How to Calculate (2/2)

Here is the answer to the position from this post on calculation.

I right away got the sense that black's last move ...e6-e5 should give me some chance for a forcing continuation, because the position is opening up and white is a little better coordinated. Also, black is conspicuously lacking a defensive knight on f6 -- instead it is on the terrible b6 square. This means the kingside is weak, and should be my focus.

So, here's what I calculated:

• After 2.Qh5 Qxd4 3.Ng5 h6, both my Ng5 and Ra1 are hanging. I can save both with 4.Be3 but then at the very least 4. ... Qg4 trades queens and ends my attack. Black is fine there.
• What about 2.d5!? - after 2. ... cxd5 3.cxd5 black cannot play 3. ... Qxd5? 4.Nf6+! (a tactic) so instead must play 3. ... Nxd5. I can keep going with 4.Ba3 Re8...what do I have in that position? Perhaps 5.Nd6 but then 5. ... Bxd6 6.Bxd6 Qxd6 7.Bxd5 and we have made too many trades, black can at the very least equalize there by returning the pawn with 7. ... Be6 8.Bxb7 Rad8.
• Going back to the position after 2.d5!? cxd5 3.cxd5 Nxd5 4.Ba3 Re8, how about 5.Nc5!? ... if black moves the Nd5 I take on b7, but maybe the position after 5. ... Be6 6.Nxe6 fxe6 is not too bad...yes, that's a strong knight on d5 now. Although white shouldn't be worse with the bishop pair and black's ugly e-pawns, I want to find something better...
• How about 2.Ba3 immediately? The rook only has one square: 2. ... Rf8. Hmm, now after 3.Qh5 I am threatening the deadly Ne4-g5, double attacking h7 and f7 ... for example 3. ... Qxd4? 4.Ng5 and black is busted; 4. ... Bf5 5.Qxf7+ and 6.Qxf5, or 4. ... h6 5.Qxf7+ and 6.Qxe8 wins for white
• So that means after 2.Ba3 Re8 3.Qh5 black must stop Ne4-g5. There are not many ways to do that; 3. ... f6 looks very dubious so probably black must try 3. ... h6 instead.
• In that case, after 2.Ba3 Re8 3.Qh5 h6 maybe I can try 4.d5 there; I am threatening d5-d6 or simply Rad1 with a crushing position, so black has to try taking: 4. ... cxd5 5.cxd5, but now once again 5. ... Qxd5? 6.Nf6+! wins on the spot, so how about 5. ... Nxd5 instead? In that position, the d-file is open, so I can continue with 6.Rad1, threatening Rxd5 followed by Nf6+, winning. What can black do about that?
• So, after 2.Ba3 Re8 3.Qh5 h6 4.d5 cxd5 5.cxd5 Nxd5 6.Rad1, black must do something to stop my threat - 6. ... Nf6 is no good because of 7.Rxd8 Nxh5 8.Rxe8+. The queen cannot move though; on any queen move I still have 7.Rxd5. Perhaps 6. ... Kh8, that would stop 7.Rxd5 Qxd5 because 8.Nf6 is no longer check. Instead though, after 6. ... Kh8 I could do something simple like 7.Nc3. The Nd5 is triple attacked and only defended once; if it doesn't move I will simply take it next turn and 7. ... Nf6 is still met by 8.Rxd8 Nxh5 9.Rxe8+, winning
• OK, so 2.Ba3 Re8 3.Qh5 h6 4.d5 cxd5 5.cxd5 Nxd5 6.Rad1 ... hm ... since ...Kh8 and ...Nf6 don't work, the knight must be defended; only way is 6. ... Be6. What do I have there? Maybe 7.Nc5 again? After 7.Nc5 b6 8.Nxe6 fxe6 once again I've just reinforced that knight on d5; white shouldn't be worse but I want more than that.
• 2.Ba3 Re8 3.Qh5 h6 4.d5 cxd5 5.cxd5 Nxd5 6.Rad1 Be6 ... maybe 7.Nc3, triple attacking the knight. But there black can get away with 7. ... Nf6 since his rooks are connected: 8.Rxd8 Nxh5 9.Rxe8+ Rxe8 and black is fine.
• 2.Ba3 Re8 3.Qh5 h6 4.d5 cxd5 5.cxd5 Nxd5 6.Rad1 Be6 ... black's position is quite shaky here ... is it crazy to try 7.Rxd5!? After 7. ... Qxd5 8.Nf6+ wins again, so that means 7. ... Bxd5 is forced. Now I play the other rook 8.Rd1, again threatening Rxd5 and Nf6+. What on earth can black do about that?
• So my main line right now is 2.Ba3 Re8 3.Qh5 h6 4.d5 cxd5 5.cxd5 Nxd5 6.Rad1 Be6 7.Rxd5 Bxd5 8.Rd1 ... OK, any queen move and I can simply play 9.Rxd5 - for instance 8. ... Qd7 9.Rxd5 Qxd5 10.Nf6+ gxf6 11.Bxd5 and what's material there ... I have queen and bishop for two rooks, and black's king is weak - should be winning for white.
• After 2.Ba3 Re8 3.Qh5 h6 4.d5 cxd5 5.cxd5 Nxd5 6.Rad1 Be6 7.Rxd5 Bxd5 8.Rd1, what else could black try there... what about 8. ... Kh8 again - a funny move but it stops my main threat, since Nf6 is not check anymore. But there again I could just play 9.Nc3. If you let me take on d5 I have two minors for a rook, should be close to winning position. The only other try is to sac the queen with 9. ... Bxg2 10.Rxd8 Raxd8 11.Kxg2. There again I have queen and minor piece for two rooks; that's winning.
• So what's left? After 2.Ba3 Re8 3.Qh5 h6 4.d5 cxd5 5.cxd5 Nxd5 6.Rad1 Be6 7.Rxd5 Bxd5 8.Rd1, ...Kh8 is no good, queen moves are no good, maybe 8. ... Bc6 but then still 9.Rxd8 Raxd8 with Q+N for two rooks; that's decisive. If 8. ... g6 then just 9.Qxh6, that doesn't help black at all. OK, this line is good for me, so black must find something else earlier.
• After 2.Ba3 Re8 3.Qh5 h6 4.d5 cxd5 5.cxd5 Nxd5 6.Rad1 Be6 7.Rxd5 the only move other than 7. ... Bxd5 is 7. ... Qxd5 and sac the queen: 8.Nf6+ gxf6 9.Bxd5 Bxd5; there black has rook and bishop for the queen, but wait, the line continues: I have 10.Qg4+ Kh7 and 11.Qd7, picking up a bishop, so white should be easily winning there.
• So I suppose then after 2.Ba3 Re8 3.Qh5 h6 4.d5 cxd5 5.cxd5, black cannot play 5. ... Nxd5 because 6.Rad1 is just too strong. 6. ... Be6 7.Rxd5 is winning for white, but there is nothing else there for black to meet both Rxd5-Nf6 and the simple Nc3.
• In that case, my main line is 2.Ba3 Re8 ... that's forced ... 3.Qh5 h6 ... that's also forced, to stop Ng5 ... 4.d5 cxd5 5.cxd5. If black cannot play 5. ... Nxd5 then my next moves are either d5-d6 or Rad1, which looks like a nearly winning position for white.

