CALCULATION
Calculation is an overall term for elaborating a probable sequence of moves. This sequence ranges from very short to very long and from vague to very forced. The exact type depends on the degree of contact with the enemy. Sometimes you have a kind of trench warfare, where both sides keep a certain distance from each other. Then there are positions which are full of tension, with many possibilities for captures or threats. In the majority of the cases, the nature of the position lies somewhere between these two extremes.
265. What type of position do I have in front of me?
In order to figure out the necessary intensity of calculation we have to define the nature of the position. Let’s work with four categories:
1. sharp
There are forced lines like in a combination. These lines branch out, as both sides normally have different options at every stage. This structure is called a variation tree. In rare cases there is one narrow long line without significant branching.
2. medium sharp
Some rather short tactical sequences mix with positionally motivated variations.
3. positionally forced
The lines basically unfold along a positional logic. Hence, it is possible to find the best moves for both sides (sometimes there are equally good options). Here, our decisions are mostly based on our positional assessment, principles and planning, which is a consequence of the overall evaluation, discussed in the previous section on the holistic view. The lines are much shorter than in forced positions. Sometimes, thinking three moves ahead (including branches) is doing the job.
4. positionally vague
There are many equivalent ideas to choose from. The value of a tempo is rather small. You can easily overlook the next move of your opponent, but it doesn’t matter much.
265. What is the difference between tactics and calculation?
These two expressions are often confused with one another or used interchangeably. Hence, there is a need for clarification. Calculation is only one part of a tactical operation (combination). Then, there are calculations with now tactics involved (see above).
Tactics is the knowledge of patterns and mechanisms with which one can turn a motif in the position into a concrete win. At its core, tactics is pattern recognition – a ‘Aha, a pin can be exploited here’ or ‘the bishop is overloaded’. It answers the question: what sort of move is actually possible here? Tactical vision is largely intuitive and associative. A strong player often recognizes a motif in a fraction of a second because he has seen the pattern thousands of times.
Calculation is the practical level: the systematic, disciplined analysis of specific sequences of moves – move, counter-move, counter-move – right through to a clear, evaluable end position. It answers the question: Does the idea actually work, and what is the exact sequence? You could put it this way: tactics provide the initial idea, whilst calculating variations verifies it.
266. What is Kotov’s method?
Kotov put this succinctly in *Think Like a Grandmaster* (1970): weak players often calculate in a haphazard and unstructured manner (‘busy calculation’ without tree discipline), whilst strong players first select the candidate moves and then calculate them in a disciplined manner, following each branch only once. While this approach provides us with a sound basis, it is too rigid to serve as a complete model. I will make clear where I deviate from it.
267. Why is it important to work with candidate moves?
Many club players just follow the motto of the villain Macbeth: “The very firstlings of my heart shall be the firstlings of my hand.” It marks the moment he resolves to abandon hesitation, deciding that from then on, whatever he thinks or feels, he will do immediately without overthinking.
The problem is that chess is too complicated to make first impressions your guide. Not only are these soaked in emotions. It also takes some time to discover more obscure alternatives. Hence, starting your thinking with brainstorming in order to generate candidate moves is generally the right way to go. Which candidate moves present themselves depends on one’s knowledge of patterns and on the logic of the position and its development.
268. How many candidate moves do I need?
As a rule, three candidate moves are usually sufficient in a regular tournament game. If you are not used to work with candidate moves, try to always come up with one alternative to your “firstling”, given that it is no “only move-situation” and you have enough time available. In blitz games you normally go with what comes up first and in rapid games, you might work with two candidate moves in critical positions.
269. With what candidate move do I start in my calculation?
The logic of the position dictates what requirements exist and how these should be prioritized according to urgency. Generally, you should start with the most forcing variations and end with the least forcing candidate move. As the forced variations might lead to convincing results, the unforced variation could easily be rendered obsolete. Starting with the unforced variation would then amount to a waste of time. The relation to a potential benchmark also influences the order of calculating candidate moves, which leads us to the next question.
270. Should I use a benchmark?
I believe this is something that happens almost automatically and requires very little conscious, methodical effort. Apart from training exercises, the player is not thrown in at the deep end, but grows into the position as he plays through the most recent moves. He therefore already has an idea of how to assess the position and what the fundamental tasks are. This means he already has a minimum objective. When compiling the list of candidate moves, he will now consider moves that are potentially capable of meeting these minimum requirements. If, during the calculation, the evaluation falls below the minimum target, the calculation is usually aborted to give the next candidate move a chance. As a rule, moves in the candidate list that have the potential to exceed the minimum target should be prioritized (“Think big!”).
271. How deep do I have to calculate?
There are three abort criteria:
1. Stability
In general, you have to calculate until the moment, when a position is clear enough to be assessed. In other words: the tactical tension must have been resolved. This is not the case, if there are still checks, captures or threats available. Only end your calculation with relative static positions. One additional trick: If you want to be on the safe side, end your position with a move of your opponent.
2. Failing the benchmark
This was already mentioned above.
3. Risk
If the variation leads to a complicated or risky position, which is difficult to assess, you should stop there for the time being and search for easier alternatives. Imagine you try to calculate a sacrifice but the result is foggy. Try to see whether there are risk-free alternatives, which grant you a decent, uncontested advantage. If you don’t find such alternatives, you can still resume the complicated line where you left it, later.
