Authors: Karel van Delft, Johan Hellsten, Dries Wedda
‘Reversed thinking is an element of thinking in chess that is underestimated’, says GM Artur Yusupov. ‘It is worth having a look at how it is connected with forward thinking and what we are doing basically, how we solve our problems, how we solve chess, sometimes consciously, sometimes unconsciously. We don’t have too much literature about it.’
Does reversed thinking in chess lead to better results, compared to forward thinking? If so, how and in what domains in chess? Or is bi-directional thinking the best way to go? Is reversed thinking trainable? If so, how? A research group of the Chessable science team asked 16 chess experts via a questionnaire about such questions.
It would seem that to be able to apply reversed thinking, a certain level of knowledge is necessary. It is important to be familiar with patterns. Recognizing them directs your thinking. The key might be repeatedly learning and practicing patterns with the same motif from simple to more complex forms.
The danger with solving positions on sites and in books is that there are solutions. To prevent false assumptions a trainer could show positions which look similar but they are not. It is also interesting to take the perspective of the defender and look for one move backwards.
Since it became clear ‘solving’ is too narrow a formulation, we chose for the broader term ‘thinking’.This research is a follow-up to a ‘Forward vs Reversed Solving’ project that the science team did in 2021 and 2022. In that research, 95 chess players via online tests solved mate patterns. In one of two conditions participants got mate-in-one positions that were followed by complex puzzles with the same end positions (in the reversed condition). Participants in the other (forward) condition received random mate-in-one puzzles, but the same complex puzzle as in the other condition. Contrary to expectations there were no significant differences in the outcomes of the tests.
A blog and report were published on the Chessable site:
Blog Prof. Barry Hymer: https://www.chessable.com/blog/solving-puzzles-backwards
Report Karel van Delft: https://www.chessable.com/blog/wp-content/uploads/2022/04/reversed-solving-research-paper-FINAL-22-march.pdf
There were several speculations about the outcomes of the research. In a conversation, GM Artur Yusupov showed Karel van Delft a Zinar study in which reversed thinking is the best way to go.
This led to follow-up research via a questionnaire for 16 chess experts. This is what Prof. A.D. de Groot in his empirical cycle called the ‘evaluation phase’.
The 16 respondents were informed about the reasons for the research. They were asked to watch two short videos, read an introduction and answer questions.
1. A video presentation by Karel van Delft in June 2022 at an online chess education conference from the FIDE Education commission and the ASPU ‘Chess’ Research Institute from the University of Yerevan in Armenia. See https://www.youtube.com/watch?v=uWw2z7Sg4B8 (from 4:23:05 min).
2. A video with GM Artur Yusupov and Karel van Delft discussing the outcomes of the research. Yusupov thinks reversed solving is a good method when solving some endgame positions with pawns and zugzwang. See https://www.youtube.com/watch?v=uULjGv46Guo
The research group consists of GM Johan Hellsten, Dries Wedda and Chessable science project manager Karel van Delft, who coordinates the project.
The 16 respondents to the questionnaire are GM Alon Greenfeld, GM Peter Wells, GM Johan Hellsten, GM David Smerdon, GM Max Warmerdam, GM Stefan Kindermann, IM and GM of chess composition Yochanan Afek, IM Arthur van de Oudeweetering, IM Ido Ben-Artzi, IM Merijn van Delft, IM Thomas Beerdsen, FM Nate Solon, CM Can Kabadayi, CCE Alan Bester, Dries Wedda, and Erick Takawira. Of these, Johan Hellsten and Dries Wedda also are involved in the research group. All respondents agreed to mention their names in the report. GM Artur Yusupov, Prof. Barry Hymer and Prof. Roland Grabner gave feedback on the research.
Here we sum up per question remarkable responses. The full report shows the complete answers.
Respondents mention concentrating on solving mating positions is very concrete, but just a limited aspect of what is going on in chess. In endgames, strategic middlegames and reversed studies thinking can play another role.
Some respondents expected more impact in the first research from mating patterns as prompts (via pattern recognition) for more complex mates.
Possible reasons for why there were no significant differences between forward and reversed conditions in the former research were mentioned. Forward thinking is the most common way of thinking in chess. Reversed thinking may seem artificial or is not considered at all. Even if trained in reversed thinking, many players stick to old habits. In the former research, the strongest participants might be strong enough to find the solution by forward thinking, while many weaker players might be too weak to make connections.
It was suggested that by training and verbal explanation in advance the relationship between simple and complex patterns might have led to higher scores. It also might have made a difference if the test positions had been based on more familiar motifs, because they are more rooted in the chess players’ intuition.
Reversed thinking (which often happens unconsciously) might be a powerful tool, but only strong players can use it. They however could benefit from conscious use of it. Planning and decision making might profit when forward and reversed thinking are combined. A methodological issue was suggested: in addition to solving percentages, response times in tests are also important.
