Ngo Khyu Bien, postgraduate
E.P. Linovitsky, associate professor, Ph.D., master of sports in chess
Russian state university of physical culture, sport, youth and tourism, Moscow

Key words: variants calculation, tight time, choice of candidate moves, working memory.

Introduction. A chess player learnt what variants are and how to calculate them at the beginning of mastering chess. Elite chess player (grandmaster, master) calculates the most complicated variants, actually consisting of simple moves (general considerations). A chess player needs special methodicalness and thoroughness to learn complex opening systems or typical - theoretical positions. This process can not fully correspond to the primary principle of didactics that is common in the best chess books - learning by induction. Here training differs from learning according to a book, which is now only a guide. Analyzing the Spanish match, for example, single versions of which were studied until the 26th move, we are facing the need of considering not only the clarity, accessibility for a chess player of some particular continuation but also the fundamental assessment of the overall strategy of the debut as a whole. The variants can be much more difficult to calculate on the 10th move than on the 20th move, when the crisis of the struggle has already passed. The same applies to certain theoretical principles of middle game and end game, which in the course of training should be considered more deeply than in the learning environment, where homework and desk review can help.

Materials and methods. The study involved questionnaire, expert poll, chess test, educational experiment and educational observation of over ten World Cup chess tournaments, European and Russian championships, held in 2013 with elite chess players.

Results and discussion. The studies performed at the Department of Theory and Methods of Chess during 2011-2013 have revealed that the main qualities that contribute to improving the analytical criteria for training of chess players are: variants calculation, combinational vision, positional sense, heuristic thinking, sense of danger, sense of dynamics, sense of time, ability to play rapid chess and blitz. We have analyzed more than a hundred of games played by elite chess players. In this paper, we present as an example the analysis of a very important event, the World Cup in 2013 among men (Tab. 1), and the results are shown only from the 1/8th of the final. The highest success rate belongs to the winner of this competition, an ex-world champion, Vladimir Kramnik (Russia) – 0,69.

Table 1. Chess World Cup 2013 among men

It should be noted that all world's strongest grandmasters except for the world champion V. Anand, challenger for this title M. Karlsen and several other GMs were among 128 participants of this compositionally strong competition.

In the game of chess it is important to choose the correct (and, therefore, the strongest) move. The skill to quickly and accurately count variants is one of the most important chess skills. A chess variant - is a series of logically related moves. Depending on responses of the opponent the variant may have different variations. Quick calculation of variants, the ability to foresee all the possible variations are the important qualities of chess players. While starting the calculation of variants, we must first of all mentally list and accurately fix all the possible moves in this position in order not to miss any important opportunity to continue the game.     

Having fixed at the start all the possible candidate moves, we will avoid serious mistakes. By identifying and listing them, we shall then start calculating options one by one. The order in what to arrange candidate moves, and, therefore, calculate the options, depends on the character and the habits of each player and the peculiarities of their position. One chess player appeals to firstly analyze the most difficult possibilities and only then check the easiest options, another does the reverse. The value of calculating variants especially increases at the advantage implementation stage. When it is time to implement the achieved advantages it becomes impossible to avoid specific calculations.

In the area of improving the methods of variants calculation the methodical recommendations of famous Soviet grandmaster A.A. Kotov are of great interest. His remarkable chess works "The secrets of chess player thinking" and "How to become a grandmaster" are invaluable for the present and future of modern chess players. He introduced the term "the tree of valuations" in which options and sub-options are presented in the form of "branches and twigs". "Starting the calculation of variants - points Kotov - one should mentally count and accurately fix all the possible in this position candidate moves". This approach to the calculation of variants should greatly discipline the player’s mindset, keeping him from the irrational usage of time. Further development of the technique of picking moves and calculation of possible variants can be seen in the works of M.I. Dvoretsky (such books as: "School of future champions" 1984. "Secrets of the debut of preparation" 1998. "Technique in a chess game," 1998 ", etc.) and A. Soltis. An important indicator of the method of variants calculation is its efficiency. In order to train it, as noted in his writings by M.I. Dvoretsky it is important to use methods of comparison, exception and logical evaluation.

Another good method is playing chess games rich in variants calculation, but if a chess player trains alone, it is not easy to choose the right material. Of course, positions on the subject can be found in various literature. But there are not many of them and not all of them are good enough. Here the training program of M.I. Dvoretsky may come in handy. To train variants calculation it is also useful to play blindly, read books and analyze positions without a board. It is important to study games and comments of chess players who have distant and accurate variants calculation abilities such as M. Botvinnik, R. Nezhmetdinov, P. Keres, G. Kasparov, A. Karpov, V. Anand, A. Shirov, V. Kramnik, et al.