4. Time consumption
If you find yourself in complicated positions, think about the amount of time required to work it all out. Often, it is better to play simpler alternatives in order to save time. As a general rule, you shouldn’t spend more than 20 minutes on calculating a move. Don’t fall victim to the sunken cost bias, thinking that after having invested 20 minutes, you must invest more time to make that effort count. Don’t throw good time after bad and cut your losses.
272. Lack of candidate moves
A wide spread mistake is to lose oneself in lengthy variations, when early alternatives make the whole line obsolete. Always check, whether there are early candidates (also on move 2 or 3) you might have overlooked.
273. Should I get a quick overview?
Remember: Kotov suggested to establish a list of candidates and then calculate each candidate line to its end, after which a comparison of the results would lead to your decision.
One problem with this method is that earlier lines could turn obsolete by a latter one. The result would be a lot of time wasted. I recommend to get a quick overview first, before delving deeply into the calculation of any specific line. Maybe the last candidate line will emerge superior without much mental effort. This overview-method also applies for the responses of your opponent. As you know, here we have to work with candidate moves, as well. That’s why we speak of variation trees.
Suppose you are analyzing a bishop sacrifice on h7. After 1. Bxh7+ Kxh7 2. Ng5+, the options are now 2..Kg8 and 2..Kg6. You spend 15 minutes analyzing 2..Kg6 and realize that you win. However, when considering 2..Kg8, you understand quite quickly – and to your great dismay – that this simply refutes the sacrifice. Maybe after 3.Qh5 there is the move 3…Qd8-d3, protecting the square h7. This clearly highlights the main problem with Kotov’s method. An initial check of both options would have quickly convinced you not only to refrain from playing 1.Bxh7+, but also from investing 15 minutes for the calculation of 2…Kg6.
274. Do I have to come up with an exact evaluation at the end of my lines?
While it is desirable to come to a precise conclusion in absolute terms, this is sometimes difficult to achieve, either because the position is complicated or due to the limited skills of the player. All you really have to do is to compare the final positions in relative terms, which is called the comparison method.
275. When should I use the process of elimination?
When you are in time trouble, the process of elimination comes into play. Let’s say you have two candidates and one of them loses. In that case, you can confidently play the other one, even at the risk of it losing even more quickly or decisively. In extreme situations, you mustn’t be too cautious. Here’s another example: in positions where playing it safe leads to a strategically poor position, you can sometimes play an unclear move on a hunch, as there isn’t that much at stake anymore.
276. When shouldn’t I use the process of elimination?
The following mistake is quite popular. You calculate two candidate moves and come to disappointing results. Then you find a third one and play it without much consideration. Often, it turns out that you come from the frying pan into the fire, when this third option is even worse than the previous ones. The psychological explanation for this phenomenon is simple. Sometimes, we don’t want to accept reality as it is. Instead of acknowledging a negative situation we are looking for an escape, even if it is the black box of an unchecked move. Very successful people try to be as objective as possible and are willing to face the facts, however unpleasant they may appear.
277. What are resulting moves?
The second point of criticism regarding Kotov’s method is that humans don’t work like brute force computers. Their way of thinking isn’t linear, but contains feedback loops. This is where resulting moves (Shereshevsky) come into play.
Let’s consider a basic situation: You calculate three candidate moves, one after the other. Kotov now wanted you to come up with your final decision. However, the results of line 3 could have brought forth ideas (tactical or positional patterns), that you didn’t have when you calculated line 1. What you have to do now is to revise line 1 with your newly found ideas in mind. Theoretically, it could happen, that your now higher level of insight after having rivised line 1 also influences line 2, which you also might want to visit again. Resulting moves are new moves (ideas) in previous variations caused by the findings in later lines. This can also be a completely new move 1-candidate move, which is now born from your increased level of understanding.
278. Should I use the stepping stone technique?
When calculating a line, it often reaches a fork with two or more options. Applying the stepping stone technique, coined by Jonathan Tisdall, means to visualize this juncture clearly in your head by some effort, before following each separate branch. As visualization is a problem for many players, applying this technique might be helpful. For instance, could it help against the problem, of still seeing phantom pieces on squares, which they have already left in the variation.
279. Should I perform a blunder check?
The blunder check – or Blumenfeld check, named after its inventor – is the final check of my planned move to ensure there are no undiscovered tactical refutations. To do this, I should pause my train of thought for a few seconds. Perhaps I’ll close my eyes or let my gaze wander around the tournament hall. I then look at the position with fresh eyes and check for my opponent’s tactical options. If you are susceptible to tactical oversights, the blunder check is the way to go.
280. How does your value system influence calculation?
The above-mentioned methods are helping you to be more systematic in your calculation. However, they are only one side of the medal. The other side is the value system. What ever we do or think, we are seeking value of some sorts. Values are giving our thoughts direction. It is difficult to calculate, if you don’t know what you are looking for or if you have no idea whether the resulting positions are desirable and to what degree. In order to become a strong chess player, it is important to build up a vocabulary of positions connected to evaluations. That way you know what to aspire or to run away from.
