Monday, September 2, 2013

Reasoning vs Calculating

Hello ICCCers!

I wanted to share some notes on the concept of reasoning about a position vs. calculating a position. To me, reasoning and calculating are the yin and yang of thinking in chess: you can't have one without the other. When we reason, we make inferences about the relative quantitative and qualitative properties of a position. We deal with the abstract nature of the position and make hypotheses about it (e.g. white is winning, black is better, etc.). The calculation that follows is the proof to the hypothesis.

Let's consider the position at move 41 in game 2 of the four game final World Cup match between GMs Vladimir Kramnik (2784) and Dmitry Andreikin (2709).

Kramnik (white) has just played the very strong

41. c7

Diagram 1: Position after 41. c7

Putting ourselves in Kramnik's head, we can guess that he must have reasoned along these lines:
  • White's pawn is extremely dangerous :-)
  • Black has only one move (Qc8) to stop c8=Q winning on the spot.
  • When the black queen reaches c8, both white rooks must stay on the c-file to guard the c-pawn.
  • The passed, guarded c-pawn greatly reduces the mobility of the black queen.
  • The black rook must guard the b7 square, else white can play Bb7! after which white will end up a rook. Hence, the black rook's mobility is greatly restricted too by the c7 pawn.
  • All I need to do is force the queen off c8 and I will win material and the game.
Andreikin probably had a similar conversation with himself:
  • White's pawn is extremely dangerous :-(
  • I only have one move (Qc8) to stop c8=Q winning on the spot.
  • I can't move my queen from c8 and I can't move my rook from a7.
  • Thus, after Qc8, I have no mobility (i.e. no counter play) ... this is BAD.
  • White has a simple plan to kick me from c8 using his bishop.
  • There is no immediately obvious way to do this, but if there is a way, Vlad will find it (Think Terminator here - JCM).
  • If white manages to do this (and it looks very possible), I will lose. 
  • I must find something else besides Qc8 or face a miserable game likely ending in a zugzwang win for white.
Andreikin must have realized that defending passively with Qc8 was hopeless. He immediately played

 41. .. Rxc7!

The exclam is for realizing that a two rooks vs queen ending is the only way to fight on. The game continued...

42. Rxc7 Qxd5
43. Re1  Kh6

White was threatening to play 44. Ree7, which would force black to trade his queen and f-pawn for both rooks due to the horizontal pin. This would be a winning pawn ending for white, so black steps out of the pin. This brings us to the main position of this article:

44. Ree7 f6

Diagram 2: Position after 44. .. f6

It was at this point that I got into a running debate with a FIDE master on ICC who claimed this was a dead draw. Now, I have a fascination for grinders like Carlsen and Karpov who are notorious for "making something of nothing". Are they really just lucky beneficiaries of their opponents' fatigue blunders, or do they really see deeper into the nature of positions, allowing them to find hidden resources? Where and when do they continue where other's quit thinking? This sure looked like one of those kinds of positions and Kramnik is definite grinder.

After a 2-3 minute think, I wasn't convinced that the FIDE master had reasoned about the position satisfactorily to reach that general of a conclusion, so I asked, "How can you be so sure? I believe white can win this."

Here was my checklist:

  • What qualities or key features does the position have in terms of pawn structure?
  • Who has the better king position, control of lines and squares and why?
  • Where are the weak squares and lines for both sides?
  • What resources (e.g. tactics) does the position offer both sides?
  • What is the optimum placement of pieces? Where should they go?
  • What trades can be made? Who do they favor and why?
Also, what about all the different pawn endings that could arise if white trades:
  • Black's queen and f-pawn for his rooks.
  • Black's queen and g-pawn for his rooks.
  • Black's queen and h-pawn for his rooks. 
Now here's a challenge: Try reasoning about this position yourself using my checklist and anything else you can think of about the position. Don't give variations! None of this involves calculation.. yet.

In Part II, we'll compare notes and discuss how the game ended.



  1. This is a fun position to study, thanks for the puzzle! I personally feel as though white will win this game based off of blacks sketchy king position. If white puts his king on h2, the black queen is totally helpless. IM only 1700 player, so my reasoning maybe to amateurish for such a position.

  2. It is a very practical position to study for a number of reasons:

    1. There are ways to win it, but the problem is given as open-ended.
    I'm not looking for a variation solution here. I'm asking folks to *reason about * the position first as a prelude to calculating a winning line.
    2. There are false paths that look winning, but aren't.
    3. It tests your knowledge of king and pawn endings.
    4. It looks like it could occur in an amateur game.

    I invite you to dig way deeper than what you've already stated. :-)
    Happy reasoning! - JCM