Introduction
One of
Dan Heisman's list of recommended books is Bain's
Chess Tactics for Students. In the note, he provides a guide for completing that book using a spaced repetition method (
Edit: I now understand that it isn't really spaced repetition because, with that method, you typically increase the length of time between successful solves (and decrease review time for those problems you miss). My method reviews all problems regardless of accuracy and consistently decreases review time, thus being more like the woodpecker method). Here's my rough outline of that guide:
1) Set a limit of 5 minutes per problem the first time through the book. If you don't get the answer, look it up.
2) Each time through the book, cut the time in half.
3) Repeat going through the book faster and faster until you can get 85%+ within 10-15 seconds per problem.
It's some form of de la Maza's Seven Circles Method.
1001 Chess Exercises for Beginners is quite an easy book for me and that's the book I've chosen to start with. I'd already started working through the first part of the book multiple times when I came across Dan's list. The first half of the book encompasses 492 problems categorized by motif along with hints so it's pretty easy to find the right idea. So at the time of writing, I'd decided to wrap up the first half and then more diligently follow this Seven Circles Method for the later sections.
Here's my plan moving forward:
1) Complete the 492 problems with 95+% accuracy (completed 6/19).
2) Complete the other sections of the book in piecemeal fashion, doing small 150-200 problem sections at a time until I can complete them at a rate of ~15 seconds per problem with 95% accuracy.
3) Systematically review all problems.
4) Complete the entire book in one day with at least 85% accuracy.
The Four (Half-Assed) Circles through first 492 problems
I just completed this last weekend, June 19. What a crazy Friday night. For my records, here are the solutions I got incorrect:
[removed to different section] That list will be helpful to review before I try the entire book! I finished with 477 correct out of 492, or
96.95% accuracy.
The REAL Seven Circles
I should note that the Seven Circles idea is not without controversy, probably due to some things I mention in the
Reflections section below. I'm just going to ignore that and use it as a reason to continue to train tactics diligently. I tend to be better at finishing things if I keep metrics on my progress and the Seven Circles method is a format that allows me to do just that. My only other note is that the study routine requires going through 1000 chess exercises
every cycle. As already explained, I'm breaking the second half of this book into smaller subsets, only to try the final 1001 exercises later on. Here is the breakdown for the second half of the book:
Mixed Motifs - White to Move
Problems 493-690 - 198 total
Mixed Motifs - Black to Move
Problems 691-864 - 174 total
81 Mate-in-3 problems
33 Mate-in-4 problems
23 Curiosities
I will begin with the 198 White to Move problems. As inspiration, I'm taking ideas from
this blog and so I will take some statistics throughout my work. For each problem, I will start a timer, get my solution, and write it down along with how long it took me and whether it was correct. I'll compile and summarize numbers at the end.
Seven Circles for Mixed Motifs - White to Move
My goal is to complete the set with 95% accuracy at a rate of ~15 seconds per problem. I hope it doesn't take me seven cycles, but we shall see. Once I reach that milestone, I know it's time to move on to the next section.
Cycle 1 (completed 6/25):
Number of days of study:
4
Overall Time:
5h 11m (18669 seconds)
Time per problem:
94 sec/problem
Overall Accuracy:
87.88%
Cycle 2 (completed 6/29):
Number of days of study:
2
Overall Time:
2h 1m (7260 seconds)
Time per problem:
36.7 sec/problem
Overall Accuracy:
92.9%
Cycle 3 (completed 6/30):
Number of days of study:
1
Overall Time:
47m (2843 seconds)
Time per problem:
14.3 sec/problem
Overall Accuracy:
97.3%
Summary:
So after three cycles, I've reached my goal for the
Mixed Motifs - White to Move section. As expected, my accuracy improved and I went faster each time. Here are some graphs to visually represent how quickly the time-to-solve metrics dropped after each cycle. To make them easier to read, I decided to segment the time metric into larger "chunks" of time.
So in the above graph, you can see the blue bars are my first cycle through the set of 198 problems. As mentioned, the problem set is relatively easy for me and I did a pretty good job of solving many of them in 0-30 seconds or 31-60 seconds. Granted some were incorrect but I decided not to display them in this graph since I was more concerned with showing how time-to-solve changed through the cycles. As expected, the blue bars are more evenly distributed throughout the time chunks but with the second cycle (orange bars) and third cycle (gray), I started to get a lot more confident and faster in my solving. The third cycle shows nearly all were solved within 1 minute.
Here's a graph of smaller 5- or 10-second chunks:
This shows a little bit more detail. Looking at cycle 1 first, you can now see how many took me over 60 seconds to solve. The second cycle shows more even distribution and by the third cycle, I was solving a lot more under five or ten seconds.
Here's the data:
The Rest of the Second Half (edited on July 24)
I did the same process on the other sections from the second half of the book (509 problems) but I'll forego any deeper analysis. Here's a quick summary of my time spent working on the second half:
- June 22 to July 23 - I completed the second half in piecemeal fashion.
- 19 sessions (days) of solving
- 13 rest days
- 1527 total tactics solved
- 80.4 tactics solved per session
Reflections on the Second Half
I cannot say for sure if this is worth it.
