How to Improve You Puzzle Rating? Part 2

In Part 1, we already discussed a few ideas on how to improve the puzzle rating. Part 2 continues with some additional ideas. These are:

• Identify the puzzle type
• Try to find the opponent's best moves as hard as your own moves
• Analyze puzzles afterwards

The first point may speed up the process of finding the solution. The second one can help with the correctness, and the last one is about what to do, when you get it wrong.

Identify the Puzzle Type

When playing a regular chess game, you are usually aware of the material situation and most of the threats on the board. However, in a puzzle, you are presented a position for the first time. That's why it makes sense to get an overview of the position. This can help to direct the solving efforts properly.

In Part 1, I already referred to Adriaan de Groot's doctoral thesis Thought and choice in chess (in English, 1965), where he dissected a chess player's thought process. He splits the thinking process in phases. The first phase is orientation. During this phase the player gets familiar with the position before actually trying to analyze it. I would assume this phase exists partially because of Adriaan de Groot's experimental setup, which resembles a puzzle position in the sense that the players sees it for the first time. In an actual game, this phase could be much shorter, because the position is already familiar and only the opponent's last move has changed it.

In my approach, counting the material is the first step. Some tactical patterns usually jump at you, when you first glance at the position. I try to restrain from calculating lines before knowing the objective though. For example, you could calculate an elaborate combination winning a knight. But if you were a rook down to begin with, that's wasted work. So the material balance could be one of the three:

1. I am down a lot of material. If there are no immediate recaptures or promotions, it's likely that this is a checkmate puzzle. The larger the material difference, the more probable it is. If the opponent's king is exposed or short of escape squares, it is even more probable. Then I can start looking for a series of checks that leads to a checkmate. If no such sequence exists, then I can continue with other options.
   
   https://lichess.org/study/1LhspKix/9YE3d899#0
2. I am up a lot of material. In this case, winning more material is not required, so this might be a defensive puzzle. The main objective is to ward off the opponent's attack or perpetual check. Looking for attacking moves can be a waste of time in this case. It could even be beneficial to flip the board (figuratively or even physically) and look at the attacking possibilities from the opponent's perspective.
3. The material balance is not severely flipped to either side. This is quite common and requires further examination of the position.

After the material has been counted, I usually check if the opponent has checkmate threats. If they have, this is likely a checkmate puzzle, where you have to deliver it first, or a puzzle where you defend against the checkmate, while creating your own threats. In both cases, the list of candidate moves is usually short.

If the puzzle is clearly neither checkmate nor defensive puzzle, I try to list all the tactical ideas that I see in the position. I try to refrain from starting calculation of lines yet. More than once, have I calculated a long line, only to notice that I have missed something in the first move. Listing the ideas makes it easier to see, what moves should be considered. In lower rated puzzles, the correct course of action can already be seen at this point. But if the puzzle has a high rating, it means there is something non-obvious or laborious, because many have failed to solve it. In the following, I'll consider two kinds of positions that can cause troubles.

Sometimes there are lots of potential checks, captures, or threats. For lack of a better term, I call these messy puzzles. The challenge in these kind of positions is to find the correct moves among all the possibilities. It is also important to find the correct move order. As discussed in Part 1, there is only one solution, so my task is to refute all but one of the move sequences. There is no short cut, so I think the best approach is just to go through the move sequences one by one. This is tedious, but not necessarily difficult, at least if you do it systematically. It is not beneficial to worry about the complexity of the position, because this could lead to the temptation to take a short cut, and just choose a move even if the analysis is superficial, or spend time looking for a killer move that doesn't exist. Instead, each calculated line should be seen as a step towards the solution.

The opposite of a messy puzzle is a dry puzzle. So there are no checks, captures, or threats. Or the ones that are available are obviously bad. Such a position may also occur after an initial forced sequence. In these positions, the solution involves a quiet move. To find a quiet move, the first step is to find an idea that is so strong that the opponent has difficulties defending against it, even if they are given the right to move. There are usually hints such as weak squares, open files against the king, or uncoordinated pieces. The quiet move can be transferring a piece to a better attacking position or cutting of the opponent's pieces from the defense. The laborious part is then to go through all of the opponent's moves after the quiet move, because the response is not that forced as it is after a check, capture, or threat. But this task is also quite straightforward, albeit time consuming.

Note on Endgames

Related to the material situation is the question: is this an endgame? It seems that the percentage of endgame puzzles among all puzzles goes up with increasing puzzle rating. Instead of drawing the conclusion that endgames are difficult, I would look at the people who solve the puzzles. Rating is always relative to the population. So I think endgame puzzles having high ratings tells about hobby players' attitude towards the endgames. Typically, they are thought to be boring and kind of opposite to the tactical melee frequently seen in middlegames. But I would argue that endgames are the most tactical phase of the game, the type of tactics is just different.

