It is widely believed, for example, that you are born either with or with out calculating ability, that it cannot be taught. Almost everyone agrees, furthermore, that computers calculate much better than humans. And it is stated with the utmost authority that there is one and only one correct method of counting out variations, which all masters follow rigorously.
None of these statements is true. Calculation is a skill that can be studied, learned, and sharpened. A player can calculate much more efficiently than any machine. And masters select moves and visualize and evaluate their consequences using a wide variety of methods. Let us look at a few more myths.
The Myth Of The Long Variations
A popular view among amateurs is that grandmasters are grandmasters because they routinely see 10 moves ahead. There are, of course, examples of this by Gms, but they are relatively rare.
Much more common is the kind of calculation that calls or seeing not more than two moves into the future. And most of the time these two-move variations lead only to minor improvements in the position But these improvements can add up.
When Mikhail Botvinnik lost on first board during the 1955 Soviet-American match, the world champion explained the result simply; "It shows I need to perfect my play of two move variations."
Positional Players Don't Calculate
You might conclude that positional players do not calculate. Yet the image persists that strategists, such as Reshevsky and Botvinnik, choose their moves abstractly, using only general principles, while the attackers are the ones who announce "Mate in 27!"
But let's hear what a former world championship challenger has to say.
"Often a player who gravitates towards combinational solutions is automatically numbered among the calculating, logical brains,". wrote David Bronstein. "In contrast," in added, "the one who is inclined towards positional play is said to possess an intuitive cast of mentality."
"Sometimes these characteristics are wrong by 180 percent, if only when one is talking about Capablanca or Tal."
By this Bronstein was suggesting that a positional minded player could be a constant calculator, like Jose Capablanca. Or he could be a combinational player who relies to a great deal on intuition rather than long variations like Mikhail Tal, another world champion. Of today's generation we can speak of remarkable calculators as different in playing style as the "tactical" Viswanathan Anand and Alexey Shirov are from the "positional" Gata Kamsky and Boris Gelfand.
Or consider Aron Nimzovich, sometimes called the Father of Modern Chess. In his notes analyzing some of his original maneuvers, you find a remarkable number of long variations. And they are not necessarily forcing variations, as demonstrated by one of Nimzo's most famous combinations.
Calculation Means Finding Mates and Sacrifices
Most calculation is concerned with minor aspects of the game: Can I win a pawn here? What are the risks of repositioning my Knight? Can I afford to trade rooks? How favorable is the approaching endgame?
When we say it is essential to calculate major decisions well, we don't necessarily mean combinations. A major decision may be a primarily positional one.
Sometimes calculation means the simple visualization of a plan. Instead of "I go here and he goes there and then I'll think of something." it can be "I win by doing this, this, and that." The more forceful the moves involved the easier it usually is to calculate a series of moves. Yet even when a master uses mating ideas he is often seeking no more than a positional edge.
We have just seen what is myth, now let us look at the facts
Calculation is an enormously valuable tool
Calculation is an enormously valuable tool because it can compensate for a lot of other deficiencies. It can, for example, make up for a player's poor winning technique.
A player can think one minute over each move and then lose because he failed to visualize one important move. The power to consider positions that have yet to occur and to recognize the possibilities is essential to calculation.
Many newcomers to chess believe such visualization to be almost magical, so extraordinarily difficult that it's an ability you must be born with. Actually, it is a skill like any other chess skill.
Before a player can begin his calculations he need some thing to calculate. It will probably come from a tactical or strategic pattern, perhaps from a particularly fortunate configuration of his pieces or weak spot in his opponent's position.
In short ideas inspire calculation. Without them we'd have to think like computers, searching through dozens of moves and evaluating hundreds of irrelevant positions. The absence of an idea is the most common cause of oversight. When we miss a two move combination it's usually because we simply weren't aware of the primary tactical idea in the position. And usually this is because it didn't occur to us that there was one.
Why masters calculate better than novices.
Most people who don't play much chess, and many who do, believe the greatest difference lies in how far ahead a player can see. "The master can see 10 moves ahead, the amateur maybe only two." is a common attitude.
