## Thursday, 2 December 2010

### 7 Circles

Michael de la Maza famously improved by 620 rating points as an adult, using his 7 Circles method as part of his training.  See:

http://www.chesscafe.com/text/skittles148.pdf
http://www.chesscafe.com/text/skittles150.pdf

In his 7 Circles programme, he solved 1,000 tactical chess problems 7 times using the CT-ART 3.0 tactical trainer program.  He worked through the problems in order of increasing difficulty, beginning with simple one-move mates and two-move combinations and progressing to 7-8 move mates and combinations.  He said that the tactical trainer saved him hundreds of hours because he did not have to enter complicated positions manually into a chess program when he failed to understand the solutions.  (Personally, I take the view that if you need a computer to understand the solution, the problem is too hard for you, and you should cross it off the list!)

His schedule was:

Circle 1:  64 days, 10 minutes per problem
Circle 2:  32 days, 5 minutes per problem
Circle 3:  16 days, 2.5 minutes per problem
Circle 4:  8 days, 1.25 minutes per problem
Circle 5:  4 days, 30 seconds per problem
Circle 6:  2 days, 30 seconds per problem
Circle 7:  1 day, 30 seconds per problem

In the 64 day circle, he spent up to five minutes trying to find the first move and up to an additional five minutes working out all of the variations.  This is odd on the face of it.  How can you possibly know that you have found the correct first move, without having worked out all the variations?  I expect that he was guessing the solution a move at a time, and entering it a move at a time into the computer program, which told him whether or not each move was right, and probably also prompted him with each defensive move.  Needless to say, this is not what you do in a game, but it worked for him.  However, his articles said he had trouble carrying over the improvement he had made at the 7 Circles into chess games.  I expect that he would have had less trouble carrying over this improvement if he had worked out all the variations before consulting the computer, but his 7 Circles would then have taken longer.

If you have read the cognitive psychology section, you will realise that the main disadvantages of this programme are that during your first few circles, your memory of the previous circles will be weak and your progress will be slow, and that your memory of the last few circles will soon fade away.

During the 64, 32, 16, and 8 days circles, de la Maza believed that he was improving his calculation ability - and during the remaining circles, he believed that he was improving his pattern recognition ability.  That is probably accurate.  The problem is that most of the improvement in his pattern recognition ability would have been short lived.  It is perhaps noteworthy in this context that he took part in one tournament, achieved an outstanding result, and promptly retired from chess.  What he lacked was a revision programme.  He needed to continue to practice his seventh circle to maintain his pattern recognition ability.

Another objection here is that working on calculation ability and then on pattern recognition ability is putting the cart before the horse.  Dan Heisman recommends doing a 7 Circles type programme on a large number of very simple tactical problems until you can do them very fast, and then moving on to more difficult problems, which looks more logical to me.  Again, a revision programme would be needed.

Another issue here is that of what happens if you cannot match de la Maza’s achievement of halving the time taken for each circle - and it is going to be more difficult if you cannot afford as much study time - and have to stretch the programme out.  7 Circles is a catchy name, but I believe that the real end point of the learning phase for his programme is to be able to solve the 1,000 problems at under 30 seconds apiece, not the completion of seven circles.  I expect that most players would need more than seven circles.

The following link gives to rating improvement for the 22 players who are known to have completed the 7 Circles programme (or some variation on it):

http://temposchlucker.blogspot.com/2005/05/ratingprogress-of-knights-errant.html

The link says that it is difficult to compare the ratings before and after the 7 Circles, because: some players modified the plan, trained tactics for much longer, had no official rating, had a rating from a different source, have not finished the programme, had to play more to get their new rating, did not have published ratings, abandoned the program, or their start ratings were unknown so a later (higher) rating had to be used or estimated.

More to the point, the 7 Circles has attracted a lot of attention (de la Maza’s articles the most visited on ChessCafe, according to Dan Heisman), and I expect that many more than 22 people have made a serious attempt at it.  The players who completed the programme are likely be the most capable and highly motivated ones, who would have improved anyway, and those who did make an improvement are the ones most likely to report their results.

Another difficulty is that the players may have been doing other training, and would have to be playing chess to get a rating, so we have no way of knowing what caused the improvement.  A third difficulty is that with a typical number of games played in a season, there is a large uncertainty in the ratings both before and after the 7 Circles, and the relatively small rating improvement typical of players rated over 1600 (the median improvement is currently 75 points) could easily have been due to chance.

The only way round these difficulties is to measure any improvement achieved in the ability to solve fresh problems (which could be measured much accurately and reliably than any change in rating).  These problems could be in the style of Ray Cheng’s Practical Chess Exercises (tactical and positional moves, including tempting but unsound sacrifices, in random order) to approximate the conditions of a game.

Nonetheless, the achievements of de la Maza and a few others with the 7 Circles are remarkable.  All the more so in de la Maza’s case, because he had a strident disregard for all forms of chess skill except tactics.

My own experience of the 7 Circles was that by the time I had tackled all of Reinfeld’s 1,001, and returned to the beginning, I found that I did not remember much!  My accuracy improved a little (I just tackled the problems that I had got wrong the first time through), but I was not obviously faster.  Nonetheless, this failure to learn was a good learning experience for me.  There had to be a better way.

Also see my later article: Michael de la Maza - the Verdict?