The Method of Calculation
If you landed on this page, most probably Google has brought you here. Alternatively, you could access my article here: http://jose-franco-de-arevalo.quazen.com/games/board-games/the-method-of-chess-calculation/
What follows is a brief definition of what calculation is based on hours of trial-and-error and concrete experience in trying to effectively calculate in chess, followed by a simple exercise on how to acquire and develop chess calculation skills. I have gathered (from my two years and counting of chess learning) what I have understood/realized about the elusive process of calculation (at least for beginners) and developed a training method that has vastly improved my ability to calculate.
What Chess Calculation is:
The first ones are on the method itself, while the ones with footnotes are my general learnings on calculation:
1. Calculation is, at least, both a spatial and a visual task. It involves mental projections of the senses. (More on this in the Training Program).
2. Calculation is an automatic process, which can be developed through the right training methods. A useful exercise is included at the end of this post.
3. The quality of calculation improves when more of the senses are involved in it; it is useful not only to "see" but also to "feel" the pieces and their relative locations on the board with your mind (you could even try smelling, tasting and hearing the pieces if you like, though these are not really necessary).
4. The trick in calculation is not in the depth but in the evaluation of the position at the end of it.*
5. Calculation and positional understanding go together; they are two faces of the same coin. Understand the position, determine a goal, and then calculate along that purpose.**
6. There's a reason why grandmasters (an other masters), like Kasparov and Karpov, mention "concrete variations." Calculation is a real process involving real possibilities. ***
7. Calculation is an inevitable part of learning chess, and it starts by considering the possible replies of your opponent. ****
8. Calculation is a skill, and like all skills it can be acquired and developed. *****
* - There is no limit to the depth the human mind can calculate. I have performed and completed books on chess calculation to a depth of 39 ply, but it has not significantly improved my chess. One must be able to evaluate the position at the end of the calculation in order to benefit from the calculation itself.
** - Efficiency in calculation increases with increasing positional understanding. Many unnecessary lines can be weeded out based on your understanding of the position. The best example is the weeding out of 1. h4 or 1. a4, since the starting position calls for active play (play in the center and immediate activation of the pieces). Positional understanding is simply a SWOT (Strengths, Weaknesses, Opportunities and Threats) Analysis of the elements of the position, which are nonetheless the pieces (and pawns) and squares: Which squares are strong? Which of my pieces are active? What opportunities do my active pieces give? What opportunities can I give to my inactive pieces? What are the weaknesses in my position? Are there threats against my weaknesses? What threats can I impose on the weaknesses of my opponent's position? etc.
*** - It is not enough, for example, to have a vague idea on how the position would evolve, such as "After going there, he might go there, then somehow I would be able to get my pieces here and there..." NO. 1.d4 d5 2. c4 e6 3. Nc3 Bb4 4. Qc2.
**** - In reading books on chess theory, it is a MUST to understand why all of the moves are made to increase one's positional understanding and, in effect, reduce the amount of calculation needed. One MUST set the pieces up on a board and follow the chess notations one at a time. Most beginners don't benefit from reading texts on chess simply because these MUSTs are missed.
***** - While it is true that there are those who are born with talents inclined to performing well in chess, but it is a myth that those skills in chess are limited to those who are "born" with them. Remember Susan Polgar, Garry Kasparov, and even Mir Sultan Khan (dubbed the most naturally talented chess player of all time despite being illiterate)? The fact that someone who can't read chess notations acheived GM norm means that the abilities that GMs have are not exclusive to GMs - it all depends on the training method, and of course one's dedication. This is possibly the reason why GMs are elusive when it comes to their method of calculation.
Training Method for Chess Calculation
1. a set of chess diagrams
2. a chess set, preferrable with a board larger than 10"x10"
1. Depending on your level, select any chess diagram. For beginners, I recommend the simple King vs King and pawn endings, i.e. Black king on e8, White King on e6 and White pawn on f6. Of course, you could choose more complicated positions, but it is important to start with diagrams which you can handle first; you won't want to overload yourself where you'll most likely make no improvements at all, or you might even get worse.
2. Set the pieces up on the board and just be familiar with the position (this is a MUST, for it would be easier for the mind to see something once something like it has been already seen before). Take in as much sensory information as you can: see the colors on the pieces; observe how the light reflects on them; notice the colors of the squares they are on; feel the textures of the pieces; how many pieces can your hand cover as they stand on the board? (yes, sensory information, but it would not be advisable to taste your chess pieces...).
3. Move the pieces as though you were analyzing position, i.e. alternately moving White then Black using legal moves, until you reach a satisfying conclusion. In the King vs King and pawn example above, it would not take more than three ply to know which side is winning depending on whose turn it is. Again, take note of the sensory information: what does it feel like to move the pieces from one square to another? what sounds do they make? How heavy are they? (Again, it is not advisable to taste your chess pieces... though by all means you can.)
Building steps: (here's where the real training begins)
4. Reset the pieces to their initial position based on the diagram. Observe their relationships and how they interact. Take a final Gestalt look, and then clear the board.
5. With the board empty, recreate the sensory information you have mentally taken note of earlier. Relax, and just allow yourself to recall the sensory details (it is important not to exert too much effort, so as not to give yourself a headache): mentally see the color of the pieces; mentally see the reflections; mentally feel the textures; where were the pieces on the board? (If you actually tasted the pieces, mentally recreate the taste.) After three or more attempts, you would begin to clearly see (at the back of your mind) the image of the pieces as if you were looking at them on the empty chess board. If it takes you more than 10 (or even 20!) attempts, there's no problem with that; in the end, you would be able to say that you worked hard for this chess skill.
6. Once the image is clear enough at the back of your mind (and only when this happens), begin mentally analysing the position by mentally making the moves. Again, recreate the sensory information - this is important. The more senses you involve, the more connections your brain will form, making the task of calculation easier.
7. At the end of the calculations/variations, check the validity of the moves you've mentally made by setting the pieces up moving them about the lines you've calculated. Again, this step is important, for it is here where the mind would realize where it went wrong and therefore make the necessary adjustments to improve your calculation.
In step 6, it is completely normal to lose track of the mental image you're working with. Don't worry. Just relax and return to the clearest position you've made (remember Kotov's suggestions?). If you're really lost, just return to the initial position and start over... but do NOT get frustrated; we chess players, you know, are generally calm and composed, so just relax and re-do the steps.
Repeat steps 1 - 7 for the other diagrams. Naturally, you would have moved from simple ones which are straightforward and have less depth, to more complicated diagrams with more variations to consider and more depth. A good source for chess positions is GM-RAM by Ziatdinov, but it is rather difficult to find. Any other book, especially those that contain endings, typical middle game positions and some discussions on common openings, would be enough. Soon, you would have graduated from the endgame, to the complicated middle game and then finally to the theoretical openings.
And you're done! Good luck, and see you at the top of your chess career!