This whole process took me about 15 minutes of completely focused thought, and the game continued 2.Ba3 Re8 3.Qh5 h6 4.d5! cxd5 5.cxd5 After some thought black could find nothing better than 5. ... f5?! - this wasn't a move I calculated, but there was no need to: at the very least I can always retreat with 6.Nc3 and retain the strong pawn on d5 or 6.Nc5 planning to meet 6. ... Nxd5 with 7.Rad1. After thinking I found the stronger 6.d6! Bb8 7.Nc5 and won quickly.

Now, if you also sat down and calculated this position for a good length of time, we can analyze your thinking process. It doesn't matter if you didn't see everything or if you made mistakes - we can identify those things as places to improve. In general, I find that people make three main kinds of mistakes when calculating (all of these can be reduced with specific types of exercises):

1. Technical Errors - for example the "ghost piece": after Bc1-a3 you try to move the bishop again from c1 to g5 later in a variation; or after a piece gets captured you still try to make moves with it on the board. This is very common, and I've even seen GMs do this on occasion!
2. Tactical Errors - overlooking a tactical shot in a variation in your head. Everybody is vulnerable to this, even masters and grandmasters.
3. "Blind spots" - This can vary from person to person. For instance, do you often miss sideways queen moves or backwards moves (many people struggle with those). Or maybe you frequently overlook simpler "quiet" moves. Regularly missing defensive resources or your opponent's counterplay could also be a blind spot.

