How to get better at calculation

First, have a go at doing some calculation. Pick the best move in a couple of these positions that appeal. They are taken from Aagaard's Inside the Chess Mind, so you can later compare your answers with some 'official' answers from a computer (Fritz 8) but also with the recorded thoughts of some other human beings who tackled the same positions. I've given the opponent's last move when I know it.  Take 5-10 minutes or so for your thoughts and record or write them down if you can (but you can take as long as you like over the Murphy one).

 

Click [...] to see the list 

 [Event "Taastrup 30th anniv op"] [Site "Taastrup"] [Date "2002.11.28"] [Round "7"] [White "Nohr, Finn"] [Black "Nielsen, Michael"] [Result "1/2-1/2"] [ECO "B22"] [WhiteElo "2157"] [BlackElo "2095"] [Annotator "Exeter,DrDave"] [SetUp "1"] [FEN "r1b1k2r/pp1qpnbp/1n1P2p1/8/4N3/1B3Q2/PP3PPP/R1B1R1K1 b kq - 0 18"] [PlyCount "1"] [EventDate "2002.11.22"] [EventType "swiss"] [EventRounds "9"] [EventCountry "DEN"] [SourceTitle "CBM 091 ext"] [Source "ChessBase"] [SourceDate "2003.01.09"] [SourceVersion "1"] [SourceVersionDate "2003.01.09"] [SourceQuality "1"] {[#]} 18... O-O 1/2-1/2 [Event "Bled ol (Women)"] [Site "Bled"] [Date "2002.11.10"] [Round "14.3"] [White "Arakhamia Grant, Ketevan"] [Black "Benderac, Ana"] [Result "0-1"] [ECO "C10"] [WhiteElo "2413"] [BlackElo "2300"] [Annotator "Exeter,DrDave"] [SetUp "1"] [FEN "2r1k2r/1b3ppp/pn1Q4/1p2N3/8/2P2P2/qP4PP/2KR1B1R b k - 0 23"] [PlyCount "1"] [EventDate "2002.10.26"] [EventType "team-swiss"] [EventRounds "14"] [EventCountry "SLO"] [SourceTitle "EXT 2003"] [Source "ChessBase"] [SourceDate "2002.11.25"] [SourceVersion "1"] [SourceVersionDate "2002.11.25"] [SourceQuality "1"] [WhiteTeam "Georgia"] [BlackTeam "Yugoslavia"] [WhiteTeamCountry "GEO"] [BlackTeamCountry "YUG"] {[#]} 23... Bd5 0-1 [Event "World Cup"] [Site "Skelleftea"] [Date "1989.08.??"] [Round "3"] [White "Portisch, Lajos"] [Black "Kortschnoj, Viktor"] [Result "1-0"] [ECO "A40"] [WhiteElo "2600"] [BlackElo "2655"] [Annotator "Exeter,DrDave"] [SetUp "1"] [FEN "1r4k1/4nppp/2p2n2/2N1R3/1pb5/1N4P1/PP3PBP/6K1 b - - 0 21"] [PlyCount "1"] [EventDate "1989.08.??"] [EventType "tourn"] [EventRounds "15"] [EventCountry "SWE"] [EventCategory "16"] [SourceTitle "CBM 014"] [Source "ChessBase"] [SourceDate "1990.02.01"] [SourceVersion "1"] [SourceVersionDate "1990.02.01"] [SourceQuality "1"] {[#]} 21... Kf8 1-0 [Event "USSR"] [Site "?"] [Date "1952.??.??"] [Round "?"] [White "Stern"] [Black "Kushnitzky"] [Result "1-0"] [Annotator "User"] [SetUp "1"] [FEN "2r3k1/2q2ppp/5n2/5Q2/2pPb3/2P3R1/3BB1PP/6K1 w - - 0 1"] [PlyCount "0"] [SourceVersionDate "2022.11.25"] {[#]} 1-0 [Event "Lugano op"] [Site "Lugano"] [Date "1989.03.06"] [Round "4"] [White "Miles, Anthony J"] [Black "Kortschnoj, Viktor"] [Result "0-1"] [ECO "E33"] [WhiteElo "2520"] [BlackElo "2610"] [Annotator "Exeter,DrDave"] [SetUp "1"] [FEN "2r2rk1/1p3pp1/1p1b1np1/pP1Pp3/4P3/P2Q4/1Bq1BPPP/R4RK1 w - - 0 21"] [PlyCount "1"] [EventDate "1989.03.03"] [EventType "swiss"] [EventRounds "9"] [EventCountry "SUI"] [SourceTitle "TD"] [Source "ChessBase"] [SourceDate "1994.03.01"] [SourceVersion "1"] [SourceVersionDate "1994.03.01"] [SourceQuality "1"] {[#]} 21. Rfb1 0-1 [Event "Belgrade Investbanka"] [Site "Belgrade"] [Date "1987.??.??"] [Round "?"] [White "Salov, Valery"] [Black "Gligoric, Svetozar"] [Result "0-1"] [ECO "E48"] [WhiteElo "2575"] [BlackElo "2525"] [Annotator "Exeter,DrDave"] [SetUp "1"] [FEN "7R/8/5p2/1p1rk3/5p2/7P/5KP1/8 b - - 0 76"] [PlyCount "1"] [EventDate "1987.10.18"] [EventType "tourn"] [EventRounds "11"] [EventCountry "YUG"] [EventCategory "14"] [SourceTitle "CBM 004"] [Source "ChessBase"] [SourceDate "1988.06.01"] [SourceVersion "1"] [SourceVersionDate "1988.06.01"] [SourceQuality "1"] {[#]} 76... Kd4 0-1 [Event "Bundesliga 9697"] [Site "Germany"] [Date "1997.??.??"] [Round "?"] [White "Bosch, Jeroen"] [Black "Tischbierek, Raj"] [Result "1/2-1/2"] [ECO "B36"] [WhiteElo "2425"] [BlackElo "2490"] [Annotator "Exeter,DrDave"] [SetUp "1"] [FEN "r4rk1/pp2ppbp/3p1np1/3P4/4P3/4BP2/PP1K2PP/2R2B1R b - - 0 14"] [PlyCount "1"] [EventDate "1996.10.12"] [EventType "team-tourn"] [EventRounds "15"] [EventCountry "GER"] [SourceTitle "GER-chT"] [Source "ChessBase"] [SourceDate "1999.07.01"] [SourceVersion "1"] [SourceVersionDate "1999.07.01"] [SourceQuality "1"] [WhiteTeam "Bochum"] [BlackTeam "Empor Berlin"] [WhiteTeamCountry "GER"] [BlackTeamCountry "GER"] {[#]} 14... Rfc8 1/2-1/2 [Event "Wageningen zt"] [Site "Wageningen"] [Date "1957.??.??"] [Round "17"] [White "Larsen, Bent"] [Black "Teschner, Rudolf"] [Result "1/2-1/2"] [ECO "D17"] [Annotator "Exeter,DrDave"] [SetUp "1"] [FEN "rnbqkb1r/pp3ppp/2p2n2/4P3/P1Bp3N/2N5/1P3PPP/R1BQK2R b KQkq - 0 9"] [PlyCount "1"] [EventDate "1957.10.26"] [EventType "tourn"] [EventRounds "17"] [EventCountry "NED"] [SourceTitle "MCD"] [Source "ChessBase"] [SourceDate "1999.07.01"] [SourceVersion "1"] [SourceVersionDate "1999.07.01"] [SourceQuality "1"] {[#]} 9... dxc3 1/2-1/2 [Event "Belgrade Investbanka"] [Site "Belgrade"] [Date "1987.??.??"] [Round "?"] [White "Salov, Valery"] [Black "Gligoric, Svetozar"] [Result "0-1"] [ECO "E48"] [WhiteElo "2575"] [BlackElo "2525"] [Annotator "Exeter,DrDave"] [SetUp "1"] [FEN "2R5/8/5p2/3r4/1k3K2/1p5P/6P1/8 w - - 0 81"] [PlyCount "1"] [EventDate "1987.10.18"] [EventType "tourn"] [EventRounds "11"] [EventCountry "YUG"] [EventCategory "14"] [SourceTitle "CBM 004"] [Source "ChessBase"] [SourceDate "1988.06.01"] [SourceVersion "1"] [SourceVersionDate "1988.06.01"] [SourceQuality "1"] {[#]} 81. Rc1 0-1 [Event "IRL-ch"] [Site "Dublin"] [Date "1952.??.??"] [Round "?"] [White "Murphy, PJ.."] [Black "Turner, AW.."] [Result "1-0"] [ECO "B45"] [Annotator "Exeter,DrDave"] [SetUp "1"] [FEN "r1b4r/pp1pR2p/2q2ppk/8/3BR3/2PB4/P1P2PPP/6K1 b - - 0 23"] [PlyCount "1"] [EventDate "1952.07.??"] [EventType "game"] [EventRounds "1"] [EventCountry "IRL"] [SourceTitle "EXT 2001"] [Source "ChessBase"] [SourceDate "2000.11.22"] [SourceVersion "1"] [SourceVersionDate "2000.11.22"] [SourceQuality "1"] {[#]} 23... g5 1-0 [Event "URS-ch18"] [Site "Moscow"] [Date "1950.11.22"] [Round "7"] [White "Boleslavsky, Isaak"] [Black "Flohr, Salo"] [Result "1-0"] [ECO "B11"] [Annotator "User"] [SetUp "1"] [FEN "r3kb1r/pp4pp/1qp1Rn2/8/8/5Q1P/PPPB1PP1/2KR4 b kq - 0 16"] [PlyCount "1"] [EventDate "1950.??.??"] [EventType "tourn"] [EventRounds "17"] [EventCountry "URS"] [SourceTitle "URS-ch"] [Source "ChessBase"] [SourceDate "1999.07.01"] [SourceVersion "1"] [SourceVersionDate "1999.07.01"] [SourceQuality "1"] {[#]} 16... Kf7 1-0
DO YOU KNOW HOW TO ANALYZE?

