What Are the Prerequisites for Calculation?
In a recent episode of the Perpetual Chess Podcast, host Ben Johnson asked GM and trainer Jacob Aagaard about the biggest thing he’s changed in his coaching practice. Jacob’s answer was that he now focuses more on drilling basic patterns. I found this answer especially interesting since Jacob is known for fiendishly difficult books like Grandmaster Training: Calculation. If Jacob is focusing on easier puzzles, maybe we should too.
Let’s introduce a little terminology. Rather than “easy” and “hard” puzzles, I prefer the categories Ben uses in the Perpetual Chess Improvement book, “pattern recognition” and “calculation”. This emphasizes that these are fundamentally different things that require different training techniques, not just different levels of the same thing.
My own progression as a coach has been similar to Aagaard’s. I used to think it made more sense to focus on calculation, since many patterns arise in a single calculation exercise. By doing calculation, you get pattern recognition thrown into the mix for free. That’s what I thought, anyway. The problem is that unless you’re already really solid on the patterns, it’s impossible to calculate meaningfully.
At the same time, after reviewing many amateur games in coaching sessions, I’ve noticed that games are rarely decided by deep calculation errors. Far more common is for a player to miss a key move early in the line, often on move one. When it comes to winning more games, it’s far more impactful to focus on getting really good at recognizing common patterns and spotting the key options for both sides than to calculate very long lines.
One player who’s had a lot of success drilling the basics is Alex Crompton. He was stuck at 300 after learning chess, but quickly ascended to 1500 when he hit on a plan of drilling pattern recognition.
But there may come a time when you have to switch over to calculation. Alex’s focus on pattern recognition got him up to 1500, but once he got there, he experienced a plateau. That’s why I’m now thinking about pattern recognition as a prerequisite: it’s necessary before you can start meaningful calculation work, and as a bonus, it’s very effective for gaining rating points early on. But once you pass a certain point, you might need to shift your focus back to calculation.
There might be another, less obvious, prerequisite to calculation. Lately I’ve been reading Aiden Rayner’s work in visualization. Actually, he prefers the term conceptualization, since it turns out that many players don’t actually visualize a chess board in their head. In any case, what we’re talking about is building your “mental chessboard” so that you can hold a position in your head for multiple moves.
As with pattern recognition, I used to think you got visualization “for free” with calculation training, because in order to calculate, you have to visualize multiple moves. But similar to pattern recognition, without a certain level of visualization, meaningful calculation is impossible. You simply can’t hold the position in your head.
So it may also be necessary to train visualization specifically before moving on to calculation, for example, with blindfold training exercises. I haven’t yet fully incorporated this into my training programs, but it’s something I’m looking at.
How has your experience been with calculation? Are you able to work through a difficult calculation exercise? Did working on pattern recognition, visualization, or anything else help to unlock calculation for you?
This article resonates with my experiences as a relative beginner. When I try to solve challenging problems, I struggle for the two reasons you've outlined.
1) I don't have the "reps" to recognize patterns. Every position seems completely unique and impenetrable.
2) As I begin to explore candidate moves, I find it difficult to keep the position in my head beyond a move or two. And I often overlook opponents' resources because I'm not practiced at seeing the whole board.
I have been dedicating myself to training tactics (using the Steps Method - level 1), and I find that my pattern recognition is increasing. My conceptualization is also improving as a result. But I will need to eventually begin doing more direct work on that.
As I finish the Step 1 books, I plan to start Step 2, and included in that set is a "thinking ahead" book, which I beleve addresses visualization.
Love this thought-provoking essay!
Before chess.com and chessable.com, and similar, people studies chess from books. You had no choice but to visualize, because you'd have to play a few move in your head, until you reached the position shown on the page.
I've been playing a few years, computers only, and recently tried learning from books. Woah it's hard. I'm clearly not nearly good enough to do this. Yet. So I have this theory that computers help people reach, maybe 1500, quite easily. But without the visualization that people used to develop while learning from books, we might struggle to get past that.
Maybe anyone who really cares about progress should force themselves to always also be learning from a book.
After all, as you say Nathan, visualization is a prerequisite to calculation!