My teacher recommended a couple things to improve my speed and accuracy of calculation. One is a book, Chess School volume 3: the Manual of Chess Combinations, by Alex Mazja. It arrived in the mail this week. I had ordered it from an independent bookseller through Amazon, but apparently, as far as I can tell, from papers and notes inserted in the book, that seller was Igor Khmelnitsky, which for some reason makes me glad. I read the introduction, and note that the text is designed for a 2000 player, and it claims that if she masters the material in it, she should improve to 2200 level. This is marvelously well suited to not only my current state and my goals, but my terrible weakness of inaccurate and inefficient calculation.
The other thing is a concrete daily exercise using Laszlo Polgar's ponderous "5334 Problems, Combinations, and Games" - The Brick, as some of my chess friends call it. I am to take a page of mates in two - there are six problems per page - and record how long it takes me to solve all six. The idea is to gradually improve my speed over time. The mates in two are divided into practical mates, which for some reason are all Black to Play, and composed mates, which are all White to Play. The latter are obviously much more challenging, whereas I can solve any of the former in under a minute, so those are not worth my time.
The Brick arrived in the mail first, so I started with it first: Wednesday, at 2:27 AM, I set to work on a page of composed mates in two. To my surprise, the first problem, number 1471, was extremely difficult, and after fifteen minutes of staring at the diagram I could not find the solution. I was not tempted to look in the back of the book for the answer, but I did spend ten minutes looking online to see if there were some flaw in the problem. There was not, so I returned to work, this time setting up the pieces on the board. I finally did solve it after another ten minutes, and it was worth it - a nice, subtle queen retreat.
Naturally, if it was going to take over half an hour to solve each problem like this, I had an insurmountable task ahead of me, but it seemed that setting the position up (but without moving the pieces) was helpful. So I continued at a reasonable pace, solving each of the next two in about five minutes each, until I got stuck on the fourth problem, so stuck that suddenly I was woken up by my girlfriend coming downstairs to check on me. I had fallen asleep sitting on a bar stool, hunched over the position set up on our kitchen counter. I assured her I was alright, she returned to bed and I checked the clock: I had been asleep for twenty minutes.
I finally solved the fourth position, and the final two, wrapping up the sixth at 3:56 AM - 89 minutes after the start! I'm not sure how to count that. Maybe I should just throw it out. But at least I had started. However, to my chagrin, once I checked the answers (covering them up with a slip of paper and moving it down, so that I would not inadvertently expose any future answers), I discovered that I had gotten two of them wrong. Apparently it is legal for the black King to capture undefended white rooks, and also, white pawns do not move backwards. If only I had known! Not coincidentally, the errors I made were in 1472 and 1473, which I had "solved" so quickly.
I do note that because the problems are composed, some of the skills involved in solving them may not necessarily be quite the same skills needed to solve problems over the board, just as test-taking ability is correlated with, but not identical to, mastery of the subject covered by the test. Because there is an art to composition, and some of the conventions have nothing to do with games of chess, certain patterns arise unusually often. For example, starflights, where the black King can move only to one of the four adjacent squares on a diagonal. Problemists love this king of thing, and having an eye for it surely helps one solve faster.
But I digress: that is only a detail, and I do not think it should detract from the overall effectiveness of this exercise. Today, I began the next page, and although the phone rang once or twice, and pizza arrived at the door, I finished all six in 46 minutes, and this time, I was relieved and excited when I uncovered the sixth answer and I had gotten them all correct. My teacher says the eventual goal is to finish one page in 15 minutes, that is, two and a half minutes per problem, but for now, baby steps. Even shaving a few minutes off my time will be progress. I am optimistic.