Recently I was invited to the closing ceremony of a team tournament in which candidate masters and first-category players were playing. I asked my audience what they would like me to talk to them about, and I was inundated with requests. Some asked me to demonstrate some interesting combination, others wanted to know how to play the Sicilian Defence correctly for Black.

'But do you know how to analyse variations?' I asked my listeners, and without giving them time to reply went on, 'I will show you how to analyse variations and if I'm wrong, then stop me. Let us suppose that at one point in your game you have a choice between two moves, Rd1 or Ng5. Which should you play?' You settle down comfortably in your chair and start your analysis silently saying to yourself the possible moves. 'All right I could play Rd1 and he would probably play Bb7, or he could take my a-pawn which is now undefended. What then? Do I like the look of the position then?' You go one move further in your analysis and then you pull a long face - the rook move no longer appeals to you. Then you look at the knight move. 'What if I go Ng5? He can drive it away by h6, I go Ne4, he captures it with his bishop. I recapture and he attacks my queen with his rook. That doesn't look very nice...so the knight move is no good. Lets look at the rook move again. If he plays Bb7 I can reply f3, but what if he captures my a-pawn? What can I play then? No, the rook move is no good. I must check the knight move again. So, Ng5, h6, Ne4, Bxe4, Qxe4, Rd4 No good! So I mustn't move the knight. Try the rook move again. Rd1, Qxa2.' At this point you glance at the clock. 'My goodness! Already 30 minutes gone on thinking whether to move the rook or the knight. If it goes on like this you'll really be in time trouble. And then suddenly you're struck by the happy idea - why move rook or knight? What about Bb1?' And without any more ado, without any analysis at all you move the bishop. Just like that with hardly any consideration at all. My words were interrupted by applause. The audience laughed, so accurate was my picture of their trials and tribulations.

