Improving at chess: calculation as a skill

I am frustrated. Naturally, on The Internet, nobody cares about that. But hold on. Let me explain, so that perhaps we can be frustrated together.

For a very long time, I have been wanting to write a blog post about improvement in chess. This, of course, is an insanely sensitive topic. Nobody in the whole world knows how to improve at chess. Alright, perhaps some people do, but I fear their voice simply isn’t loud enough to make themselves heard above the masses of people that claim they know how to improve. Some of them salesmen trying to sell their amazing ‘new methods’ or ‘opening courses’ or whatever. I have much difficulty believing anyone on this topic, to be honest.

Knowledge versus skill

So here is the frustration: how do I prevent myself from being just another voice in the crowd? I thought very deeply about chess improvement and why I don’t believe what others say. Here’s my conclusion: many improvement instructions treat chess as a game of knowledge. You read a book or watch a video to learn new concepts; you have to study all kinds of tactical principles; and, oh gosh, you have to memorize all possible opening variations. Just for me personally, I reached 2150 FIDE with extremely limited knowledge (I barely knew what a ‘bishop pair’ was), and the last 10 years I obtained massive amounts of knowledge, but my rating is basically the same. The importance of pure chess knowledge is highly overestimated, I think.

I want to treat chess as a game of skill. In particular the skill of correct and efficient calculation. The goal of calculation is to correctly predict what possible scenarios could arise after certain possible moves in order to pick out the variation most favorable to you. Unfortunately (or fortunately), the human brain is not capable of calculating the enormous amount of possible variations in chess (in contrast with for example tic-tac-toe), so we have to be strategic and effective. I claim this is a trainable skill. Whilst doing some puzzle training, I noticed there are actually certain well-defined techniques I use myself and I want to provide my dear readers with a list. For very strong players, it’s probably too obvious to be helpful, but perhaps others consider it useful.

Just a small disclaimer: no, I haven’t done extensive research on what others have said. I can fully imagine I’m not the first one who came up with this.

Several calculation techniques and principles

[List goes from ‘easy’ to ‘difficult’]

1) Candidate moves (numbering)

This one is fairly obvious, but in the heat of battle, often forgotten. Candidate moves are moves that you deem worth considering even before you started calculating anything. When calculating, there is a big risk of trying to analyze certain moves very deeply, only to complete overlook another stronger move. Or even worse, you pick one move you (unconsciously) like, and the whole calculation process is only there to confirm your unfounded bias. Taking some effort to select some candidate moves before diving in deeply, tends to pay off.

By the way, if you have trouble keeping track of all possible lines you calculated, and which conclusions you managed to make, here is a strategy I use. Number the candidate moves (in your head). Extremely simple, but it works wonders for me. Just the idea of quantifying ‘I have 5 candidates moves to look at, this is number 1’, gives a tremendous amount of structure, at least in my head.

2) Piece count

So imagine you’re calculating a tactic where the board is on fire and everything can basically take everything. To calculate such a bloodbath, keeping track of the piece count is vital. Generally speaking, the first line to calculate, would be the line were both players capture the highest valued pieces first. Making this the ‘main line’ in your head gives structure. If this main line doesn’t work, then you start calculating alternatives.

Material count is insanely important when assessing a chess position. When going through a line, make sure to keep track of all captured stuff. Like, “white takes B, black takes R, white takes N, black takes B, white takes R”, means that white gained material in the end. Well, admittedly it’s obvious when written like this, but when calculation gets fuzzy in my head, I tend to lose track.

3) Tactical patterns

Everyone that ever made the dire decision to click the ‘puzzle’ button on lichess, has undoubtedly noticed there are huge numbers of tactical motives. Knowing these, and how to name them, is really helpful. They guide you in selecting candidate moves. Just saying to yourself: ‘this piece is pinned’, opens up ideas to exploit it. Or perhaps ‘this piece is undefended’ will motivate you to attack it. Once again, they provide structure in your head, whereas without them, chess is really just a mess of pieces flying around.

