Encouraged by my success with the Bain Experiment, I decided to conduct a similar experiment with the next book on Dan Heisman’s list: Al Woolum’s Chess Tactics Workbook. The main part of this book has 132 pages of problems with six problems per page, i.e. 792 problems. (This is just over twice the 388 problems in my issue of Bain, after excluding Bain’s exact duplicates and the two duds.) I divided the 792 problems into six batches of 132 problems, which I labelled A to F. Batch A was the first diagram on each page, batch B was the second diagram on each page, and so on. The problems on each page appeared to be in random order of difficulty. I did not have any good argument that each problem batch was of the same level of difficulty, but thought it unlikely that Woolum would have deliberately made the later problems on a page easier than the earlier ones. The early part of my schedule was:
Sat Mon Wed Fri Fri Wed Mon
Week 1: A1, A2, A3, A4 Days: 1-7
Week 2: B1, B2, B3, B4, A5 Days: 8-14
Week 3: C1, C2, C3, C4, B5 Days: 15-21
Week 4: D1, D2, D3, D4, C5, A6 Days: 22-28
Week 5: E1, E2, E3, E4, D5, B6 Days: 29-35
Week 6: F1, F2, F3, F4, E5, C6 Days: 36-42
Week 7: F5, D6 Days: 43-49
Week 8: E6, A7 Days: 50-56
Week 9: F6, B7 Days: 57-63
Where A1, A2, A3.… are passes 1, 2, 3... of batch A, and similarly for the other batches. I did my first four passes of each batch at two day intervals on a Saturday, Monday, Wednesday and Friday. I did the fifth pass of each batch on a Friday, and the sixth pass on a Wednesday. This schedule is a slightly more aggressive version of the one that I used for batches C+D and E+F in the Bain Experiment. For the first ten passes, the day on which each pass takes place is given by the table:
Pass: 1 2 3 4 5 6 7 8 9 10
Day: 1 3 5 7 14 26 50 96 185 355
From Pass = 4 onwards, the pass takes place on Day = 1.92 ^ (Pass-1), rounded to the nearest whole number. I used the Empirical Rabbit Timer to time my solutions and collect the results. As in the Bain Experiment, incorrect solution times were counted as more than 30 seconds irrespective of the actual time spent. In Woolum, the title at the top of each page often gives essential information, such as mate in 2 (i.e. mate in 3 is not acceptable). The title also usually gives a helpful clue for finding the solution, but is sometimes highly misleading. I decided not to hide the title. I was reasonably generous with the scoring, counting my solution as correct if I got the right idea and the right first move. Here is a comparison of my performance on my first pass through batches A+B, C+D and E+F in the Bain Experiment, and my first pass through batch A in the Woolum Experiment:
(0-5 denotes 0-4.999... seconds, and similarly for the other “buckets”.) I did worse on Woolum A1 than I did on Bain E1+F1, which is not surprising because Woolum is harder overall than Bain, and contains many problems which are unlike anything in Bain. I did better on Woolum A1 than on Bain A1+B1 and about the same as on Bain C1+D1, except for the increased number of solution times over 30 seconds. Woolum has a sizable proportion of easy problems, but its harder problems are a lot harder than anything in Bain, which accounts for the larger number of solution times over 30 seconds. Not surprisingly, I improved at the problems I was practicing, but what about problems that I had never seen before? Here is my performance on my first passes through batches A-F:
Clearly, the overall picture here is one of steady improvement. My best performance was just little behind that on Bain E1+F1, which was much easier. However, my performance on the last two batches had fallen a little. Possible explanations are:
(1). The last two problems on each page were harder, on average, than the problems earlier on the page.
(2). The fall off was due to chance variations in my performance.
(3). My rate of improvement had slowed.
The next diagram shows my performance on the fourth pass through each of the batches:
Even after four passes my relative performances on the last three batches were similar to those on the first pass. This suggests that the fall off in my performance on the last two batches occurred because they were harder. This is another very encouraging result for this training method.
For an update, see my later article: Basic Tactics Revision.