Endgame puzzles are specific types of puzzles, because there is some theoretical knowledge that can be helpful, when solving them. Knowing basic endgames, such as those presented in Jesus de la Villa's book 100 Endgames You Must Know (any similar book will do) can be crucial when there is only very little material left. In some cases, the game is still theoretically drawn, although one side is up a lot of material.

Another thing that makes endgame puzzles special is the importance of promotion. So creating passed pawns, pushing them, and stopping the opponent's passers are important. Often it comes down to one tempo deciding who promotes first. Also the role of the kings is more active. Finding the difference between two king moves can require a lot of calculation. But there are often subtle differences which separate a win from a draw or a loss.

Try to Find The Opponent's Best Moves

Attack is easier than defense. The reason is that we are often biased to our point of view. Our ideas seem more important than the opponent's ideas. Or at least thinking about our own moves feels more fun. Our moves drive our ideas forward, while the opponent's moves try to hinder them or advance their ideas to our detriment. Could the problem be that we are connecting our person to the position on the board, instead of thinking objectively?

What separates the top-GMs from us mortals is that they are very objective about chess positions. They consider ideas from both sides of the board. While they do care if they win or lose, and sometimes very much so, they seem to approach the positions like a scientist would approach an experiment. Or they are impartial like a referee in sports and approach each position as it is. Any emotion that could bias the view is harmful to the process of finding the best moves for both sides.

Trying to be impartial like a referee helps to see chances for both sides. (Image credit: https://pixabay.com/photos/basketball-game-jump-ball-referee-1608864/)

Many of the higher rated puzzles require that you find the best defense for the opponent. The logic is that if even one move by the opponent refutes a tactic, it is totally refuted, and you need to find another move to play. If you miss this one defensive move, you may end up choosing the wrong move for the solution. There is the temptation to play a move that almost works, and think that the missing pieces in our solution are not there just because we haven't found them yet. But in the higher rated puzzles, there can be many lines, that almost work, because that's what have lured people to wrong solutions. Acknowledging this can help to avoid choosing a move before finding a perfectly working solution.

So you should work as hard for finding the opponent's moves as you do for your own moves. In some positions, especially in the non-forcing ones, this could mean going through all of the opponent's responses to a move. I call this process scanning. One by one, I visualize the opponent's responses to my move, no matter how foolish they seem, and see if they refute my move. In an average middlegame position, there are about 40 moves, so this is tedious. But the process is also fool-proof, so I don't miss any moves, which could happen if I only went through moves that "do something" or that feel intuitive.

Analyze Puzzles Afterwards

Learning requires feedback. When solving a puzzle, you get the immediate feedback: correct or incorrect. But that's just a binary value. As such, it doesn't really do anything, but boosts your confidence or lowers it, unless you go a step further. So let's consider the levels of feedback:

1. Binary: Right or wrong?
2. Primary variation: What was the sequence of moves in the correct solution?
3. Analysis: Go through each move in the solution and all the reasonable responses by the opponent. Also find out why another move didn't work for us.
4. Classification of errors: Identify what types of errors you made in the calculations.
5. Introspection: Carefully consider possible reasons why you did certain types of errors.

Binary Results and Primary Variation

Unfortunately, it is too easy and too common to just jump to the next puzzle after you completed one, either successfully or not. As already mentioned, the binary right-or-wrong result doesn't help much. It doesn't give you actionable steps to remedy the problems with your thinking.

Only a little more effective is looking at the primary variation given in the puzzle solution. It could give you an aha-moment: "Oh, that's what I should have done!" But one should not confuse understanding the correct solution in a position with understanding what went wrong in your thinking process. The position is unique, so the solution doesn't really generalize into other positions without some extra steps.

Analysis

Also an important point is that, regardless of the results, you need to know what you did right and what went wrong. You cannot assume, you got everything right even if you played correct moves in the puzzle. It is totally possible to play the right move for wrong reasons. Or the puzzle ended before a critical move, which you would have needed to play to justify the earlier choices. So spending time doing the analysis helps to see what you actually missed.

Fortunately, computers can help with the analysis of tactical positions afterwards. Just start with the puzzle position, switch on Stockfish, and see what was the move the computer suggests. If you got the move right, go forward and see all the opponent's moves that are reasonable defensive tries. Did you find them all? If you did, good for you, but if you didn't, you have some material for the next steps. Also, if you got your move wrong in the first place, you should go and see the computers refutation.

