## Thursday, 1 September 2011

### The Susan Polgar Experiment

My next experiment was with Susan Polgar‘s Chess Tactics for Champions.  This book contains 570 problems.  I divided them into four batches (of 142 or 143), 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.  The early part of my schedule was:

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. This schedule is the same as for the Woolum and CHP Experiments, but with the omission of the third pass in those experiments.  For the first nine passes, the day on which each pass takes place is given by the table:

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

From Pass = 3 onwards, the pass takes place on Day = 1.92 ^ Pass, rounded to the nearest whole number.  I used the Empirical Rabbit Timer to time my solutions and collect the results.  Incorrect solution times were counted as more than 40 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 comparison of my performance on my first pass through batch A with corresponding performances in previous experiments:

Where H+P denotes Heisman + Pandlofini (in the CHP Experiment).  (0-5 denotes 0-4.999..., and similarly for the other “buckets”.)   SPolgar was clearly harder than the previous problem sets, but I nonetheless did better on my first pass through SPolgar than on my first pass through Bain, which is much easier.  Here are the results for the first six passes through batch A:

Despite reducing the number of passes in the first eight days from four to three, I made good progress here.  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-D:

(0-5 denotes 0-4.999... seconds, and similarly for the other “buckets”.)   Again, I appear to have made progress, but a large number of difficult problems in batch D rather rained on my parade!  (A poor performance on the day does not appear to be the explanation here. On the first pass, 33% of the problems that took me over 40 seconds were in batch D. On the second pass 34% of the problems that took me over 40 seconds were in batch D.  Batch D appears to be harder than the others.)  The rough calculation that I presented last month gives the graph:

SPolgar: Rating Difference vs. Problems Learned

This graph, in conjunction with that for Heisman + Pandolfini (H+P), suggests that SPolgar is about 130 Elo points harder than H+P.  The graph also suggests that my improvement during the SPolgar Experiment was about 25 Elo points.  (The corresponding standard deviation is about 14 Elo points, so there is a high level of uncertainty in this number.)  25 points may not sound much, but 25 points in one month would be excellent progress!  My graphs also suggests that, between starting the first batch in the Bain Experiment and finishing the last batch of SPolgar, I improved by about 100 Elo points + the rating difference between Bain and SPolgar.  I expect that SPolgar is a good 200 Elo points harder than Bain.  I do not have any good way of checking this, but someone who is unfamiliar with both problem sets could time themselves solving both, and estimate the rating difference.

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

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