:)
It's at least interesting to do and I encourage everyone to try it. It gives you a sense of mastery of tactics but I'd guess it is partly artificial. I sensed a feeling of "memorizing the book" on more than one occasion. To be fair, I certainly also noticed times where I was picking up on general patterns, my eye quickly jumping to the idea, and only needing a quick calculation check before I had the solution (the goal I think!).
If I recall correctly, in the introduction to
The Woodpecker Method, the authors state that the reader should make it a point to go through ALL calculation no matter which cycle you're doing. I found that during my final cycles, because I was timing myself and I was aiming for the quickest solve that was possible, I would often get the idea and stop the clock after 1 second. I wasn't doing the full calculation.
When I say I was "memorizing the book" I mean to say that there are some puzzles in this set of 198 (and in the larger set in the first half of the book I'd done previously) where I had simply made some mental shortcuts. I had been noticing small little details in the position, say an unusual king placement in relation to pieces, and I really quickly remember that puzzle in particular and I see the move instantly. No extra calculation required. Going through the positions the third cycle, an obvious example might be "Oh this is that one where the king is boxed in by two rooks and I have that simple queen fork." I may have just been remembering "king boxed in, so play the queen-fork" without checking for counter-play or other moves the opponent might have.
Another example is an endgame problem I remember taking me over four minutes to solve and I didn't get the solution right the first time. The solution was a crazy castle-queenside move that ended up forking two pieces. Since it was an endgame position, 0-0-0 is really off your radar. Granted it was a bit tricky, but the point is the first cycle through, I'd calculated and analyzed for nearly five minutes and had to write some answer down. Once I saw the real solution, the second and third cycles through, I got that answer in a matter of seconds. "Oh this is that dumb one with the long castle." Did I learn much from that? Did I hardwire in some master-level pattern recognition or automate some calculation techniques? I doubt it, at least as far as positions like that are concerned.
So that's a case against this method. How about
some positivity?!
In this set, there is a king and pawn endgame position with locked kingside pawns but there is a possible breakthrough. When I first encountered the puzzle, I saw the pawn breakthrough idea (the only non-king move actually) so I calculated it but it took several minutes of checking pawn races and if black had other intermediate moves or tricks. By my second cycle through, I recognized the puzzle immediately and knew the answer was g3-g4. Again, the question is, "Upon my second, third, fourth cycles through this position, am I truly practicing pawn-race counting, checking intermediate moves, or am I just seeing that familiar locked-pawn configuration that I saw the previous cycle and I know without having to check anything that the solution is the only pawn move in the position: g3-g4?" I'd have to say in cases like this, I may be simply memorizing the solution, but is this okay? Maybe it is, at least for positions like this. Perhaps next time I have a similar locked pawn position in one of my games, I'm hopefully more tempted to immediately check what pawn breakthroughs I have--thanks to this training and seeing this pawn breakthrough many times over in the last few days. Granted I will still have to calculate and count, as I did in the first cycle through, but the hope is that I'll have a shortcut now to know what to look for.
And lastly, I think the biggest revelation is that, regardless of the pluses and minuses, at least I was doing many hours of tactics training per day. Sometimes it was legitimate full calculation during the first and second cycles, and other times it was simple memorization with only minor pattern recognition. But still......tactics? They say any time spent studying chess is good to some degree. Did it help to see a bunch of these very easy problems a second and third time and know the solution in a matter of seconds? To be determined I guess. All I know is that I just devoted an entire month of training in which two out of every three days I was solving an average of 80 tactics per session.
A final
final reflection: It is really slow going, especially during the third cycle when you know the solution but you have to stop the clock, double-check the solution, write down the time, and then get the next position pulled up. That's the main reason I didn't continue the diligent time-keeping stats for the other sections of the book. :)
For Future Cycles
Another idea to do in the future is to try Ray Cheng's Practical Chess Exercises using this repetition method. With that much more challenging book, I think I will have to try the true "X number or problems per day" version of the 7 Circles method as it was intended whereby you pick a number of problems to do per day and stick with it for the first cycle, doubling that number for the next cycle. Say 10 problems per day for the first pass through, the next cycle through would be 20 problems per day, the next cycle is 40 problems per day, then 80, 150, 300 and then all 600 problems in a day. That is following the 7 circles exactly.
Other Information
For my records, here are problems to review before full attempt:
Incorrect problems in first 492: { 26 , 109 , 154 , 241 , 245 , 263 , 274 , 293 , 358 , 366 , 426 , 429 , 459 , 464 , 476 }.
Incorrect problems in "White to Move - Mixed Motifs": { 503 , 505 , 507 , 509, 511 , 521 , 522 , 523 , 525 , 526, 531 , 538 , 542 , 552 , 558 , 560 , 563 , 564 , 565 , 567 , 571 , 577 , 578 , 590 , 596, 602 , 609 , 613 , 619 , 624 , 639 , 640 , 644 , 651, 654 , 657 , 658 , 661 , 662 , 664 , 674 , 680 }
Incorrect problems in "Black to Move - Mixed Motifs": { 745 , 750 , 759 , 767 , 774 , 777 , 778 , 783 , 785 , 794 , 806 , 807 , 809 , 817 , 831 , 856 , 863 }
Incorrect problems in Final Section: { 884 , 890 , 891 , 894 , 902 , 915 , 923 , 924 , 954 , 957 , 960 , 961 , 964 , 969 , 970 , 991 , 992 }