Kotov's introduction to his famous book, Think Like a Grandmaster, is very engaging, although his subsequent recommendations are not easy to follow.

Calculation and analysis require you to visualise possible future positions and pick a move that gives you the best chances.  You need to have working knowledge of tactical patterns and a good thinking process to tackle more complicated positions.

`1. Tactical patterns e.g. fork, clearance, decoy

  • You need a good stock of tactical patterns 'live' in your memory -- so do a few chess tactics puzzles daily (or as often as you can). 
  • These need not be deep -- the point is to keep your tactical vocabulary active. 
  • Start with themed collections (e.g. a chapter about forks) then move to mixed puzzles. 
  • Feel free to tackle the same puzzles again.  Remember, this is about tactical fitness, lots of low-key repetitions, not asking for peak performance.
  • There are some good habits you will get into -- looking first at checks and captures and threats and being able to spot clues as well as the tactical patterns themselves (vulnerable King, loose pieces). 
  • You may start to develop a sense of the types of moves that are harder to spot (for you, or everyone) e.g. backwards moves
  • There are some things that you must not learn from doing these: every position has a tactical opportunity and tactics always work.
  • You also need spot clues about when to calculate more deeply (obviously complex positions, a mismatch between your current assessment and best end-of-line assessment) -- and when not to bother.

2. Analysis

    You can add speed to accuracy more easily than the other way around!  So do some analysis study slowly and carefully at first, concentrating on thoroughness, and then put yourself under time pressure later.  [Puzzle Rush is fun but perhaps think of it as a test of how good you are, not your main way of getting better. ]

  • You need to be thorough (I sometimes think being thorough is the most important chess skill) - not skipping past any key alternatives nor stopping analysis too soon (quiescence error).  Part of getting seriously more thorough is being reflective about your mistakes and failures -- do you assume recaptures are forced?  And part is having some sort of organised approach (candidate moves), being practical (avoid analysis paralysis) and having some tools for solving (mnemonics (e.g. ABCDX), short-cuts (e.g. everything else is hopeless, quick recce to start with, safety nets), progressive deepening, move order, stepping stones, comparisons, verbal summaries, imagination (e.g. fantasy: what move would I like to make?)). [I intend to make a video or something to explain all these ideas if they aren't obvious to you]
    • You should have more than one candidate move for practically every turn, not just when you are calculating: just making yourself stop to think of an alternative will get your head out of 'fast' mode and stop you missing things.
    • Each line you analyse should have an evaluation, and you should always know what the best move so far is.
  • You need to be able to visualise upcoming positions accurately -- try reading chess books without moving the pieces on a board -- or maybe try blindfold chess!  The position in front of you is going to change, maybe quite a lot, while the position you want to get to is in the future, so seeing where the pieces are right now may be in some ways unhelpful (that piece you are relying on in 4 moves time gets swapped on move 2). This explains why you can see some GMs deliberately look away from the board while analysing (e.g. Ivanchuk, Naroditzky)
    • When Fischer and Petrosian were playing their match in Buenos Aires 1971, the power was cut in the hall and they were in total darkness. The clocks were stopped. After a while, Petrosian complained to the arbiter that Fischer was analysing the position in his head. Fischer agreed and so the clocks were restarted.(often quoted but citation needed)
  • You need to stretch your mental muscles -- so do analysis puzzles (not just simple tactics) at the edge of your comfort zone (and preferably a little outside) e.g. Gambit Book of Instructive Chess Puzzles, Perfect Your Chess. The ChessDojo has a list of puzzle books suitable for each rating level, and you could use books above and below your level.
  • For all puzzles, commit your answer/analysis to paper before looking at the solutions.  It is too easy to say to yourself, oh, yeah, I got most of that, so 10 points for that puzzle.
  • Good tips while playing:
    • Review all checks and captures and threats.
    • Focus on things changed by your opponent's last move.  Don't assume it has only one idea!
    • Check the position after your chosen move.  Again, focus on things that change: have you given your opponent new opportunities?
    • Remember Blumenfeld's Rule: before moving, look afresh through the eyes of a beginner!