4) Forceful moves / threats

Ever heard of the expression to look at moves like checks, captures and threats first? No? Well, then you must be new to The Internet. Everybody seems to give this advice. And admittedly, it is kinda true. Forceful moves tend to limit the amount of possible replies by the opponent, and they are therefore easier to calculate in depth. The definition of ‘threat’ can be very broad, by the way. For strong players, a minor positional threat can already be a forceful move, limiting the options for the opponent, who has to find a defense.

5) Only move

Even with the techniques provided so far, the number of variations that can arise from any random position, grows beyond human capabilities very soon. What we need, is a way to eliminate irrelevant variations. The most powerful way to do so, is by using the principle of the only move. If there is only one reply that doesn’t result in checkmate or heavy material lose, that move has to be made. No alternatives have to be calculated, which is awesome for efficiency purposes. In many cases (but not all!), simple captures lead to an only move: the opponent has to take back in order not to lose material.

But the only move principle is way more powerful than that. Sometimes, moves that seem reasonable at first glance, turn out to be losing upon further inspection. If that’s the case, we can eliminate them from the calculation, and we might end up with an only move situation. I noticed that saying ‘this is an only move’ in my head after firmly establishing it, helps a lot.

6) In between move

There hides an enormous danger in the only move principle. Because it’s so powerful, the brain really likes to use it in abundance, in order to make life easier for itself. Don’t let it! There is a special name for moves that interrupt a seemingly only move: An in between move. Back ago when I still was member in a local chess club, I very often observed my (lower rated) teammates. The thing I still remember, is how often they analyzed by saying ‘white must do this, black must do this’. Really, chess is much more fun and inspiring if you give yourself options. Finding a nice in between move to get out of a nasty tactic, or to ruin the opponents plans, can completely change the pace of the game.

7) Single refutation principle

This one works wonders during puzzle training, but it’s also very applicable in real games. So, imagine you have a normal position, and you want to check if a promising looking move works for you. It’s complicated, and you find multiple possible candidate moves for the opponent as a reply. The single refutation principle states that once you find a single move that refutes your idea, you don’t have to look at all the others. It saves a tremendous amount of time, obviously. It’s not your job to find your opponents best reply for a move you’re not going to play. It’s pretty funny in analysis with opponents afterwards. Then I explain ‘yeah I didn’t play this because it loses a pawn’, and then the opponent goes ‘bruh, it just hangs checkmate in 2 as well’. The conclusion is the same though: don’t play that move.

8) The bail out principle (initiative)

This one happens often in sequences of captures. The person initiating the sequence usually has the initiative. With every new capture, this person can bail out of the sequence, by not capturing another piece, but instead bringing their own pieces into safety. The opponent has a lot fewer options. They have to take back in most cases, in order not to lose material. Keeping track of the player with the initiative is helpful for me, because for that player, many moves should be calculated, whereas much fewer moves are calculated for the other player. Hence, the player with initiative has the option of finding a favorable outcome, without completing the entire sequence of captures.

9) Process of elimination

This technique is waterproof in tactic trainers where there is always one winning move, but it is somewhat useful in normal chess too. If you have established that all-but-one candidate moves are losing, the remaining candidate move has to be played. It must be the correct answer. In normal chess, things aren’t that clear, because you might just have messed up so extremely badly, that all moves are losing. Fairy tales don’t always exist. Winning moves don’t always exist. But the process of elimination can still be effective. If all-but-one moves are clearly losing, and the other move is very messy and difficult to calculate, you’re best bet is just playing that one, without calculating much more.

10) Process of sufficiency

And guess what, the complete opposite exists too! I gave it a cool name: the process of sufficiency, which works poorly in puzzles, but is pretty useful in normal chess. The idea is to opt for a move that’s ‘just winning’, instead of trying to find the best move. I found that especially in time trouble, I have difficulty just converting winning positions, as I waste all time trying to play optimally. Perhaps it’s an even more useful technique when calculating different variations. When you realize that you can answer your opponents move by a strong reply, you don’t have to calculate any other replies. The longer I think about it, I realize it’s just the opposite of the single refutation principle.

