My current focus is on what I shall call the Expanding Repetitions (ER) method for improving your chess tactics. This method was inspired by Michael de la Maza’s 7 Circles, and Dan Heisman’s Novice Nook articles:
The 7 Circles and ER methods are similar in that with both, you solve tactics problems repeatedly, but there are some important differences:
* With the 7 Circles method, you tackle 1,000 problems all in one go, solving them 7 times, whereas with the ER method, you tackle problems in bite sized chunks that you can solve (or have a good attempt at it) within one day’s study time.
* With the 7 Circles method, you halve the time interval between each repetition (64 days, 32 days, 16 days, 8 days, 4 days, and 2 days), whereas in the ER method you roughly double it (e.g. 1 day, 2 days, 4 days, 8 days, 16 days, 32 days, 64 days…).
* The 7 Circles method is once and for all exercise, whereas the ER method is an incremental process that you can continue for your entire chess playing life, or for a long as you need it.
The main motivation for the ER method was my experience of studying tactics. My main insight was that although I learned a lot from my training, I soon forgot most of it! I decided to adapt a heavy duty learning system that I had devised as a student, and try it on Fred Reinfeld‘s 1,001 Winning Chess Sacrifices and Combinations. Shortly after starting my experiment, I discovered that cognitive psychologists had got there first, and that expanding the intervals between each repetition was the standard approach, and formed the basis of many successful systems for learning by repetition, notably those for learning foreign languages:
(Cognitive psychologists use the term Spaced Repetition, which is defined to be learning by repetition with expanding intervals between each repetition. This is confusing in a chess context, in which the 7 Circles method uses spaced repetitions, but decreases the intervals between them.)
I subsequently found out that the repetition scheme that worked best in my tests was similar to that underlying the SuperMemo learning system:
Most learning systems present the questions that are causing difficulty more often than those that are not, but this approach is problematic when applied to chess problems - where you will be spending proportionately more time on the difficult ones anyway - but this technique is not fundamental to SuperMemo.
The main benefits of the ER method are:
(1). You do not have to learn and forget. The closely spaced repetitions allow a high level of capability to be built up rapidly, and the more widely spaced repetitions ensure that this capability is retained.
(2). A large commitment of time is not required. A little effort often is all that is needed - but a lot of effort often will work quicker!
(3). Superhuman efforts are not required. You do not have to solve 1,000 problems in a day!
(4). Blind faith is not required. The method can measure your progress, not only from one repetition to the next, but also on problems that you have never seen before. This can be accomplished by presenting the problems as a series of “tactics exams”, and comparing your performances when each one is tackled for the first time.
I found many references to using standard learning systems for chess - particularly for memorising openings - but only one reference to applying these techniques to chess tactics:
I have only been able to scratch the surface in this introduction, but will flesh it out in future posts.