Resources

I have lots of books, and several about calculation, yet few give good advice about how to analyse.  But the first part of John Nunn's Secrets of  Practical Chess is pure gold, and Jacob Aagaard's Excelling at Chess Calculation is also good about 'how'.

Video: https://www.youtube.com/watch?v=B9JqyCJtjV0

Mate in one:

-Bb---BN
R--Pk--r
-Q-----B
----q--R
--bN----
----Q-BK
-p------
-bq-R-rb

P.S.

Tips from the books

Kotov (the Tree of Analysis)

1. Start with a list of candidate moves
2. Go through each variation until it settles down, evaluate the result
3. Choose the best; do not check your analysis

Dvoretsky 

1. Candidate moves
2. What could I have missed?
3. Should we re-check our calculations?
4. Keep a mental note of the evaluation of each variation
Good places to start thinking:
5. What does my opponent want to do?
6. What is the drawback of my opponent's move?

Thinking tools

1. Start with forcing moves
2. If you are confident your move will work, start with your opponent's weakest replies;
if you suspect it might not work, start with the strongest replies
3. Is there an 'emergency exit' e.g. you have perpetual check at least
4. Process of elimination (nothing else is worth trying)
5. Method of comparison
6. If it's too hard, rely on your 'feel'

Zlotnik

1. Start with a list of candidate moves
2. You can look at lines more than once

Krasenkov

1. Define what you are trying to do with your next move
2. Look for ideas and start with a list of candidate moves
3. Decide on an order of priority
4. Analyse in that order
5. If you find a move which achieves your aim...
 a. and you are short of time, check it then play it
 b. and you have plenty of time, put that idea in the bank, and continue
6. If no move meets your aim...
 a. and you are short of time, change your aim, revise your list, and continue
 b. and you have plenty of time, review your analysis looking for new ideas.
    If your new idea applies to a different variation, finish your current variation before looking 
7. Check (Blumenfeld's Rule)

Tisdall

https://devonjuniorchess.co.uk/sites/devonjuniorchess.co.uk/files/tisdal...

Nunn

  1. The Tree of Analysis - useful guide, not a law of physics
    • start with a quick scan -- it may be all you have to do
    • complete your list of moves!
    • if you get the variations confused, you may need to start again
  2. Evaluation functions
    • Use to decide between moves
    • If you initial assessment is bogus, your analysis is on shaky ground
  3. When to analyse
    • You will see more in the first 5 minutes than the next 5
    • If the evaluations are similar, just punt
    • don't fruitlessly search for an escape (The time to think is before you get into trouble - DR)
    • don't try and build a perfect case for a move -- try and find something wrong with it!
  4. DAUT (Don't Analyse Unnecessary Tactics) [if you have a simple way to a good result]
  5. Safety net (=emergency exit)
  6. Sometimes the tactics have to work
  7. Implicit commitments (burnt boats) -- when the long-term chances lie with your opponent, you must act
  8. Familiar structures help planning.  If unfamiliar, make a plan that:
    • helps you (and not your opponent)
    • has no tactical flaw (what is your opponent doing meanwhile?)
    • is realistic (fairly short-term)
    • If circumstances change, change your plan!
  9. Method of comparison (evaluation doesn't matter)
  10. Make your opponent think
  11. Trusting your opponent?
  12. Warning signals
    • One mistake follows another
    • LDPO (Loose pieces drop off)
    • Basic tactical patterns
    • (DR: the opening phase is the most dangerous)
  13. 'Hard-to-see' moves
    • hesitation moves, collinear moves, switchbacks, rejected moves
    • (DR: backwards moves)

attachment: 

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