Calculation and judgement

The black king has no g7-pawn, the white bishop already stands on f6, and the queen on h5 is close by. The first move here is found at once: it is a check. The second one decides, and it is neither a check nor a capture.

Such a move is called quiet. It is hard to find because the eye looks for checks and captures, while here the queen simply steps to the next square. In this chapter we learn to calculate so that quiet moves do not slip away: choose candidates, follow the branches of a line in order, keep the position in your head and stop at the right moment.

The chapter continues the chapter “Sacrifice and combination”. There we looked for combinations through forcing moves. Here the subject is how to carry the calculation to the end and not go wrong on the last move.

Candidate moves

Calculation starts with a list. Before you calculate, find all the moves worth checking. They are called candidate moves. Usually there are two to four. If there are many more sensible moves, the position is most likely quiet: plans and judgement decide in it, and long calculation is not needed.

The order of the search is this. First checks, then captures, then threats, including quiet moves after which mate or the win of a piece is threatened. Forcing moves are checked first: the opponent has few replies to them, and the line is calculated quickly. A quiet move leaves the opponent freedom, and their replies have to be examined more widely.

The method was described by Alexander Kotov in the book “Think Like a Grandmaster” (1971): draw up a list of candidates, calculate each line only once, and only then choose the move. Kotov advised against jumping from one line to another and back: every return eats time and brings almost nothing. Later coaches argued with this advice: strong players often calculate one main line and test it against the opponent's replies. But the habit of making a list is useful at any level; it saves you from the main mistake, playing the first move that comes to mind.

Here there were few candidates: there are no checks, and trades give nothing. The move Nc6 is found if you ask yourself: which of the opponent's pieces can I attack in one move? An attack on the queen is also a forcing move, even without check: it has to be answered at once.

You need a list for the opponent too. Before calculating your own line, ask: what do they want to do themselves, what checks and threats do they have? Sometimes the best move in the position is the one that takes away the opponent's candidate. And when you calculate your own line, the same candidates of the opponent become their replies at every branching point. Whoever knows them in advance is surprised less often in the middle of a calculation.

The tree of variations

Each candidate produces a branch: your move, the opponent's replies, your next move. Together the branches form the tree of variations. It has to be calculated in order: follow one branch to the end, judge it, go back to the branching point and take the next one. The main rule: at every branching point, check the opponent's best reply. A line in which the opponent makes a mistake proves nothing.

Branches multiply fast. If the opponent has three sensible replies to every move, after three moves there are already twenty-seven lines. Forcing moves come to the rescue: after a check the opponent often has one or two replies, and the tree stays narrow. That is why long combinations almost always consist of checks and threats: only these can be calculated to the end.

Look at how the calculation in this example is built. On the moves with check there were one or two replies, and the branches closed at once. After the quiet move Ra6 Black had many replies, and all of them had to be checked: checks, trades, pawn moves. But each of them ended the same way: mate. This happens often: a quiet move sets up a threat that cannot be met, and examining the opponent's replies comes down to checking that their checks run out.

In such branches it is easy to miss the opponent's check in reply. Before each of your moves in a line, ask the same questions as before a move in the game: what checks, captures and threats does the opponent have now? This is the check from the chapter “The in-between move and blunders”, only done in your head, several moves ahead.

Kotov also described the opposite trouble, and it is called just that: Kotov syndrome. A player calculates a complicated line for a long time, gets lost, sees the clock running, and at the last moment plays a different move that they have not calculated at all. The cure is simple: if the calculation gives no clear answer, choose a reliable move that you have checked at least two moves deep. And if two candidates win, take the one that is easier to calculate: an extra pawn in a clear position is better than an extra piece in a line where you are not sure of the last move.

Blindfold calculation

During a game you cannot move the pieces. Everything that happens in a line has to be seen in your head: where each piece stands after three or four moves, which lines have opened, which squares have been vacated. This skill is called blindfold calculation. Its mistakes are all alike: a piece that has already moved away in the line stays on its old square in your mind, or the line it used to block stays blocked.