To wrap up, how can we improve?

Technical Errors:

These mistakes we make because beyond a certain depth the position starts to get "fuzzy" and we no longer have a clear grasp on where the pieces are. The critical depth this happens at can vary a lot from person to person, but it can also depend on other things like your level of focus and if you're hungry or tired etc.

If you did the exercise, you can roughly estimate your maximum depth - go back and find the longest variation that you calculated. Even if the variation isn't relevant to the solution, as long as all the moves are legal, record its depth as the total number of half-moves made for each side. For example, my maximum depth was 19 in the variation 2.Ba3 Re8 3.Qh5 h6 4.d5 cxd5 5.cxd5 Nxd5 6.Rad1 Be6 7.Rxd5 Qxd5 8.Nf6+ gxf6 9.Bxd5 Bxd5 10.Qg4+ Kh7 11.Qd7. From what I've heard anecdotally, a typical GM can do around depth 25 comfortably! Most positions do not require that level of depth to find the right solution though. Consistently being able to visualize at depth 10 (five moves ahead for both sides) is plenty good enough for most situations.

You can improve your depth with visualization exercises:

• At the basic level, just start with having a friend tell you the name of a square on the chessboard. Without looking, say what color that square is (e.g. "c4: white").
• Find a friend and an empty chess board. Have your friend put any two pieces on the empty board on any two squares (color doesn't matter). Without looking, say if any of the pieces attacks the other. Then have your friend make a move with one of the pieces, telling it to you out loud. Repeat, saying if any of the pieces attacks the other, but without looking. This can be scaled up with more pieces for greater difficulty.
• Try to win a simple position (e.g. mate with king and queen vs. king) blindfolded against a friend, only saying the moves.
• Find any game and read through the first 5-10 moves. Then, go to a chess board and set up how you see the position resulting from those 5-10 moves, comparing it to how the position actually is.

Some people find these exercises easier or harder than others, and your visualization ability is not necessary correlated to rating. Doing calculation exercises like the position we did in this post will also naturally stretch your depth, as will solving puzzles without moving the pieces.

Tactical Errors:

Even if we can perfectly visualize a position at depth 10, sometimes we still overlook a one or two-move tactical shot. For example, if you analyzed 2.Ba3 Re8 3.Qh5 h6 4.d5 cxd5 5.cxd5 Nxd5 6.Rad1 and clearly visualized that position but didn't notice that you were threatening Rxd5 followed by Nf6+, you would have made a tactical, not technical error.

Most of the time, I find that tactical and technical errors actually tend to go together, and the logic is straightforward: if the position is getting fuzzy, you're less likely to notice a key tactical idea. For this reason, training your depth will also tend to improve your ability to see tactics in any variations you analyze.

However, another solution is to simply practice solving basic tactical puzzles. All of these tactics are really just patterns, and pattern-recognition is something our brains are naturally good at. Those forks, pins, skewers, discovered attacks and basic checkmating patterns frequently repeat themselves throughout chess games, and simply taking the time to regularly solve puzzles - even just 15 minutes a day - will put you on the road to mastering them. Of the three kinds of errors here, tactical errors are the easiest to train. This is why one of the very first things I teach my students is how to solve tactics so they are able to find those simple one-move shots in a position.

Blind Spots:

Last but not least, we have the tricky ones, where for some reason, you frequently overlook certain types of moves. Rest assured it is not just you -- the following are generally tricky for everybody:

• Backwards moves
• Long sideways queen/rook moves
• "Co-linear" moves (you move towards an opponent's piece but stop just short of capturing it)
• Quiet moves, particularly in non-quiet positions
• Forgetting about/overlooking opponent's counterplay

I personally chalk these up to pattern recognition, because usually we have blind spots for unusual or unexpected moves that break patterns. However, with more experience calculating I've noticed these gradually fade away from my own thought process. A big part of overcoming blind spots is knowing that they exist and to specifically make yourself look for them while you're thinking. For example, if I'm stuck on a position I might literally ask myself, "do I have any quiet moves here?" to force myself to look for them.