Today's article is dedicated to the technique of calculation in chess and the examples will show different aspects of this skill. I will also try to give some recommendations for how to train this invaluable skill.
Let's jump right away into the first position. White's pieces are menacing around black's king - there has to be a winning continuation. Grandmaster Shabalov did not find Rxg7+ and played Rg4 after which the game ended in a draw. It doesn't make any sense! How can such a strong GM not see Rxg7? Well, this is where the value of annotations comes handy. All good coaches recommend analyzing the games of strong chess players, especially if they are annotated. Here, it turns out that Shabalov calculated Rxg7 but did not see 35. Qf1!
I think the reason Qf1 can slip from our calculations is that the last five checks white gave were from the dark squares but Qf1 is a check on a light square. So automatically we might look for a check from a dark square but e1 is taken so we might stop there and not find Qf1. Overall, it is safe for white to go for this line because even if he doesn't see the Qf1-Bg5 idea one can easily see the perpetual starting with Qe1 instead of Qf2, and thus a draw is always in one's pocket.
This example is a perfect illustration that even grandmasters with top-notch calculation skills suffer from miscalculations. When I gave this position to solve for GM Shankland - it took him a few seconds to see the winning sequence until the end. It took me some time to figure out all the nuances but from the speedy solution by Shankland it is possible to assume that many GMs will calculate the position until the end very fast. Why didn't Shabalov do that during the game? During the game one can never to be sure that their position is "white to move and win"...there is always a doubt that the position is not as winning as it feels or looks. When one is given an exercise to solve starting from a certain position, one does not know the history of the game, the change of evaluations, the emotions--one has a task to find a win and this significantly simplifies one's task. This is why in his books Dvoretsky never gives evaluations when giving positions to solve, one almost never knows whether the position is about tactics or if there's some positional solution. This way of exercising simulates the conditions of the real game very well. However, if one's aim is to improve calculation, it would be enough to go straight to calculation books and exercises and solve positions such as "white to win", and even though it will not improve one's positional evaluations, the calculation skills will improve. But as we can see from this example, one should have faith in the position and believe that the win is there to be found.
While in the first example one had to calculate to the very end and possibly miss Qf1 in the next one it is the first move that GM Gawain Jones missed. It is refreshing to read Jones' annotations to his games in New in Chess periodicals because he is critical of his and his opponent's moves alike. In many of the annotations done by other players you can find their moves marked with "!" while the opponents' moves are marked with "?", so it takes some time and effort to dig a game or two where the player shares the experience of miscalculating something badly. Jones's annotations are included.
There are two moments of interest in this short fragment. The first one is missing the Rc4 possibility - where the rook attacks the b4-pawn because he was fixated on Qd2. The other moment is more interesting - when Jones didn't see Ra5! as indicated in the annotation to 15...Rb5. Ra5! comes at the end of a forced line where one has to see that from a5 it is defended by Qd8 - and this is not easy to see in my opinion. Geometric motifs can look obvious when shown at the board but visualizing them inside one's head is something one should work one. Solving chess studies will develop this vision. We will talk about combinative vision in future articles but I would like to mention here that studies are excellent training tools when it comes to developing calculation skills or tactical vision.
I would like to conclude this article with an example showing that surprise and psychology play a big role in our abilities to rationally move from one line to another during the calculation process. Probably everyone has had the cold-shower realization at one point or another that he/she blew the winning position. The sequence of events usually is like this: 1. My position is winning, 2. My position is really winning, what am I going to get for dinner, hmm 2/3 is not a bad result... 3. I missed this move he played but it cannot be good - probably I can win right away now; 4. Cannot find the winning move (panic sets in), his last move was not that bad; 5.... 1/2-1/2.. Leko had a winning position for a long time but Caruana found the absolutely brilliant 35...Qh1!! and let's read what Leko has to say upon facing this unexpected defense:
This position is highly complex because it requires both evaluations and calculations. I like Leko's honesty about being afraid of 27...Ne1 and later he found the defense Bf1! but it is such a hard move to make. I am not sure how to train psychological toughness and precise calculation when facing an unexpected strong move. One method off the top of my head is to play a training game and once you reach a strong advantage switch sides with the opponents so you have their pieces and have to defend. I can imagine this could be quite a frustrating experience but might help the mind to adjust better when the position changes from winning to drawing/losing.
Today we looked at three examples where in the first example one had to calculate a long line flawlessly, in the second find the hidden geometric motive and in the last lower the expectations and accept that the variations that give only a slight advantage instead of a win. Next week we will see how some masters of the past handled calculations and the brilliant moves that they never played!