The Ivashchenko 1b Experiment

My next experiment was with Sergey Ivashchenko‘s Chess School 1b, which comprises Stage 4 and Stage 5 of Chess School.  I divided the book into four batches, which I labelled A to D.  Batch A was the 1st, 5th, 9th problem, and so on.  Batch B was the 2nd, 6th, 10th problem, and so on.  Batches C and D were constructed in the same way.  I found that I had bitten off more than I could chew here.  The endgame studies at the end of Stage 5 caused me particular trouble, so I set them aside, which left me with 539 problems (134 or 135 problems per batch).  The early part of my schedule was the same as for the Susan Polgar Experiment:

         Sa  Mo  Fr  Fr  We  Mo  
Week 1:  A1, A2, A3              Days: 1-7
Week 2:  B1, B2, B3, A4          Days: 8-14
Week 3:  C1, C2, C3, B4          Days: 15-21
Week 4:  D1, D2, D3, C4, A5      Days: 22-28
Week 5:              D4, B5      Days: 29-35
Week 6:                  C5      Days: 36-42
Week 7:                  D5      Days: 43-49
Week 8:                      A6  Days: 50-56
Week 9:                      B6  Days: 57-63

Where A1, A2, A3.… are  passes 1, 2, 3... of batch A, and similarly for the other batches. For the first nine passes, the day on which each pass takes place was again given by the table:

Pass: 1  2  3  4   5   6   7   8    9
Day:  1  3  7  14  26  50  96  185  355

I again used the Empirical Rabbit Timer to time my solutions and collect the results. Incorrect solution times were counted as more than 60 seconds irrespective of the actual time spent.  I counted my solution as correct if I got the right idea and the right first move. Here is a cumulative graph of my first pass through each of the batches:












The results show a rising trend for time limits of 30 seconds and more.  Here is a comparison of my performances for my first pass through the batches of the Susan Polgar Experiment, Stage 4 and Stage 5:













(N.B. I have aggregated the results over all the problem batches here, for each problem set.  0-5 denotes 0-4.999... seconds, and similarly for the other “buckets”.)  It is clear that I found Stage 4 harder than SPolgar, despite any improvement that I made between the corresponding batches for the two experiments.  It is also clear that I found Stage 5 harder than Stage 4.  Here are the results for my first pass through each batch for Stage 4:













I appear to have made good progress here, particularly for the longer time limits.  The results for my first pass through each batch for Stage 5 were less tidy:












I appear to have made good progress here too, for time limits over 30 seconds, except for batch D, which appears to have been harder then the others.  For Stage 4, the problems are divided into sections according to the problem type.  My method of dividing the problems into batches ensures that each of the four batches contain (nearly) equal numbers of each type of problem, which helps to equalise the difficulty of the batches.  In contrast, the problems in Stage 5 are in random order, which does not help here.

Applying the method of calculation that I described in my earlier article, Rating Points Revisited, to the whole of 1b, gives the table:

Sec   Gain    SD    Gain/SD
 5     46     55     0.84
10      8     43     0.19
15      1     38     0.03
20    -13     38    -0.34
25    -24     44    -0.55
30     41     47     0.87
35     49     54     0.91
40     59     91     0.65
45     68     65     1.05
50     78     84     0.93
55     94    106     0.89
60     71    114     0.62

Where Sec is the time limit, Gain is the Elo points gain, and SD is the corresponding standard deviation.  The accuracy here is one standard deviation at best, so we cannot draw any reliable conclusions, but it is likely that I made a significant improvement.  The same method of calculation suggests that Stage 4 is about 100 Elo points harder than SPolgar, and Stage 5 is about 50 points harder still.

For an update, see my later article: Susan Polgar + Ivaschenko Revision.