal.

  6. Jacob Aagaard
    April 23rd, 2013 at 10:02 | #6

    @Erik
    Yes. We were debating whether or not anyone would spot it; and if so, would they get the joke as well :-).

  7. Jacob Aagaard
    April 23rd, 2013 at 10:25 | #7

    @Patrick
    Let me try to describe it differently then.

    Tactics and dynamics are on the board. Calculation is a process in your head.

    Unlike combinational vision, calculation is a lead process that has to be “forced” in some way. Your vision just “sees” the options. Calculation is a (more or less) systematic process extending the variations you see without effort.

    Vizualisation is seeing the pieces move around in your head.

    All of this is important, because when I or others talk about “before calculation”, we do not talk about before moves, but before this deliberate and focuses process, which unlike the others is highly conscious.

  8. Jacob Aagaard
    April 23rd, 2013 at 10:27 | #8

    @Borwas
    Dan is a nice guy and a serious person and as we are not talking about the latest Everyman book on 1.g3, you are not in trouble :-).

  9. Jacob Aagaard
    April 23rd, 2013 at 10:28 | #9

    @Phille
    This is indeed another decent way of expressing it. Obviously it is always a fluid area, as we are discussing what is happening in our heads; and for sure the same is not happening in all heads!

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