I see only one move ahead, but it is always the correct one.
—JOSÉ RAÚL CAPABLANCA,
THIRD WORLD CHESS CHAMPION
Without a doubt, the question I am most often asked is “How many moves ahead do you see?” As with most such questions, the honest answer is “It depends,” but that hasn’t stopped people from asking or generations of chess players from concocting pithy replies. “As far as needed” is one, or “One move further than my opponent.” There is no concrete figure, no maximum or minimum; in a way, it’s like asking a painter how many brushstrokes he uses in a painting. Calculation in chess is not one plus one; it’s more like figuring out a route on a map that keeps changing before your eyes.
The first reason it is impossible to reduce chess to arithmetic is because the possibilities are so numerous. For every move there might be four or five viable responses, then four responses to each of those moves, and so on. The branching of the decision tree grows geometrically. Just five moves into the game, there are millions of possible positions. The total number of positions in a game of chess is greater than the number of atoms in the universe. True, a majority of these are not realistic game positions, but the vast scope of what is possible in chess should manage to keep humans occupied for another few hundred years.
Like a weatherman’s forecasts, the further ahead you look, the more likely it is you will miscalculate. We can define calculation as a sequence in which the outcome of step C depends entirely on the accuracy of our conclusions about steps A and B. Each added step into the hypothetical future increases the chance of making a mistake.
We often hear just about any type of mistake referred to as a miscalculation. It’s more useful to think of this as a specific type of error, one in which the factors were known but the conclusion reached was incorrect. In chess both players know all the factors, but this is of course impossible in politics. It is still impressive how many political blunders derive from “obvious” assumptions.
Through military might and clever diplomacy, Otto von Bismarck created a German empire in the second half of the nineteenth century. After unifying Germany he managed to isolate France and cut off Russia while he allied with Austria and Italy. He was sure that France and Russia would never join forces because an absolute monarch such as the Russian czar would never “take off his hat and listen to ‘The Marseillaise,’ ” the anthem that had accompanied the march of so many royals to the guillotine.
In 1894, four years after Kaiser Wilhelm II had replaced Bismarck as chancellor, the French signed a military alliance with Russia. And when a fleet of French ships visited Russia, the czar not only listened to “The Marseillaise” but indeed took off his hat. Bismarck had had all the information he needed, but he came to the wrong conclusion and underestimated the growing Russian economy’s need for French credit. Most of all he assumed royal pride would outweigh fiscal necessity; his miscalculation had repercussions that lasted into the First World War. Bismarck was a great tactician and strategist, but in this case he failed to credit others with the same qualities. He committed the blunder of counting on his opponents to make a mistake he would never have made himself.
Calculation Must Be Focused and Disciplined
You might imagine that a game limited to a board with sixty-four squares would easily be dominated by the calculating power of today’s computer technology. But as it turns out, deep calculation isn’t what distinguishes the champions. Studies performed by Dutch psychologist Adriaan de Groot have shown that elite players don’t in fact look ahead that much further than considerably weaker players while solving chess problems. They can, on occasion, but it doesn’t define their superior play. A computer may look at millions of moves per second, but lacks a deep sense of why one move is better than another; this capacity for evaluation is where computers falter and humans excel. It doesn’t matter how far ahead you see if you don’t understand what you are looking at.
We have seen that precise calculation is the first key to effective decision-making. The second is the ability to evaluate both static (permanent) and fluid factors. When I contemplate my move, I don’t start out by immediately running down the decision tree for every possible move. First I consider all of the elements in the position—such as material and king safety—so I can establish a strategy and develop intermediate objectives. Only when I have these goals in mind do I select the moves to analyze.
That analysis must be ordered to be effective. Anyone who has ever written down a list of errands understands that tasks can more effectively be done when prioritized and performed in optimal order. My experience guides me to select two or three candidate moves to focus on. Usually one can be discarded relatively quickly as inferior, and often another comes into consideration to take its place. Then I begin to expand the tree one move at a time, looking at the likely responses and my answering moves.
In a complicated game this tree of analysis usually stays within a depth of four or five moves—that is, four or five moves for each player, or eight to ten total moves. (We call these half moves: one move for white and one for black equals one full move.) Unless there are special circumstances—a particularly dangerous position or a key moment in a game—I know from years of experience that’s a safe, practical amount of calculation.
The decision tree must constantly be pruned. Move from one variation to the next, discarding the less promising moves and following up the better ones. Don’t jump to another before you’ve reached a conclusion on the move you’re analyzing; you’ll waste precious time and risk confusing yourself. You must also have a sense of when to stop. Discipline yourself to keep calculating until you have determined a path that is clearly the best, or until further analysis won’t return enough value for the time spent.
Imagination, Calculation, and My Greatest Game
In some cases, the best move will be so obvious that it’s not necessary to work out all the details, especially if time is of the essence. This is rare, however, and it is often when we assume something is obvious and react hastily that we make a mistake. More often you should break routine by doing more analysis, not less. These are the moments when your instincts tell you that something is lurking below the surface, or that you’ve reached a critical juncture and a deeper look is required.
To detect these key moments you must be sensitive to trends and patterns in your analysis. If one of the branches in your analysis starts to show surprising results, good or bad, it’s worth investing the time to find out what’s going on. Sometimes it’s hard to explain exactly what makes those bells go off in your head telling you there is more to be found. The important thing is to listen to them when they ring. One of my best games came about thanks to this sixth sense. The scene was the strong traditional “supertournament” (roughly the equivalent of a grand slam tournament in tennis or a major in golf ) in Wijk aan Zee, the Netherlands. My coactor was again the “Battling Bulgarian,” Veselin Topalov.
Topalov also deserves marquee billing, because it takes two to create a truly beautiful chess game. His stern resistance pushed me to the limits of my calculation abilities in this game, in which I played the deepest combination of my career. An entire booklet dedicated to this one game was later published in Greece, and I admit that ninety percent of its analysis didn’t enter my mind during the game. Once I registered a few of the exciting possibilities to chase black’s king across the board, I focused and concentrated on his most likely attempts at defense. In my calculations I realized that it would be like walking a tightrope: one slip would be fatal. I would sacrifice half my pieces to flush his king out into the open. If it didn’t work, I would be completely lost, so I had no choice but to invest the extra time to be as sure as possible. I kept pushing deeper into my mental image of the position, sure there must be something, until finally I saw the final winning position, an incredible fifteen moves away.
It was a feat of calculation, but there is no way your mind can go that far without help from your imagination. The combination would never have occurred to me had I taken a purely deductive approach to the position. It was not the product of logical analysis showing a mathematically perfect conclusion. As proof I can only point out that at least at one point I missed the strongest move, found in later analysis by other Grandmasters.
As an aside, although it turned out well for me, my missing the best move illustrates one of the perils of becoming fixated on a distant goal. I was so entranced by my vision of the gold at the end of this rainbow that I stopped looking around as I approached it. I’d convinced myself that such a pretty finish must be scientifically correct too—a potentially dangerous delusion.
The key to calculation is understanding its limits. You have to recognize when you are leaving the realm of what can be confirmed beyond a reasonable doubt. At that point you have to fall back on more general considerations and your intuition. In any endeavor it can be fatal to believe you are absolutely sure when in fact the situation is too complex— or the outcome too far away—to be solved by calculation alone.