But the key element is the master's ability to recognize patterns of pieces. A master can quickly memorize the placement of pieces in a particular position, breaking down the board into four or five chunks. Each chunk will have features that he remembers from other games and other positions. Masters show no superiority whatsoever in memorizing bizarre, problem like positions. Such positions have no rational order, no "meaning" to them.
Many familiar chunks, each having as few as five to as many as 16 squares, can be said to be "tactically neutral." Nothing much is happening in them. But many chunks do have tactical ideas inherent in them, ideas that masters recognize much faster than amateurs. This is particularly true of weaknesses in an opponent's camp.
Master vs Novice
An amateur might first note the balance of material on the board or whether one player is in check. A master, however, might be drawn to other features, particularly the diagonal leading to Black's King. As White, he immediately begins thinking of getting a checking piece, a bishop or queen, somewhere between a2 and a6. A pity, he thinks, that my bishop is pinned. An amateur might miss that idea entirely. Or he might give up on exploiting it after a brief search of ways to unpin the bishop. But the master will be so struck by that long light squared diagonal he will probably search and search until he finds the winning move. It's Qa2!!! and once you spot it, the position seems easy.
According to De Groot and others, masters assimilate many more chunks than nonmasters; some claim that masters have 50,000 plus patterns in their heads.
How can you build up your storage of chunks? One obvious method is to play over many tactical games. Most combinations are inspired by previous games that the calculator recalls. Some tactical themes, made famous by ancient brilliancies are so familiar to modern masters that even a spectacular examples can be reduced to a matter of routine.
As you play over master games you will notice patterns, both tactical and strategic. A strategic pattern might be a favorable pawn structure or a thematic Knight maneuver. A typical tactical pattern would be a formula for checkmate,
Hints
Beside mating patterns a position will contain other hints. They include:
1. Vulnerable, unprotected or otherwise exploitable pieces.
2. Stretched pieces.
3. Invasion squares.
1. Vulnerable Pieces
Most calculated sequences involve, at least in part, the exploitation of hanging pieces. The more enemy pieces that are unprotected, the greater the chances that you can calculate something favorable.
Even in the early stages of a game, when few pieces venture beyond the fourth rank, those that do run a risk.
2. Stretched Pieces
Related to unprotected pieces are ones we can call "stretched." These are pieces that are being overused, they are performing more functions than they are capable of. Knowing how to recognize such pieces sometimes requires a fine tactical nose.
3. Invasion Squares
Often an unoccupied square is more important than any square with a piece on it. Noticing such a vulnerable point is the hard part.
How to Build Trees
Once you've identified the primary ideas in a position, you task is to work out the details of exploitation. Ultimately, these details will result in a calculated sequence, a series of moves that lead to a position about which you can form a judgment.
How Good Chessplayers Really Think
Kotov argued that a player must approach the tree carefully. He must examine each branch once and only once. To jump from one to another is "an unforgivable waste of time," something that no grandmaster would countenance, he claimed.
In reality, grandmasters think no more systematically than amateurs. They sometimes jump from branch to branch and back again. Or they calculate only a few moves deep into what should be a very large tree. As Mikhail Tal once put it, "To calculate sometimes all of the so-called tree of variations is not simply difficult but impossible."
Tal spoke instead of a "zone of certainty" that allows a trained calculator to stop his calculation after a relatively brief testing of the various branches. There are many masters who follow Tal's example, calculating what end positions they can see and then evaluating other branches on instinct.
In the late 1970s, the English master Simon Webb conducted a series of experiments, the results of which appeared in the magazine Chess. Webb gave players of different playing strengths a position to look at and had them describe how they'd go about choosing a move. None of the positions were forced wins.
His results were surprising for followers of Kotov. For example, the grandmaster in the test group jumped around from one idea to another and then back again. In another case, the two strongest players tested spent 10 minutes failing even to consider what was clearly the best candidate move and then selected moves they had considered for less than a minute.
What really distinguished the better players, Webb found, was that they could come to accurate conclusions faster, thought in terms of concrete variations, and were therefore more efficient calculators.
There is no perfect calculating method for all players, Kotov notwithstanding. We all think differently. In reality there is a strong element of serendipity in chess. When we look at one idea, we sometimes come up with another.
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