It was time to review my progress, and look for ways to speed up my tactics training. There were a number of issues to address.
Redo problems that give me trouble? In the Woolum Experiment, I repeated the 25% of the problems that had given me the most trouble on Pass 6. I repeated them half way between Pass 6 and Pass 7, to maximise their effect on long term memory. (N.B. Passes 1 to 8 took place on days 1, 3, 5, 7, 14, 26, 50 and 96.) The chart below shows my results aggregated over all six problem batches for Passes 3 to 6:
(0-5 denotes 0-4.99... seconds, and so on.) Not surprisingly perhaps, repeating the harder problems did not noticeably slow the decline in the number of problems that I was able to solve in under 5 seconds. It also did not clearly reduce the number of problems that took me over 20 seconds, which does not appear to have been a problem anyway. I repeated this measure on the first three batches in the CHP Experiment (which had the same schedule), and it did not show any benefit there either. I decided that the peak at Pass 4, in the number of problems that I could solve in under 5 seconds, was probably the result of doing too much work in the first 8 days, rather than too little subsequently.
Omit Pass 3? In the CHP Experiment, I found that repeating the 25% of problems that gave me the most trouble on Pass 1 (half way between Pass 1 and Pass 2) had almost no benefit a week later. I also found that restricting Pass 3 to the 25% of problems that gave me the most trouble on Pass 2 had no discernible effect on my results nine days later. Since replacing Pass 3 with something ineffective did not have any lasting effect, it seemed highly likely that I could omit Pass 3 entirely without any lasting effect. Having to work harder as a result of omitting Pass 3 might even improve the learning process, particularly for harder problems. It was worth a try! The resulting schedule was remarkably close to my original conception for the Reinfeld Experiment, but with more precise timings.
Move to harder problems? In the CHP Experiment, the problem set from Jeff Coakley’s Winning Chess Strategy for Kids appeared to have been ineffective. I exceeded my best performance in the Bain Experiment from the outset, and did not measurably improve. This result suggests that I should move on to more difficult problems. The next three books on my list were: Susan Polgar’s Chess Tactics for Champions, Sergey Ivashchenko’s Chess School 1b and Jeff Coakley’s Winning Chess Exercises for Kids. The Susan Polgar book looked the easiest of the three, and the other two looked to be of a similar level of difficulty, with Coakley probably the harder. Coakley had the most exercises, and split well into ten problem batches, which looked likely to be of roughly equal difficulty. The other two books looked best suited to short experiments to adapt my methods to harder problems. (I decided to use only four problem batches for Polgar and Ivashchenko to speed things up, at the cost of making it more difficult to measure progress.)
Continue with speed training? Another issue that I had to address here was whether to continue with my speed training in which I gave myself full marks for finding the right first move and the right idea. This is ideal for developing my ability to spot tactics quickly, but potentially encourages impatience and sloppiness. However, that is only one cause of mistakes - the more important cause is failure to see moves. (N.B. When speed training, I stop the clock when I think that I have found the solution, but then I check my solution. If I find a mistake, I have another try at finding the correct solution. If I fail to find a solution within the time limit, I have another quick look at the position. It is surprising how often the solution pops up as soon as the time pressure has gone! If even that fails, I always take the trouble to study the solution carefully.)
When to stop? My pattern matching model suggests that Woolum was sampled from about 1,000 patterns (see my earlier article A Pattern Matching Model). When I get to Pass 9 of Woolum, I will have solved about 3,000 other problems one or more times since beginning Pass 8. These 3,000 problems should contain about 95% of the patterns in Woolum (see my earlier article Distinct Random Selections). There will then be little point carrying out Pass 9. Any fall in my performance at Woolum should mostly be the result of fading memory of the positions, rather than forgetting the underlying patterns. (If you take on problems at a slower rate, you may have to carry out extra repetitions to reach this stage.) If I had missed out Pass 3, I would have needed only seven passes to reach this stage. After Pass 1, subsequent passes take about half as long, so the level of effort in doing seven passes is about four times that of doing one pass.
In summary, decided to:
* Not use extra passes for problems that were giving me trouble.
* Remove Pass 3 from my schedule.
* Move on to Polgar, Ivashchenko and then to Coakley.
* Continue with speed training.
* Finish Woolum at Pass 8.
[I later decided to also stop CHP at Pass 8.]