Respondents were struck by what GM Artur Yusupov had to say about pawn endgames and corresponding squares in relation to zugzwang. Note that to reason reversed players need to have knowledge of theoretical endgames (strategical or tactical) to start reversed thinking. So this tool only can be used by strong players. Some respondents say the best way to go is a combination of forward and backward thinking.
Some respondents wonder how useful reversed thinking is during their own games. Others say they will give it more thought because it might be useful for them. How trainable is reversed thinking?
Reversed thinking is not exclusively a weapon for the attacker – the defender can use it to find ways to obstruct the plan of the attacker. Elimination of possibilities (‘branching factor’) is important. Route planning exercises are suggested such as the Dutch Steps method.
Some respondents apply reversed thinking in games and/or training. It is not always seen as efficient in practical play. A GM uses it as a demonstration during trainings with students to show what he calls ‘fixing a line during calculation’. Reversed thinking implies an optimal position one should aim for. But who tells you during a game what the optimal position is? A suggestion to think about an optimal position is asking yourself which piece of the opponent should be eliminated for a variation to work. Then you can proceed via reversed thinking to the initial position. Several trainers show their students first basic tactical or strategical ideas and then more complex ones where the same motif is the kernel. A GM respondent makes an association with prophylaxis. He asks students to find the opponent’s plan. Then he asks them to prevent it. So they have to think forward and then think back how to stop it. Reversed thinking is definitely used for composing endgame studies. A study is most often created by starting at the final highlight and creating the solution backward. A few respondents use the reversed thinking methodology as authors in their Chessable courses.
Several respondents say reversed thinking can be useful in pawn endgames and combinations. Also, sometimes in strategy, for example when making decisions in trading pieces. In the case of strategy with long-term goals, there is not a concrete optimal position, but more a kind of position with certain characteristics. In openings there might be possibilities to compare superficially unrelated positions. Some respondents say they think reversed thinking is useful for every area in chess, since it is always helpful to create an image of where you would like to go and then do some sort of reversed thinking. A respondent says he thinks you could use it to figure out where your pieces are best placed to start or continue an attack. A comparison is made with how Capablanca approached positions.
In his book ‘Chess Recipes from the Grandmaster’s Kitchen’, GM Valeri Beim says ‘inverse thinking’ is ‘frequently applied, rarely formulated’. There is a relation with pattern recognition and how reversed thinking is used in many study books. A question mark is put at Beim’s definition of what he calls ‘inverse thinking’ as the ‘ability of a player to recognize familiar…motifs in an unfamiliar position.’ A respondent feels Beim’s book touches more on pattern recognition and general principles than on the principle of practicing the method of inverse thinking.
Also mentioned is Jon Tisdall’s book ‘Improve Your Chess Now’, particularly the lengthy Chapter 4 ‘Pattern Training and other useful exercises’.
An example of retrograde chess puzzles is the book ‘Chess mysteries of Sherlock Holmes’ by Raymond Smullyan.
Reversed thinking is one of the steps in the book ‘Köningsplan’ (Kingsplan) by GM Stefan Kindermann and GM of chess composition Robert K. von Weizäcker.
A respondent thinks many books related to chess strategy describe a reversed thinking concept. For example, chapter 6 in ‘Endgame strategy’ by Shershevsky describes schematic thinking and draws on similar things.
There is broad consensus that the concept ‘reversed solving’ is too narrow. ‘Reversed thinking’ better describes the broad array of cognitive processes involved.
Respondents gave several suggestions for follow-up research. A new test could include more typical patterns, for example mate images, positional goals, endgame themes, etc. Benefits of reversed thinking methods could be found via online experiments on a more massive scale by e.g., a platform like Chess.com, including the suggestions by Grabner to explore the psychological mechanisms. That would vastly increase statistical power to detect a main effect as well as heterogeneous effects by strength, age and gender (which the first study of 95 participants didn’t have).
Making training methods explicit and guiding the students on what they should look for are suggested.
The two positions on the top of this introduction are from the game Alexander Alekhine vs. Fred Dewhirst Yates, London 1922. See https://www.chessgames.com/perl/chessgame?gid=1012123
About the authors:
Karel van Delft is the science project manager of Chessable. He is the author of the book ‘Chess For Educators’ and co-author of the book ‘Developing Chess Talent’. He is running Schaakacademie Apeldoorn (Chess Academy Apeldoorn, www.chesstalent.com) in The Netherlands.
GM Johan Hellsten is a chess trainer in Ecuador. He is a former Swedish champion and the author of several Chessable courses, including ‘Mastering Chess Strategy’.
Dries Wedda studies Artificial Intelligence at the Rijksuniversiteit Groningen. He is an online international chess trainer from The Netherlands.
Correspondence: [email protected]