Somewhat later, after A.A. Kotov it was theoretician V.I. Dydyshko who researched the technique of variants calculation (in his book "Logic of modern chess"). By the way, he also has a high-rank chess title of international chess master. The graphic image that was first suggested by A.A. Kotov and then prolonged by V.I. Dydyshko, helps to understand the complexity of the position, to visualize concealed possibilities. Surely, during a game a chess player does not, and moreover has no right to take any sketches, but in the process of studying the chess theory (during the training process) for better understanding of the methods of calculation the chart provides significant assistance.

There are three types of various situations of calculation and their respective trees in chess. A complex calculation with an abundance of long and confusing options is called "thicket". On the other hand, only one variant calculation is drawn in a straight line, and the tree itself is called "column". Finally, the third type of calculation, and thus the third type of the tree of calculation - "bush" is where the variants are short - only one or two moves, but there are many of such variants.

The main rule of the variants calculation is that a chess player should develop the habit during a tournament game of running through the branches only once. No repeats should be allowed during the calculation of variants, because it is rather time-consuming and, ultimately, and inevitably leads to a time trouble.

It is not easy to inure oneself not to rush through the variant branches, mentally running through all of them just once. However, that is necessary to learn. We'll talk more about calculation training methods later. As for now we shall repeat it once again: in any case do not go back to the variant once already considered! Believe in yourself. Only in some individual cases in particularly difficult positions a GM will sometimes check again the chosen variant. But as a rule, he doesn’t flounce around the calculation tree. There are very useful recommendations for players of any level by B.M. Blumenfeld. Often, a player, having performed a complex calculation, does not notice that there are elementary possibilities already on the 1st move. He penetrated into the depths of the position, checked the possible moves of the opponent and his responses on the 7th or 10th moves, but did not notice what could happen on the 1st move. To avoid such gross mistakes B.M. Blumenfeld recommended: «…Having finished the calculation of complex variants, write your selected move on the tournament form, then for a moment take a look at the position with the eyes of a beginner. Are you about to get checkmate in one move? Are you going to lose your queen? bishop? knight? pawn? Just after making sure that there is no inevitable catastrophe, move the figure”.

Conclusion. Without detracting the methodological value of the above-stated recommendations for training the discipline of variant calculation, it is to be marked that the real thinking process of a chess player, as marked by, for example, M.M. Botvinnik and N.V. Krogius, and as confirmed by the results of the experiments carried out by B.A. Zlotnikov, V.B. Malkin, N.G. Alekseev et al. on the chess department of SCOLIPhC, does not fully fit the system of calculation of variants, suggested by A.A. Kotov, namely:

1. It is extremely hard to trace all candidate moves in complex positions immediately when starting thinking and in fact they arise in the course of deep analysis and evaluation of positions.

2. Right move - a nuance in the calculation of one variant frequently arises when calculating another one, so repeated calculation of variants is inevitable in difficult situations.

3. Efficiency of calculation is a rather important indicator of its technique. As stated by M.I. Dvoretsky, it can be trained using the methods of comparison, exclusion and logical assessment.

References

1. Grabuzov, S.G. Improving chess skill / S.G. Grabuzov, V.V. Artamonov, E.P. Linovitskiy. – Moscow: Voenizdat 4th branch, 2002. (In Russian)
2. Dvoretsky, M.I. School of Chess Excellence. Combination game / M.I. Dvoretsky. - Kharkiv, Fakt, 2002. (In Russian)
3. Kobaliya, M.R. Chess and Psychology / M.R. Kobalia, E.P. Linovitskiy // Sportivny psikholog. – 2004. – № 2. (In Russian)
4. Kotov, A.A. How to become a GM / A.A. Kotov. – Moscow: Fizkultura i sport, 1985. (In Russian)
5. Krogius, N.V. Psychology of chess creativity / N.V. Krogius. – Moscow: Fizkultura i sport, 1981. (In Russian)
6. Soltis, A. The inner game of chess. – D.M. Company, 1994.

The paper is devoted to the influence of calculations of variants as a major analytical function on decision-making by choosing a move in a chess game by elite players.

Corresponding author: fizkult@teoriya.ru