This is a question and not an answer. I always wanted to improve my calculation skills when I play chess. I was frustrated to see the mistakes I made when I went over my games. Many of them were just 2 moves deep. To improve my calculation skills I went over lots of master’s games. I finished two volumes of Alekhin’s Best Games book, Tal’s best games, Capablanca’s best games and recently Anand’s best games. I had the biggest jump in my rating while going over Alekhin’s games. After that it has improved slightly and right now it is almost fixed for nearly 3 years.

Another training which I do is solve tactical problems. There were great problems on the book Combinational Motifs by Maxim Bloch. The problems were realistic and most of them are from real games. I don’t like the artificial mate in two problems which could never occur in a regular chess game. But I don’t know how much they helped my calculation skills.

When I look at a position, I don’t go over calculating in an organized way like a computer. I have Kotov’s book which I didn’t read after a few pages. His book promised to teach how to calculate. I lost him after the mention of choosing candidate moves. How would I know what is a good candidate move?
Below is an example thinking of mine on a chess problem.

Black to play and win.

This is a problem from the book Chess School 3 by IM Alexander Mazja.
It is black to play and win. You can quickly see that white is just hanging on a thread and there are a lot of weak points. After looking at the exchange Bxe4 which does not yield anything Bd2 and Be3 popped into my head. For Be3 I did not find anything after Qxe3. It is hard to say how I even though of Bd2 in the first place. It just popped into my head. It looked interesting and I looked at it much closer. Black is threatening Bxc3. White has many options. But I looked only at captures of the Bishop. Qxd2 looses to 1. … Bxe4 2. Nxe4, Qxe4 3. Kg1, Qg2 4. Rg2 Rf1#. I was very happy to find 3. … Qg2. I did not find it immediately. I was just having the mental image of the position after 3. Kg1 and was looking for the next best move.

Just then the right connections fell in place in my brain in noticing that if Rook at f2 is diverted Rxf1 was mate and the move Qg2 immediately popped into my head. I thought that I solved the problem. I looked at the answer and was happy to find the first move Bd2. But then it gave totally different variations. First of all after 1. … Bd2 I did not notice 2. Rxf5, Rxf5 3. Nxd2, Rxf1 4. Nxf1 e4 5. Nxe4 Qxe4 which also wins for black. But the cute and the main variation was 1. … Bd2, 2. Qxd2, Bxe4 3. Kg1, Qxg3 4. hxg3, h2 5. Kh2, Rh7 6. Kg1, Rh1#. I get dejected after missing a variation like this for every other problem. I don’t know how to get better at this.

Positions with a lot of forced moves are obviously a bit easy to calculate. For example whenever a variation involves a ‘check’ it restricts the number of possible moves to a great extent. Checks are embedded into the minds of any one who knows how to play chess. They are part of the rules. Just to extend a little farther, would it not be nice if automatically some bad moves of the variation appear, as bad as moving the king into a check or not stopping a check. This is called pruning. I have to learn to identify bad variations quickly and reject them. In the same way good (candidate) moves also should pop into the head like instinct. That can come only by practice.

It is also not possible to calculate all the variations of a position by anybody. That is why there are positional strategies. You pick a move based on some thematic elements of the position. To improve my positional ideas I am also reading Silman’s book, “How to Reassess your chess”.

In Sports Star magazine’s interview Viswanathan Anand said it beautifully. (Sports Star page is not found anymore. But excerpts can be found in chessbase article).
“The stronger you are you get to see more connections. The pieces and positions come alive with patterns. You start seeing possibilities in these patterns. First you think the white has the advantage and then you look carefully and realise that the black has the edge. As you refine your analysis the more sharp your understanding of the position gets. The pieces are there standing and suddenly when you see the connections they become beautiful. In specific openings you find pieces assuming their own distinct characters.”

I wish I can think like that. There is also another nice quote by a recent GM Jesse Kraai in Chess Life magazine. When he talks about Kamsky he says, “He’ll have all sorts of ideas about the position, bound up in very specific long variations. This is the amazing thing about top players in the world – they think in ideas and variations at the same time”.