There is a real risk though with using this method too much. If your position is winning, and you keep making minor concessions in the spirit of sufficiency, you might find yourself in a position where the win only gets more tricky. Winning games effectively is a good skill to have, so if there is time, I would recommend not playing the first move you consider winning, but to look for an even better one.

11) The forced draw

Whilst calculating, any sane person would agree that winning is desired, and that losing is undesired. But what about draws then? What if, in a variation, the possibility of a forced draw arises (a perpetual is most common)? Well, it depends, but it’s worth keeping in mind that it sets the stage for the next moves to calculate. If you have a forced draw, you only have to look at positions that might be winning for you. On the other hand, if your opponent has a forced draw, then don’t try to calculate winning variations for you, it just isn’t going to happen. In puzzles, forced draws are never the answer, which gives you a very powerful tool to straight out eliminate many variations.

12) Assessment of complexity

So far, I’ve assumed that all variations could be calculated until a certain conclusion was arrived. But realistically, that’s not always the case. Instead of spending all your time and brain neurons to find answers, it can be helpful to just assess it’s complex. Depending on your alternatives, you might or might not want to go there. If your position is good and healthy, you might prefer a simpler move that is easier to calculate, just to make sure you maintain your advantage.

13) Easiest move first principle

This technique is logically impossible, but somehow practically doable. When calculating, it is often smart to start analyzing the easiest move first. Otherwise, there is a risk that a variation doesn’t reach a conclusion because of complexity, and then the next one as well, and other one... and before you know it, everything is just a fuzzy, unsolved mess. The easiest move principle, combined with the piece count principle and sufficiency principle, can be strong to have some initial conclusion to in mind, that you can use to compare other lines.

Now, how to find the easiest move to calculate first? Well, you have to calculate that... Which, by definition, is something you haven’t done yet... So we reach a paradox. In practice though, chess players do have a pretty good intuition for which moves are easy, and which moves are complex. A quick scan through the candidate moves helps too. But yeah, it’s not the most theoretically well-grounded principle, admittedly.

14) Intertwined lines

This is something I would love to improve, but I’m struggling. In chess, the same position can sometimes be reached with different move orders. This happens frequently in openings, but it occurs in middlegame and endgame variations too. Instead of keeping track of two identical variations in your head, it would be awesome to say that two lines are intertwined, and their conclusions should therefore be identical. In practice, I just have difficulty keeping track when the amounts of variations grows beyond control.

15) Calculation from a fixed point

Imagine a fun little pawn endgame puzzle. You have to choose between some difficult options, and in all cases both players spend 10 moves making obvious pawn/king moves, and then a new difficult decision arises. Wouldn’t it be amazing if you could just make a mental screenshot of this position 10 moves ahead, and uses it as a fixed point to calculate all new possibilities from? I just cannot do it. For every single variation, I need to calculate the same 10 moves over again, to recall the exact position of the pawns/kings. As a result I spend the majority of my time in pawn endgames puzzles calculating the same line over-and-over again.

Conclusion

The attentive reader might notice that I promised to talk about skill, but continued to dump a massive amount of knowledge over my audience. Even I start to notice my blogs have a tendency to not do the thing their introduction sets out to do...

But I hope I created some infrastructure of what calculation actually contains. If anyone gives the beautifully meaningless advice to ‘calculate better’, there is now something that’s actually trainable. I think that each of the points above could actually be trained independently, to really improve the structuring of variations in your head.

Ideally, I would follow up this post with some more examples, perhaps in some kind of exercise form, to really practice getting the hang of each technique, one by one. But that takes a lot of time. So no guarantees.

Thanks for reading, I hope it was interesting and mildly refreshing.