How Far Do You See? Garry Kasparov on Search, Calculation, and Memory

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How far do you see? Garry Kasparov on search, calculation, memory, and fantasy

Search and calculation

“How many moves ahead do you see?” That’s the question that people like to ask of former chess grandmaster Garry Kasparov. And the answer? Well, “it depends”, as Kasparov writes in his book How Life Imitates Chess.

People cannot play chess like a game of pure arithmetic. There are just too many permutations. Kasparov likens the search and calculation process to weather forecasting: “the further ahead you look, the more likely it is you will miscalculate”.

While calculation is important for chess grandmasters, it “doesn’t define their superior play”. Kasparov himself begins by first understanding the elements of a given position. This allows him to define his strategy and intermediate objectives. “Experience [then] guides [him] to select two or three candidate-moves to focus on”.

With candidate moves in mind, he climbs the decision tree, pondering about his opponent’s response and his counter response in turn — pruning out bad moves along the way. Kasparov says that search and evaluation are done usually “within a depth of four or five moves [for each player]”. (For reference, chess engines search regularly between depth 10 and 50.)

“When I look at a chess position, … there is very little that is consciously systematic about my move search process…  Before any real search begins in my mind, I have selected several to analyze more deeply, what we call candidate moves. Of course, I’m not starting from scratch if it’s my own game; I’ve been planning my strategy and looking at the most likely variations… And often I will plan out a sequence of four or five moves in advance, only pausing to double-check my calculations if the sequence plays out as expected.”

Garry Kasparov. (2017). Deep Thinking.

Principle and limitation

All of this is reminiscent of Herbert Simon’s work on bounded rationality (which was inspired in part by decision-making in chess). Simon observes that to make decisions under uncertainty and complexity, given our cognitive limitations, we have to look for satisfactory solutions using an effective search function, evaluation scheme, and stop rule.

Critical to calculation, Kasparov says, is an understanding of our limits. Whether in chess or business, we will sometimes encounter nebulous environments in which we have to rely on general principles over calculation to make a move. It’s dangerous to expect perfection when reality is more complex than we can conceive.

I’m reminded of a wonderful anecdote from Yasser Seirawan in Play Winning Chess on the 1960 championship match between grandmasters Mikhail Botvinnik and Mikhail Tal — between calculation and principles:

“Tal was on the attack, Botvinnik, thinking for a long time, decided on the correct defensive strategy and drew the game. Afterwards, Tal listed a huge series of move variations, thinking that Botvinnik had arrived at the correct strategy by calculating the same possibilities. The younger challenger was dumbfounded when the champion stated that he had decided on an overall strategy by weighing his position in the light of the principles — he had made very few calculations. The two different approaches had, however, led to the same solution!”

Yasser Seirawan. (1990). Play Winning Chess.

Memory and understanding

Kasparov makes a similar point about memorization for games. Amateur players often spend hours committing chess openings to memory. And exhibitions of blindfold chess games, likewise, are very impressive to the layperson. But supreme recollection, Kasparov writes, “is useless without understanding”.

Chess games, much like life, rarely repeat themselves. Sooner or later, we will exhaust our memory banks and have to think for ourselves. What’s more, memorization by its lonesome is pure imitation. If we want to innovate at the frontier, we have to move beyond history and adapt to the successes and failures of our predecessors.

“The transition from imitator to innovator is seen in every aspect of society. In chess, a young player can advance by imitating the top Grandmasters, but to challenge them he must produce his own ideas. … Just like Darwinism in nature, innovation is quite literally about survival. We have to keep evolving, and that means staying aggressive instead of standing still.”

Garry Kasparov. (2009). How Life Imitates Chess.

Fantasy and analysis

Somewhat ironically, Kasparov describes how modern chess computers excel at finding novel ideas and breaking established molds. Unlike the habitual human player, computers “hold no prejudices against moves that [look] ugly… or absurd”. Sometimes, their solutions are so otherworldly that we cannot help but appreciate their beauty.

Human players, by contrast, pursue innovation through “fantasy”. Kasparov himself begins with the question “wouldn’t it be nice if…”, and proceeds to “daydream” about the possibilities. While fantasy without analysis is dangerous, rejecting every odd-looking sequence is equally limiting. We should ask “what if” and “why not” more often.

Former Intel CEO Andy Grove calls this the first version trap in Only the Paranoid Survive. Grove laments, for example, his early dismissal of Apple’s Macintosh in 1984 because “it was a ridiculous toy”. The machine’s overt problems hid from him just how important graphical interfaces and uniform software applications would someday become.

“Fantasy must be backed up by sober evaluation and calculation, or you spend your life making beautiful blunders. … Too often, we quickly discard apparently outlandish ideas and solutions, especially in areas where the known methods have been in place for a long time. The failure to think creatively is as much self-imposed as it is imposed by the parameters of our jobs and of our lives.”

Garry Kasparov. (2009). How Life Imitates Chess.

Fuzzy formulas

Sound decision-making it seems is an inherently fuzzy formula. We have to combine calculation, memory, and learning with good search functions, evaluation schemes, and stop rules. Fantasy, likewise, can help us to navigate the adjacent possible. But we have to pair it with principles, analysis and sensibilities.

As Kasparov writes:

“Having spent a lifetime analyzing the game of chess and comparing the capacity of computers to the capacity of the human brain, I’ve often wondered, where does our success come from? The answer is synthesis, the ability to combine creativity and calculation, art and science, into a whole that is much greater than the sum of its parts. Chess is a unique cognitive nexus, a place where art and science come together in the human mind and are then refined and improved by experience.”

Garry Kasparov. (2009). How Life Imitates Chess.

Chess is an illuminating game. Two players, thirty-two pieces, sixty-four squares and a small set of rules, over many centuries, have generated a remarkable amount of competition, evolution, complexity, and beauty — a fascinating microcosm, I think, of choice and consequence in life.

Sources and further reading

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