A simple technique helps: make stops in a long line. After two or three moves, stop and set up the position again in your mind, piece by piece. Which pieces have left their squares? Which lines have opened? Whose squares are no longer protected? It is at such a stop that blows like …Qxg2# are found: the queen has left f2, and the rook behind it suddenly comes into view. Without stops the position in your head blurs, and by the fifth move you are calculating a different position from the one that will appear on the board.

How do you train blindfold calculation? Solve puzzles without touching the pieces. First find the solution and say it aloud move by move, then check it on the board. It helps to set up on the board the position that arises after a line of four or five moves and compare it with what you saw in your head. Another exercise: read game scores without a board and from time to time set up the position to check yourself. It is hard at first, but after a few weeks the position starts to stay in your head longer.

The quiet move

A quiet move is a move in a combination that is neither a check nor a capture. It does not force the opponent to answer with a particular move, but it sets up a threat against which there is no defence. Quiet moves are found less often than others: the eye looks for blows, while here a piece simply goes to a square from which the threat becomes unstoppable.

Here the quiet move was made by a pawn, and it came first. The check was at hand, but after it the king escapes. First the square had to be taken away, and only then could the check be given. This is a common pattern: the quiet move shuts the king's exit, and the check comes next.

To find such moves, after checks and captures ask yourself one more question: which move creates a threat the opponent cannot defend against? If the opponent has no checks and cannot protect the mating square in time, a quiet move is stronger than any blow.

Quiet moves happen in defence too. Against the opponent's combination a move often helps that takes the king off a dangerous diagonal in advance, protects the mating square or frees a retreat for a piece. It too has to be looked for among the candidates: if the opponent's threat cannot be answered with a check or a favourable trade, ask which calm move takes the sting out of the blow. This is the same prophylaxis, only calculated several moves deep.

Where to stop

A line cannot be calculated forever. You may stop when no forcing moves are left in the position: neither you nor the opponent has checks, good captures or direct threats. Such a position is called quiet. In it you can already give an evaluation: count the material, look at the safety of the kings, at the activity of the pieces and at the pawns. The engine does the same: at the end of its search it plays out the captures and only then evaluates the position.

The most common mistake is to stop too early. The line seems finished because you have won a piece, but on the next move the opponent has a capture or a check. Check the last position of a line as strictly as the first: if the opponent still has a blow, the line is not finished.

And the material at the end is not the whole evaluation. A combination may win a pawn but leave your king exposed and your pieces scattered on the edge of the board. Then the opponent gets an attack, and the extra pawn means nothing. Before starting a combination, look at the final position as a whole: where the kings will be, which pieces will stay active, whether the opponent has a passed pawn. If at the end you have nothing to defend your own king with, such a line is worse than a calm move.

There is also the opposite mistake: calculating too long. If there are no forcing moves in the position, deep calculation gives nothing: there are too many lines, and the opponent is obliged to play none of them. In such positions plans and judgement decide, and calculation is needed two or three moves deep, to check that the move does not blunder.

The order of calculation

Let us put it all together. When there are forcing moves in the position, calculate like this.

• Draw up a list of candidates: checks, captures, threats, quiet moves with a strong threat.
• Start with the most forcing candidate and follow its branch to a quiet position.
• At every branching point look for the opponent's best reply, above all their checks and captures.
• At the end of the branch judge the position: material, kings, activity of the pieces.
• Go back to the list and check the other candidates if the first one did not give a decisive advantage.
• Before moving, check the first move of the line once more: does it blunder a piece?

How much time should this take? In a game with an hour per player, a few minutes are enough for a critical moment, and these are exactly the moments worth looking for: positions with a sacrifice, with the opponent's king exposed, with pieces under attack. In a quiet position it is better to save the minutes for later.

Calculation is trained with puzzles. Solve them without a board, write the solution down in full and only then check it. Solve puzzles with long lines where you need to see a quiet move on the third or fourth move. And after every game, look at where you went wrong in your calculation: you missed a check in reply, stopped too early, lost a piece in your head.

What's next

It is easier to analyse your own mistakes with an engine: it will show where the calculation went wrong and which move was best. That is the subject of the next chapter, reviewing your own games. There we will also learn to find the critical moments of a game: positions where you should have stopped and calculated longer.