Sometimes seeing the computer's moves don't make sense at first. Then, comparing the variations after different moves may reveal some details that make other moves work and other ones fail. For example, if you got your move wrong, go and see the computer's refutation, then go to the correct move, and play the refutation against it. Seeing why the refutation fails in this case can help you to appreciate the details that differentiate the moves.

Another way to go through the puzzles is to play them against the computer. This can be helpful in the endgames and also when the resulting position feels unclear. It is OK to take back moves and try other approaches until you are convinced that the moves in the solution are indeed the best ones.

Classification and Introspection

People often quickly brush off their failures, because they come with uncomfortable feelings. But these feelings can be used for learning. If you can identifying the specific errors you made and associate them with these feelings, you are probably going to pay more attention in the situations, where these types of errors are likely to occur in the future.

Having analyzed the puzzle positions carefully, there should be material for further analysis. Even if one has played the moves required by the puzzle, there can still be moves that were missed. These mistakes can be categorized in order to generalize the types of mistakes. It's difficult to give an exhaustive list of categories, because people make different types of mistakes. However, the categories should be wide enough to be applicable to a large number of positions. On the other hand, they should be narrow enough to address the specific needs of a person. As an example, here are some mistakes that I have made recently:

• Missing that the opponent can close an essential file for my attack by moving their pawn passed my pawn, instead of letting me take the pawn, which would have opened the file
• Missing that after an initial exchange of pieces, the opponent's recapturing piece could help in defense, because it was now in a different position
• Missing a check the opponent could deliver after my pieces give up the control of a square
• Missing that a piece that was doing an offensive task could move backwards to help in defense after its path had been cleared, when another piece moved away

These mistakes, that are all related to missing a defensive resource, could be further classified into more general categories such as:

• Closing a file for defense
• Defense by a piece that is not initially available
• Backwards move in defense
• Checks by the defending side

Ideally, there could be custom-made puzzles to train these areas, but in practice, it's very difficult to find such puzzle categories. The second best option is to pay special attention to the types of mistakes that were revealed by the analyzes for a while. Hopefully, the process of looking for those types of mistakes becomes automatic.

To improve, you must be able to reflect on your thoughts and emotions that lead to your decisions, especially the faulty ones. (Image credit: https://pixabay.com/photos/man-think-young-thinking-male-1276384/)

In the end, the most important question is: Why? Knowing what you did wrong only helps, if you know how to avoid repeating the same mistake. "I was just careless", you might say, but it doesn't improve your puzzle solving abilities a bit. A more useful answer requires some introspection. Again, giving a generic list of questions for the introspection is difficult, but one should try to trace the thoughts and emotions during the decision process that lead to an incorrect move or omission. As an example, I came up with the following explanations for the first two cases above:

• After a long period of calculation, I found a move that I thought was brilliant. I had calculated other moves and found defenses for the opponent, but now this move worked after all those defensive moves, so I ended up choosing the move. However, the "brilliant" move was refuted by a move that was not among the defenses to the other tries. So the problem was twofold: I was too excited to find a move that looked good so that lost my objectivity, and I considered only candidate moves for the opponent that I had for the other variations, but didn't consider those specifically for this move. So actionable steps to avoid these in the future: 1) if I find a move, that I think is brilliant, calm down and calculate first, 2) re-compile the list of candidate moves for the opponent after each of my moves.
• I had calculated an idea that almost worked, but it didn't, because of a certain piece covered a key square. Then I thought about exchanging off that piece first and only then applying the idea. I thought that worked, because the opponent's recapturing piece didn't prevent that plan around that square. However, I missed that the recapturing piece could move to another square, that wasn't available before the exchange, where it could participate in the defense in another way. My mistake was that I didn't consider a defensive idea that wasn't available in the initial position or in the other variations. An actionable step in this case is: after the opponent's pieces move, check if there are new defensive ideas.

It can be useful to try to find faulty thinking patterns after the introspection. For example, I can see that in both of the examples above, I have thought carefully about some variations, but then just "copied" the analysis to another variation, which I thought fixed a problem, without considering the specifics of that variation. You may find similar or other kinds of patterns in your introspection.

Concluding Remarks

This blog post was about improving the puzzle rating. While this goal may not be that meaningful in itself, it means that you will be solving harder puzzles, which hopefully translates into better calculation skills. Only the first piece of advice in this article was specific to puzzles, but the others can be applied to games as well.

One could argue that paying attention to your opponent's ideas is even more important in games, where it is not known that you are winning. It is also vital to avoid moves that almost work, but not quite. Higher rated players usually find the only-moves, because if the alternative is to lose, they use all their skills and energy in finding a defense.

And finally, analysis and introspection are ways to improve your game too. But that's a topic for another blog post.